Notes on the Money Market and LM Curve – Eco 3202 – Fall ...
Customized Material for Econ 351 –Fall 2015 Chuderewicz
Chapter 1: Financial Markets: Part 1
To truly understand financial markets and ‘talk the talk,’ you will be required to understand a plethora of jargon. Remember, I am here to answer all your questions, so don’t be shy. The last thing we need is for you to not to understand something because of jargon. Before getting started, it would be helpful to think of financial markets as a giant poker game where it is ‘dealer’s choice’ and you are the dealer. There are many different poker games out there and when you start playing, everybody has an equal chance of winning, that is, it is a fair game. Financial markets are similar in that there are many bets one can make and everyone has the same chance as winning (making a capital gain) and losing (suffer a capital loss). Another way to state this is that there is no free money to be made in financial markets and we will get much deeper into this phenomenon a little later in the course.[1]
Glass half full or empty (Bulls vs. Bears).
As mentioned above, there are many bets you can make in the financial markets.[2] Before deciding on what particular bet to make, you essentially need to decide if you are optimistic (Bullish) or pessimistic (Bearish) as it pertains to the ‘chosen’ asset’s price. Bulls make money when prices rise and lose when prices fall. Conversely, bears make money when prices fall and lose money when prices rise. After you establish whether your are bullish or bearish, you can chose any of the ‘games’ or ‘bets’ that follow, always remembering, a) there is no free money out there and 2) different bets have varying amounts of risked attached to them.
Stocks: Long vs. Short
A US Common stock represents partial equity in the company whose name it bears. Going long, that is, buying and holding shares of stock is probably the simplest (and most familiar) investment one could make. The idea is to buy (relatively) low and sell high, reaping what is referred to as a capital gain. Mutual funds are primarily comprised of long positions in common stock. In taking a long position, the investor is betting (hoping) that the stock price (or stock market index) will rise.
Example: Use the space below: Taking a long position (buying 10 shares) in IBM stock:
In contrast to going long, an investor can go “short” on a stock and therefore benefit if the relevant stock price falls (A bearish position). Shorting a stock involves borrowing shares from a creditor (e.g., JP Morgan) and selling them immediately. The key to understanding how shorting stocks works is to recognize that your debt is in stocks and not cash. For example, if I short one hundred shares of IBM stock, I borrow 100 shares of stock from a creditor and it is 100 shares of stock that I owe my creditor (excluding transactions fees)[3]. The idea is that once the price has fallen, I can buy the (borrowed) shares back for less money than I received when I sold them. Thus, if the stock does fall you pocket the difference. If the stock price rises instead and stays relatively high, then you will (eventually) be forced to buy the stock back at a higher price than you sold it for and will thus suffer a capital loss.
Example: Use the space below: Shorting IBM stock (shorting 10 shares):
In one sense, shorting a stock is more risky than going long because it exposes the investor to the possibility of larger losses. For example, if I short shares of a small biotech company which then announces a drug approval by the FDA tripling its share price, I will lose 200% overnight.[4] Conversely, the worst-case scenario with long investments is a loss of 100%, such as occurred when Enron announced accounting scandals and its stock price went to zero.
Long vs. Short positions on Bonds
Throughout the semester, we will constantly exploit the inverse relationship between the price of bonds and the yield or interest rate on bonds.
Do the “Chud Bond” Example in the space below emphasizing this inverse relationship between the price of bonds and the interest rate on bonds (an Asian financial crisis example).
You would take a long position on bonds if you expect prices to go up, same reasoning as in stocks (above). Saying the same thing a little differently, you would take a long position on bonds if you expect lower interest rates in the future. As we will see throughout the semester, expected Federal Reserve policy (i.e., what the Fed may or may not do in the future) plays a critical role in the determination of bond prices and thus interest rates. Investors are constantly looking for clues that will aid them in this regard and naturally, the continuous stream of incoming economic data is scrutinized for possible clues. For example, if the CPI (consumer price index) report came out and suggested major inflationary pressures that were not expected prior to the report, then investors would immediately expect the Fed to be more hawkish in the future, and thus, interest rates would be expected to be higher in the future.[5] Exploiting the inverse relationship between bond prices and interest rates, the previous statement can be stated as “due to the CPI report, investors expect lower bond prices in the future and thus, investors who currently have a short position in bonds will be the winners while those investors who have a long position will be the losers. We will be evaluating the impact of NEWS on the asset markets throughout the semester with NEWS being defined as the “unexpected!” For example, if the consumer price index is expected to rise by .2% and the actual number is .2%, then there is no NEWS since expectations were exactly correct. Naturally, expectations are usually not correct so NEWS is virtually an everyday experience.
Long vs. Short positions on Foreign Exchange
If you go long on the dollar, that means you are hoping the dollar gets stronger relative to the currency that you chose or a basket of currencies as in a dollar index. For example, if I go long on the dollar relative to the Euro, then I will profit if the dollar get stronger relative to the Euro and lose money if the dollar weakens relative to the Euro. If you think the dollar is going to weaken, then you should take a short position on the dollar.
Example: In the space below, do an example of taking a long position on the euro vs. the US dollar.
The currency market is probably the hardest to predict of the three asset markets and we will keep an ‘eye’ on the currency markets throughout the semester.
Exercise
1. a) Suppose you bought (took a long position) 10 shares of IBM stock at a (previous) spot price of $100 and the current IBM spot price is $95. If you closed your position, how much money would you make/lose (assume away all transactions costs)? Show all work.
b) Suppose alternatively that you took a short position by shorting 10 shares of IBM (assume same price change as in 1. a) above. How much money would you make/lose if you closed your position (cover your short)? Explain in detail and show all work.
c) Given either position, what would determine whether or not you would close your position? Again, explain in detail.
Options
Options are contracts giving the owner the right to buy (call option) or the right to sell (put option) shares of stock at a predetermined (strike) price. One call option typically gives the owner the right to buy 100 shares of the underlying security for the strike price stated on the contract. Buying calls is considered bullish because you profit when the underlying stock price rises. A call option is “in the money” when the strike price is below the (current) spot price. In such a case, the price at which you can buy the stock, i.e., the strike price, is less than the price that you can sell the stock, the spot price, so exercising the option would be profitable.
A put option is the exact opposite (and is thus bearish) and gives the owner the right to sell the underlying security at the strike price. Put options are in the money when the spot price is below the strike price. In this case, the owner could exercise the put by buying the stock at the relatively low spot price and selling the stock at the strike price, since this is exactly what a put option allows you to do.
Option prices are quoted in premium-per-share. The premium is the price you pay for the option contract. Recall that an option contract allows you to buy or sell a specified quantity of an asset during a specified time period (i.e., they expire). To find the actual cost of an option (excluding fees and other possible transactions costs), multiply the quoted premium by 100. We will discuss the specific factors that determine option premiums during class. We will also understand why options are typically not exercised, they are bought and sold much like shares of stock or bonds. The example problem on options that follows will help us understand this entire paragraph.
Practice option problems
1. Previous HW assignment from Spring 2006
(15 points total) Use the following 3 tables to answer the questions that follow. In this example, you are bearish on Best Buy (BBY). We are going to examine and compare two bearish bets. We assume away all transactions costs and as always, use the ‘last sale’ column, i.e., the premium for your calculations.
TABLE 1
|BBY | |46.20 -4.16 |
|Sep 13, 2005 @ 10:29 ET (Data 20 Minutes Delayed) |Bid N/A Ask N/A Size N/AxN/A Vol 8587300 |
|Calls |
|05 Sep 43.375 (BXJ IU-E) |4.40 |pc |
|Sep 13, 2005 @ 15:11 ET (Data 20 Minutes Delayed) |Bid N/A Ask N/A Size N/AxN/A Vol 24252700 |
|Calls |
|05 Sep 43.375 (BXJ IU-E) |2.10 |-2.30 |
|Oct 01, 2005 @ 07:22 ET (Data 20 Minutes Delayed) |Bid N/A Ask N/A Size N/AxN/A Vol 3075600 |
|Calls |
|05 Oct 40.00 (BBY JH-E) |4.10 |+1.35 |
|Sep 08, 2005 @ 15:17 ET (Data 15 Minutes Delayed) |Bid 296.35 Ask 296.39 Size 1x2 Vol 5837641 |
|Calls |
| | | |
|Sep 13, 2005 @ 06:49 ET (Data 15 Minutes Delayed) |Bid 309.59 Ask 309.70 Size 0x0 Vol 0 |
|Calls |
|05 Sep 290.0 (GGD IR-E) |20.10 |pc |
|Sep 15, 2005 @ 06:46 ET (Data 15 Minutes Delayed) |Bid 302.41 Ask 299.00 Size 0x6 Vol 0 |
|Calls |
|05 Sep 290.0 (GGD IR-E) |13.10 |pc |
|Jan 31, 2006 @ 16:38 ET (Data 15 Minutes Delayed) |Bid 74.90 Ask 74.97 Size 34x2 Vol 32327436 |
|Calls |
|06 Feb 72.50 (QAA BE-E) |4.60 |-- |
|Feb 03, 2006 @ 15:32 ET (Data 15 Minutes Delayed) |Bid 71.35 Ask 71.37 Size 47x5 Vol 19806338 |
|Calls |
|06 Feb 67.50 (QAA BU-E) |5.10 |-0.60 |
|Feb 15, 2006 @ 16:17 ET (Data 15 Minutes Delayed) |Bid 69.18 Ask 69.22 Size 2x25 Vol 40718818 |
|Calls |
|06 Feb 65.00 (QAA BM-E) |4.30 |+1.20 |
|Sep 16, 2008 @ 10:14 ET |Bid 14.35 Ask 14.36 Size 13x40 Vol 33660766 |
|Calls |
|08 Sep 10.00 (C IB-E) |4.65 |-0.80 |
|Sep 16, 2008 @ 12:32 ET |Bid 15.63 Ask 15.64 Size 15x114 Vol 130134024 |
|Calls |
|08 Sep 12.50 (C IZ-E) |2.87 |-0.43 |
|Sep 16, 2008 @ 21:01 ET |Bid 16.25 Ask 16.29 Size 77x7 Vol 257367449 |
|Calls |
|08 Sep 12.50 (C IZ-E) |3.50 |+0.20 |
|Sep 20, 2008 @ 09:36 ET |Bid 20.00 Ask 20.54 Size 35x3 Vol 265457511 |
|Calls |
|08 Sep 17.50 (C IR-E) |
Consider the following 3 scenarios:
Scenario #1 - You sold a March futures at 116 and the contract expires at 120.
Scenario # 2 - You bought a futures option put at a price of $1,500 with a strike price of 116 and the contract expires at 120.
Scenario #3 - You wrote a future option call at a price of $1,500 with a strike price of 116 and the contract expires at 120.
1.f) (10 points) Now compare the revenue that you receive to pay the taxes under each scenario and rank them 1st, 2nd and 3rd. Please show all work.
Given that these March 10 futures contracts expire at 120, please draw the profit function for each of the three scenarios above. In particular, draw the futures profit function, the futures option put profit function and the profit function for writing the call all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).
Problem 4
1. Suppose you are a chocolate maker and you need 5000 lbs of cocoa beans in December so that you can make chocolate in time for Valentine’s Day. As a risk averse person, you want to lock in a price per lb now via a futures contract. Suppose you can make an agreement, that is, enter into a futures contract for 5000 lbs with a cocoa bean farmer with an agreed upon price of $3.00 lb (which happens to be the current spot price).
a) (4 points) Explain the terminology of the transaction – that is, what exactly are you doing and why: what is the farmer doing and why?
b) (4 points) Now suppose, for whatever reason, the spot price of cocoa beans rises to $4.50 per lb at expiration (December). Who looks smart for acquiring the futures contract, the cocoa farmer or the chocolate maker? Explain.
c) (8 points) Now, let’s assume that they are both speculators. Plot the futures profit function for the speculator cocoa bean farmer, the bear, (in one graph) and the speculator chocolate maker, the bull, (in another graph). Locate the profit or loss for each with a label of point A (where price equals $4.50).
Now assume that instead that the speculators play the futures options market. In particular, the speculator cocoa bean farmer buys a (Dec.) futures options put for 5000 lbs of cocoa beans for $3000 (strike price = $3.00 lb) and the speculator chocolate maker buys a (Dec.) futures options call for 5000 lbs of cocoa beans for $3000 (strike price = $3.00 lb).
d) (4 points) Assuming that the price rises to $4.50 lb as before, and that the futures options expire in December, which option is “in the money?” Explain.
e) (8 points) Add the profit function for each speculator to your diagram above (the futures options profit function).
f) (4 points) Finally, what is the profit / loss for each speculator in the futures options market (locate this as point B on your diagram above (show work).
g) (8 points) Find the break- even spot price (at expiration) for the farmer AND the chocolate maker and locate on these points on your diagram (label as “break even spot”) Show work as to why this is the break even point.
h) (10 points) Are these results consistent with a zero sum game (hint, there are four players here)? Explain and show all work.
Terms to be familiar with (not in any particular order):
1. Options – calls, puts.
2. Derivatives – what does this term mean and why?
3. Shorting stocks and short covering.
4. Long vs. Short positions.
5. NEWS.
6. Futures.
7. Closing your position.
8. Hedging vs Speculating
9. Bulls vs. Bears.
10. Exercise.
11. In the money.
12. Rally (apply to all three of the asset markets).
13. Spot price.
14. Zero Sum game.
15. Strike price.
16. Expiration date.
17. Futures options.
18. Determination of option premium.
19. Covered vs. Naked calls/puts.
20. Writing options.
21. Risk.
22. Expected return.
23. Liquidity.
Chapter 2: Financial Markets: Part 2
Portfolio Allocation and the demand for assets
There are three main determinants of asset pricing:
1) Expected return: The higher the expected return of the asset, all else constant, the higher the price of the asset. Naturally, we will discuss at length the factors that influence the expected return of the asset(s) throughout the course. I do want to mention at this point how important expectations and changes in expectations are in terms of determining not only asset prices, but also, aggregate economic activity.
Asset price = f (Rete) :
+
{stated as “the asset price is a positive (+) function (f) of it’s expected return (Rete), all else constant}
2) Liquidity: Liquidity is an attractive quality in any asset and a highly liquid asset has three qualities: 1) it is easy (low cost) to convert the asset into money where money is defined as transactions money; 2) it can be converted to money quickly and 3) the amount that it is converted to is representative of its fundamental value (i.e., I can sell my house very quickly and easily for $5, but that doesn’t mean it is liquid!). Typically, the more liquid the asset, the lower the return. Take money, typically considered to be the most liquid asset of all. Money earns a nominal return of zero and a real return equal to the ‘negative’ of the inflation rate.[8]
Liquidity is especially attractive in a highly uncertain environment. When we discuss financial crises and shocks like 9/11, we will see the impact on financial markets when investors demand more liquid assets. US Treasuries are often considered very liquid and thus the term: “rush to the safe haven of US Treasuries.” The safe haven refers naturally to the perceived zero default risk quality of US Treasuries.
Asset price = f (Liq) :
+
{stated as “the asset price is a positive (+) function (f) of it’s liquidity (Liq), all else constant}
3) Risk: The more risky the asset, the more uncertain as to the assets’ return. Risk arises for a variety of reasons and we assume that all else equal, investors prefer assets with less risk (i.e., on average, investors are risk averse). We also note that risk and expected return are related – typically, the higher the risk, the higher the expected return (investors require a higher expected return to take on the higher risk).
Asset price = f (Risk) :
-
{stated as “the asset price is a negative (-) function (f) of it’s Risk, all else constant}
Stock Price Determination
As most of us could gather, the obvious driving force underlying any the price of any stock is the expected future stream of profits or earnings (earnings and profits are used interchangeably). We need to be more specific, it is the present value (PV) of current and future earnings that matter. We all should recall that the present value of say $1,000 today is larger than the present value of $1,000 ten years from now. But how much larger? The answer depends on the expected nominal interest rate to prevail over the next ten years. Let’s make life simple, let us suppose that the interest rate over the next ten years will be 10% year in and year out. In this case, given these assumptions, the PV of $1,000 ten years from now would be:
PV1000 = $1,000/(1 + 0.10)10 = $ 385.54
What does $385.54 represent? The answer is that if we take $385.54 and invest it today at a 10% annual return and take the principal and interest and continue rolling it over for 10 years, at the end of the 10th year, we would have $1,000. An equivalent way of thinking about this is, and the way most relevant for understanding how stock prices are determined is the following: Given the above conditions, I would be willing to pay $385.54 today, to receive $1,000 ten years from now. In what follows, the $1,000 in this example would be the “expected profits” of the firm ten years from now. These expected profits are continuously changing given the continuous NEWS that investors digest and process on a day to day basis.
In terms of stock price determination, investors form expectations as to the future profits of any particular firm as well as the expected path of interest rates, since together, they determine the present value of the firm. Similar to the above, the present value of a firm can be thought of as the most investors would be willing to pay for the firm today, to have the ownership rights to all the current and future profits expected in the future. When we divide the present value of the firm by the number of shares of stock outstanding, we arrive at the price of the stock. Before getting into more specifics, please read the following summation.
Three major factors to keep in mind when considering stock price determination
1) Stock prices are driven by expectations and changes in expectations. Just about everything influences expectations and these changes in expectations are reflected immediately in the relevant stock price.[9]
2) Stock prices are positively related to expected earnings and expected earnings nearer to the present have a stronger influence on stock prices than do the same expected earnings further out into the future. For example, the present value of $10,000 in expected earnings 2 years from now is larger than the present value of $10,000 in expected earnings 10 years from now (assuming away zero interest rates)[10]
3) Stock Prices are typically negatively related to the expected path of interest rates. The expected path of interest rates is so important in financial markets, not to mention, aggregate economic activity. Many investors spend much of their time trying to figure out what the Federal Reserve may or may not do. Interest rates also change for reasons not directly related to Fed policy, and a big portion of this class revolves around interest rate determination. For the present, we need to understand why lower interest rates are ‘typically’ good for stocks. First, the present value of future profits rises the lower the expected path of interest rates. Let’s return to our example above. It was shown that the PV of $1,000 ten years from now, assuming 10% interest rates year in and year out, was:
PV1000 = $1,000/(1 + 0.10)10 = $ 385.54
Now let’s let the expected path of interest rates be 5% year in and year out. What is the PV of $1,000 ten years from now given this lower expected path of interest rates?
PV1000 = $1,000/(1 + 0.05)10 = $ 613.91
So if the expected path of interest rates fall, all else constant, that should be good for stocks as the PV of the firm will rise.
Second, we can not ignore the influence of the change in the expected path of interest rates on expected profits. This influence is very real but also very hard to analyze and therefore, the context must be taken into account. For example, on one hand, lower interest rates in the future should stimulate economic activity and according to this version of the story, should result in higher expected profits. On the other hand, if people expect lower interest rates due to a poorly performing economy, then perhaps expected profits will fall instead of rise. So the influence of lower expected interest rates on the expectations of future profits is ambiguous, and thus, needs to be examined on a case by case basis.
Numerical Example and some Terminology
The stock price of any firm is equal to the (expected) present value of the firm (market cap) divided by the number of shares outstanding. Any factor, and there are many, that changes the expected present value of the firm, will change that stock price.[11]
The assumption (in the numerical example that follows) is that this firm falls off the face of the earth after three years, a more realistic example would include many more terms (an infinite amount!).
[pic]
Example:
|Company ABC (10,000 shares outstanding) |
|Year |1 |2 |3 |
|Exp. Earnings |$15,000 |$50,000 |$100,000 |
|Exp. 1 yr Interest Rate |0.03 |0.04 |0.05 |
[pic]
[pic]
Price to earnings ratio (PE ratio): The price to earnings ratio is often used by investors as a guidepost as to whether a stock is “overvalued” or “undervalued.” Given that stock prices are determined by expectations of the future, we NEVER know whether a stock price is overvalued, undervalued, or valued ‘just right.’[12]
The price to earning ratio can be calculated in two equivalent ways:
1) Take the market cap, which is equal to the number of shares outstanding times the current price of the stock and divide it by current year earnings. From the example above:
PE ratio = $147,175 / $15,000 = 9.81
2) Take the price per share and divide it by current year earnings per share:
PE ratio = $14.72 / $1.50 = 9.81
We can now do some exercises:
1) Suppose the Federal Reserve makes a dovish announcement and as a result, investors expect the path of short term interest rates to be steady at 3% (as opposed to previous expectations over the three year life of the firm of 3, 4, and 5% respectively).
Exercise: What will happen to the Stock Price?[13]
Exercise: What will happen to the PE ratio?
2) Suppose the CEO of Company ABC makes a statement that the company’s expected earnings are now lower than previously expected (i.e., a pessimistic outlook) so that investors now expect profits to be ‘flat’ at $15,000 for the next three years (assume the initial expected path of interest rates of 3, 4, and 5% in year 1, 2, and 3 respectively).
Exercise: What will happen to the Stock Price?
Exercise: What will happen to the PE ratio?
3) Give two specific reasons why the PE ratio would be high for a firm and comment on the type of firm that may have a high PE ratio. Finally, does a high PE ratio imply that the firm is over valued? Why or why not?
The Optimal Forecast and Rational Expectations.
Example 1: Rational Expectations and a Question Before You Hand in Your Exam!
When I was at Grad School here at PSU, a professor told a story that I believe really clarifies exactly what we mean by rational expectations. Suppose I would say to the class before anyone handed in their exam (assume it is a multiple choice exam):
“Put an asterisk next to the three questions that you think you missed”
So let’s think about this for a moment……. which questions would you pick? The answer is that if you have rational expectations formation, you should not pick any! Why?? If you pick a question that you think you missed, then change the answer! Of course I know a lot of you are thinking that well…. some questions are harder than others and I will simply choose the three hardest questions! That is fine and consistent with rational expectations, but that is not admitting that you think you missed them because if you think you missed it, again, you would change the answer. So again, if I asked you how many questions you think you missed, your answer should be zero!
Another interesting and useful feature of this example is the concept of a probability distribution – some questions probably fall into the ‘no brainer’ category and thus, you are quite certain that you got them correct; some are in the easy but not that easy, etc. As we shall see, probability distributions and the associated uncertainty plays a critical role in financial markets and the economy.
Example 2: Using Rational Expectations on Your Drive to Work Each Day
Suppose you live in Port Matilda and work in State College. Suppose also that you do not want to arrive at work “too” early and you don’t want to arrive at work “too” late. Suppose through experience, you estimate the commute to be 15 minutes and thus leave 15 minutes before you are scheduled to work.[14] Suppose you begin work at 8 am and thus you leave at 7:45 am.
Questions:
1) Would you expect to get to work at starting time each and everyday?
2) Would you actually get to work at exactly the same time?
3) Is your forecast of the time it takes to get to work optimal? Why or why not?
Consider the following two scenarios:
a) One the way to work you get stuck in traffic due to an accident, somebody hit a deer and you end up getting to work 15 minutes late!
Question: Would you change your forecast on how long it takes to get to work and would this forecast be optimal?
b) The state begins construction (on the road you travel) and you are 15 minutes late for work. You learn that the construction is going to last for 6 months. Would you change your forecast on how long it takes to get to work and would this forecast be optimal?
Let’s define the forecast error (FE) as the starting time (8 am) minus (-) the actual arrival time. If the actual arrival time is 8am, then the forecast error equals zero; if the arrival time is not 8 am, then the FE is non-zero. What are the properties of this forecast error (there are three of them)?
a.
b.
c.
Predicting Tomorrow’s Stock Price and the Efficient Market Theory
In the driving to work example above, we had the incentive to obtain an optimal forecast for the commute and thus, we used all the relevant information available to formulate that optimal forecast. For example, if it snowed all night and you believed the roads are likely to be slippery, you would use that relevant and available information immediately and incorporate (process the information) it into your forecast of the time it will take to get to work. In terms of jargon, we would say you were irrational if you did not account for the snowfall.
Naturally, any investor would love to be able to predict the future, because if you can predict future movements in asset prices, you could place the appropriate bet(s) and make lots of money! The example that follows applies to stocks, but the same line of reasoning can be applied to the bond and foreign exchange markets.
Suppose you were to try to predict tomorrow’s stock price today. Let us define the information set available to you today as Ωt. Naturally, Ωt contains ALL information that is available at time t, where the subscript t stands for today, the subscript t+1 stands for tomorrow (next period in general).
We can write the following:
St+1 = f (Ωt):
{stated as: “Tomorrow’s stock price is a function of the (entire) information set available today.”}
Naturally, we would want to use all the relevant information that is currently available in predicting an asset price. Another way to say this is that it would be irrational if we did not use all the relevant and available information that was available today (recall the drive to work and ignoring the snowfall example). In fact, rational expectations formation simply means that agents use all the information that is available today in making their forecasts and thus, the forecast is optimal.
Predicting stock prices is very similar in that you rationally use all the relevant information that is available to you when formulating your optimal forecast.
Predicting Stock Prices: A forecasting model
In the equation below, we could add a plethora of information that is available today.[15] Naturally, we would want to use only the relevant information but how do we know what information is relevant and what information is not? In the equation below, ie stands for expected interest rates, UR for unemployment rates, CC for consumer confidence, GDP for gross domestic product, HS for housing starts, etc. Naturally, we could just keep on adding variables to the model and thus, the forecasting model will become very complex (Ωt is extremely large). Thankfully, we have the efficient market theory to make ‘life’ much easier.
[pic]
THE EFFICIENT MARKET THEORY
Definition: If markets are efficient, then the current asset price has already incorporated all the relevant and available information related to that asset. Furthermore, if markets are efficient, then NEWS, as defined as the ‘unexpected,’ is immediately reflected in the asset price. That is, asset prices process new information very quickly and accurately (as in the snowfall and commute to work example).
Implications of the efficient market theory – since efficient markets imply that the current asset price has already incorporated all the relevant and currently available information, then it would be a waste of our time (fruitless) building fancy and complex models to predict future asset prices, since today’s price has already processed all the current, relevant and available information. The good news is that it makes our forecasting equation very simple. The bad news is that in order to predict changes the stock price, we would need to predict the unexpected; e.g., we would need a crystal ball.[16] Good luck with that!
Best forecasting equation assuming efficient markets:
St+1 = f (St)
In other words, the best predictor of tomorrow’s stock price is today’s stock price. This fact supports the Efficient Market Theory which states that today’s stock price contains all current and relevant information associated with the fundamental value of the firm that is available today (it efficiently processes what is in Ωt). According to efficient markets, the only reason that tomorrow’s stock price will differ from today’s would be due to NEWS that occurs between today and tomorrow. So, in effect, the NEWS is exactly equal to FE, which is defined as the forecast error. If there is no news then FE=zero, and St = St+1.[17]
[pic]
Properties of the forecast error, assuming efficient markets (recall commute to work ex.).
1. The FE must have a mean of zero (we assume that good news is as likely as bad news).
2. The FE must be independent of Ωt, where Ωt is the entire information set that is available at time t. If FE is not independent, that implies that St is not processing all the relevant and available information contained in Ωt, and thus, violates the assumption of the efficient market theory.
3. The FE must be uncorrelated with past FE’s (serially uncorrelated). Another way to state this is that NEWs is completely absorbed immediately so that today’s forecast error does not help us predict tomorrows forecast error. Recall specifically the commute to work example when there was a 1) accident that resulted in being late for work and 2) the road construction. Even though these was a large forecast error (we were really late for work), does that forecast error help us predict the forecast error tomorrow. The answer is no, the expected forecast error would again be zero, since rational expectations formation ensures that we use all relevant information available.
TESTING THE EFFICIENT MARKET THEORY (EMT)
My goal in what follows is to give you a clue as to what many economists do for a living, and that is, crunch numbers! A good amount of economic research is theoretical, and a good amount of economic research is empirical. I much prefer empirical analysis, and empirical analysis is often utilized to test (prove or disprove) economic theories.[18]
A Primer on Regression Analysis: A Consumption Function Example
The example below should be a little familiar to you from econ 004. Consumption accounts for about 70% of GDP and is thus, very much studied by economists and other economic actors interested in understanding and predicting economic activity. In econ 004 you should, at the very least, recall that disposable income and the level of consumption are tightly related, that is, if we have data on disposable income, then we can make pretty good guesses as to the level of consumption. You should also recall that consumption is also influenced by other factors as well. In what follows, we develop a fairly realistic model of consumption, and then we simplify it when interpreting the empirical results.
Consumption Function
[pic]
where:
Yd is personal disposable income
WSM is wealth in the stock market
WRE is wealth in real estate
r is the real interest rate
EX is the exchange rate where an increase implies the dollar is appreciating
CC is consumer confidence
If we used all the variables (above) to predict consumption, the regression equation will take the following form:
[pic]
The ai’s are sensitivity parameters. They tell us which direction and by how much consumption is affected by changes in each of the variables. For instance, a1 is the marginal propensity to consume (MPC), and tells us how sensitive consumption is to changes in disposable income.[19]
Empirical Results – The Consumption Function
The set up: I estimate a consumption function that includes all the arguments: above except for the exchange rate. The purpose of this example is to get you familiar with the usefulness and interpretation of these empirical results.
Important features of regression output:
R2 represents the fit of the model; the higher the R2, the better the fit. The maximum value for R2 is 1.00 and the minimum value is zero.
t-stats; if the absolute value of the t-stat exceeds 2.00, then we say that the associated variable ‘belongs’ in the regression. t-stats basically test whether or not a coefficient is significantly different than zero. If the t-stat exceeds two, then the coefficient is said to be ‘statistically different than zero.’
Coefficient interpretation: We are typically interested in the sign of the coefficient (i.e., is it consistent with economic theory) as well as the size (this has to do with economic significance). Example: the MPC (a1) in the equation above should be positive, close to one, and significant.[20]
Empirical Results on the consumption function
Equation estimated
C = a0 + a1 Yd + a2 r + a3 WSM + a4 WRE + a5 CC
Priors:
a1 is the marginal propensity to consume and should be somewhere around 0.9 in value and very significant (high t-statistic) since we know there does exist a tight relationship between consumption and disposable income.
a2 should be negative since the lower the real rate of interest, the less in pays to save (i.e., consume!).
a3 should be positive and significant – i.e., the wealth effect in terms of stock market wealth.
a4 should be positive and significant – i.e., the wealth effect in terms of real estate wealth. Note also that the claim is that a4 should be greater than a3, that is, dollar for dollar, the wealth effect in real estate is great than the wealth effect in stocks since changes in the former (real estate wealth) are perceived by economic agents to be more permanent and stable than the latter (changes in stock market wealth ,’here today, gone tomorrow.’
a5 should be positive, the more confident you are, the more you consume!
Also, the overall fit should be quite good, since we know that there is tight relationship between C and Yd
Regression Output: 1977Q3 – 2006Q2
C = -115 + .788(Yd) – 10.486(r) + .032(WSM) + .078(WRE) + .516(CC)
|Dependent Variable: Consumption |
|Method: Least Squares |
|Date: 04/23/07 Time: 19:04 |
|Sample: 1977:3 2006:2 |
|Included observations: 116 |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
|C |-115.9823 |31.78627 |-3.648819 |0.0004 |
|Yd(-1) |0.787909 |0.015640 |50.37847 |0.0000 |
|r (-1) |-10.48553 |2.276948 |-4.605081 |0.0000 |
|WSM(-1) |0.032054 |0.005459 |5.871944 |0.0000 |
|WRE(-1) |0.078031 |0.005771 |13.52198 |0.0000 |
|CC(-1) |0.515951 |0.279377 |1.846792 |0.0675 |
| | | | | |
|R-squared |0.999554 | Mean dependent var |4512.648 |
|Adjusted R-squared |0.999534 | S.D. dependent var |2243.232 |
|S.E. of regression |48.44171 | Akaike info criterion |10.64894 |
|Sum squared resid |258125.9 | Schwarz criterion |10.79136 |
|Log likelihood |-611.6384 | F-statistic |49299.63 |
|Durbin-Watson stat |0.802282 | Prob(F-statistic) |0.000000 |
| | | | | |
We will interpret all of this in class!
Testing of the efficient market hypothesis
S = closing price of Google Stock. Daily Data from Yahoo!!
The data: Daily Data from August 20, 2004 – August 30, 2007 (790 observations)
[pic]
Equation estimated
(1) St+1 = α + β St + FEt+1
which is, if you back date (go back one day ), the same as
(2) St = α + β St-1 + FEt
Equation (2) is the equation that is estimated: What are our priors?
α should be positive, yet small, and should represent the “equilibrium” market return
β should be one, implying that the difference between today’s and tomorrows spot price is (ignoring α for a second) equal to FEt+1.
We are going to test here shortly the properties of FEt+1. Recall what they are?
1)
2)
3)
But first, let’s look at some results predicting tomorrow’s stock price with todays!
Check out the fit!
[pic]
Equation Estimated: St = α + β St-1 + FEt
|Dependent Variable: GOOG |
|Method: Least Squares |
|Date: 10/09/07 Time: 23:01 |
|Sample(adjusted): 8/20/2004 8/30/2007 |
|Included observations: 790 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|C |1.222339 |0.748589 |1.632858 |0.1029 |
|GOOG(-1) |0.998410 |0.001970 |506.8233 |0.0000 |
|R-squared |0.996942 | Mean dependent var |359.5207 |
|Adjusted R-squared |0.996938 | S.D. dependent var |125.0430 |
|S.E. of regression |6.919524 | Akaike info criterion |6.709099 |
|Sum squared resid |37729.29 | Schwarz criterion |6.720927 |
|Log likelihood |-2648.094 | F-statistic |256869.8 |
|Durbin-Watson stat |1.911456 | Prob(F-statistic) |0.000000 |
Note that β is very close to one and the fit is very good!
Lets try to improve the fit by adding more “Cats and Dogs” to the right hand side of the equation.
|Dependent Variable: GOOG |
|Method: Least Squares |
|Date: 10/09/07 Time: 22:55 |
|Sample(adjusted): 8/27/2004 8/29/2007 |
|Included observations: 784 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|C |2.977423 |4.155744 |0.716460 |0.4739 |
|GOOG(-1) |1.039484 |0.036204 |28.71193 |0.0000 |
|GOOG(-2) |-0.017874 |0.052057 |-0.343355 |0.7314 |
|GOOG(-3) |-0.045028 |0.052110 |-0.864088 |0.3878 |
|GOOG(-4) |0.079843 |0.052103 |1.532399 |0.1258 |
|GOOG(-5) |-0.071880 |0.052165 |-1.377945 |0.1686 |
|GOOG(-6) |0.014510 |0.036306 |0.399663 |0.6895 |
|YIELD10YR(-1) |1.818302 |5.814346 |0.312727 |0.7546 |
|YIELD10YR(-2) |2.780892 |8.115906 |0.342647 |0.7320 |
|YIELD10YR(-3) |-1.921781 |8.096711 |-0.237353 |0.8124 |
|YIELD10YR(-4) |-3.839147 |8.113601 |-0.473174 |0.6362 |
|YIELD10YR(-5) |1.075725 |8.157192 |0.131874 |0.8951 |
|YIELD10YR(-6) |-0.365652 |5.839052 |-0.062622 |0.9501 |
|R-squared |0.996877 | Mean dependent var |360.8032 |
|Adjusted R-squared |0.996828 | S.D. dependent var |123.5483 |
|S.E. of regression |6.958013 | Akaike info criterion |6.734107 |
|Sum squared resid |37327.15 | Schwarz criterion |6.811451 |
|Log likelihood |-2626.770 | F-statistic |20508.10 |
|Durbin-Watson stat |1.994819 | Prob(F-statistic) |0.000000 |
Note – nothing helps! The only significant predictor is today’s stock price! Is this consistent with the efficient market theory????
We now exam the properties of FE!
Let try to predict it with Ωt
|Dependent Variable: FE |
|Method: Least Squares |
|Date: 10/10/07 Time: 07:15 |
|Sample(adjusted): 8/27/2004 8/29/2007 |
|Included observations: 784 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|C |2.977423 |4.155744 |0.716460 |0.4739 |
|GOOG(-1) |0.039484 |0.036204 |1.090603 |0.2758 |
|GOOG(-2) |-0.017874 |0.052057 |-0.343355 |0.7314 |
|GOOG(-3) |-0.045028 |0.052110 |-0.864088 |0.3878 |
|GOOG(-4) |0.079843 |0.052103 |1.532399 |0.1258 |
|GOOG(-5) |-0.071880 |0.052165 |-1.377945 |0.1686 |
|GOOG(-6) |0.014510 |0.036306 |0.399663 |0.6895 |
|YIELD10YR(-1) |1.818302 |5.814346 |0.312727 |0.7546 |
|YIELD10YR(-2) |2.780892 |8.115906 |0.342647 |0.7320 |
|YIELD10YR(-3) |-1.921781 |8.096711 |-0.237353 |0.8124 |
|YIELD10YR(-4) |-3.839147 |8.113601 |-0.473174 |0.6362 |
|YIELD10YR(-5) |1.075725 |8.157192 |0.131874 |0.8951 |
|YIELD10YR(-6) |-0.365652 |5.839052 |-0.062622 |0.9501 |
|R-squared |0.008677 | Mean dependent var |0.639936 |
|Adjusted R-squared |-0.006752 | S.D. dependent var |6.934641 |
|S.E. of regression |6.958013 | Akaike info criterion |6.734107 |
|Sum squared resid |37327.15 | Schwarz criterion |6.811451 |
|Log likelihood |-2626.770 | F-statistic |0.562386 |
|Durbin-Watson stat |1.994819 | Prob(F-statistic) |0.872886 |
THE FIT IS TERRIBLE – R2 = 0.008677, We can’t predict the change in price of Google between today and tomorrow with today’s information set.
NOW LETS TRY TO PREDICT FE WITH ITS PAST
|Dependent Variable: FE |
|Method: Least Squares |
|Date: 10/10/07 Time: 07:14 |
|Sample(adjusted): 8/30/2004 8/30/2007 |
|Included observations: 784 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|C |0.606648 |0.253054 |2.397310 |0.0168 |
|FE(-1) |0.043617 |0.035867 |1.216089 |0.2243 |
|FE(-2) |0.028162 |0.035995 |0.782389 |0.4342 |
|FE(-3) |-0.022462 |0.036045 |-0.623170 |0.5334 |
|FE(-4) |0.057552 |0.036051 |1.596412 |0.1108 |
|FE(-5) |-0.013378 |0.036096 |-0.370624 |0.7110 |
|FE(-6) |-0.025935 |0.036047 |-0.719473 |0.4721 |
|R-squared |0.006995 | Mean dependent var |0.649273 |
|Adjusted R-squared |-0.000673 | S.D. dependent var |6.936333 |
|S.E. of regression |6.938667 | Akaike info criterion |6.720985 |
|Sum squared resid |37408.74 | Schwarz criterion |6.762631 |
|Log likelihood |-2627.626 | F-statistic |0.912226 |
|Durbin-Watson stat |2.004756 | Prob(F-statistic) |0.485310 |
SAME KIND OF STORY, PAST FORECAST ERRORS DO NOT HELP PREDICT FUTURE FORECAST ERRORS
ALL TOLD – IT IS IMPOSSIBLE TO PREDICT CHANGES IN THE SPOT PRICE OF GOOGLE
Does FE have mean of zero???
[pic]
Summary: Our empirical results are consistent with the efficient market theory implying that it is impossible to predict changes in stock prices, suggesting that the closing price of coke follows a random walk.[21]
Another way to state this is that it is impossible to “beat the market.”
Updated results
SAMPLE - DAILY DATA - 1/2/2007
VARIABLES
DAAA: Moody's Seasoned Aaa Corporate Bond Yield
DBAA: Moody's Seasoned Baa Corporate Bond Yield
DGS10: 10-Year Treasury Constant Maturity Rate
DGS3MO: 3-Month Treasury Constant Maturity Rate
DJIA: Dow Jones Industrial Average
SP500: S&P 500 Stock Price Index
VIXCLS: CBOE Volatility Index: VIX
CPN3M: 3-Month AA Nonfinancial Commercial Paper Rate
VIX measures market expectation of near term volatility conveyed by
stock index option prices. Copyright, 2011, Chicago Board Options
Exchange, Inc. Reprinted with permission.
VXDCLS: CBOE DJIA Volatility Index
WILL5000IND: Wilshire 5000 Total Market Index
INTEREST RATE SPREADS - 'HAND" CALCULATED
"risk structure spreads"
paperbillspread = rate on 3 month paper minus rate on 3 month Tbill
corpspread = rate on baa minus aaa
yield spread
slopeyc = rate on 10 year Treasury minus 3 month Tbill
LET'S LOOK AT THE DATA!
OUR DEPENDENT VARIABLE - WHAT WE ARE TRYING TO PREDICT!
[pic]
SPREADS
[pic]
CORPSREAD AND DJIA AVERAGE TOGETHER
[pic]
RUN A REGRESSION - PRIORS????
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:10 | | |
|Sample (adjusted): 1/03/2007 10/04/2013 | |
|Included observations: 1633 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |14837.08 |75.28027 |197.0912 |0.0000 |
|CORPSPREAD(-1) |-2298.243 |47.85215 |-48.02801 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.501559 | Mean dependent var |11855.05 |
|Adjusted R-squared |0.501253 | S.D. dependent var |1909.018 |
|S.E. of regression |1348.186 | Akaike info criterion |17.25213 |
|Sum squared resid |2.96E+09 | Schwarz criterion |17.25874 |
|Log likelihood |-14084.37 | Hannan-Quinn criter. |17.25458 |
|F-statistic |1641.203 | Durbin-Watson stat |0.013821 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
A LOOK AT THE FITTED VALUES, ACTUAL VALUES AND THE RESIDUALS
[pic]
VIX
[pic]
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:15 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1640 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |14839.96 |99.19846 |149.5987 |0.0000 |
|VIXCLS(-1) |-128.3368 |4.361714 |-29.42348 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.514798 | Mean dependent var |11851.36 |
|Adjusted R-squared |0.514501 | S.D. dependent var |1910.515 |
|S.E. of regression |1331.203 | Akaike info criterion |17.22677 |
|Sum squared resid |2.90E+09 | Schwarz criterion |17.23336 |
|Log likelihood |-14123.95 | Hannan-Quinn criter. |17.22922 |
|F-statistic |1737.911 | Durbin-Watson stat |0.062123 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
[pic]
Both together
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:17 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1629 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |15174.71 |92.57123 |163.9247 |0.0000 |
|CORPSPREAD(-1) |-1205.753 |72.93067 |-16.53287 |0.0000 |
|VIXCLS(-1) |-75.51517 |5.220112 |-14.46620 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.565048 | Mean dependent var |11854.11 |
|Adjusted R-squared |0.564513 | S.D. dependent var |1910.907 |
|S.E. of regression |1261.035 | Akaike info criterion |17.11909 |
|Sum squared resid |2.59E+09 | Schwarz criterion |17.12903 |
|Log likelihood |-13940.50 | Hannan-Quinn criter. |17.12278 |
|F-statistic |1056.172 | Durbin-Watson stat |0.034814 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
[pic]
LET'S ADD SOME MORE 'CATS AND DOGS'
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:20 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1583 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |16168.56 |103.1214 |156.7915 |0.0000 |
|CORPSPREAD(-1) |-1247.905 |57.17984 |-21.82422 |0.0000 |
|VIXCLS(-1) |-86.68247 |5.108776 |-16.96737 |0.0000 |
|PAPERBILLSPREAD(-1) |674.9472 |40.23692 |16.77433 |0.0000 |
|SLOPEYC(-1) |-449.4423 |28.91532 |-15.54340 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.666942 | Mean dependent var |11933.80 |
|Adjusted R-squared |0.666098 | S.D. dependent var |1867.028 |
|S.E. of regression |1078.849 | Akaike info criterion |16.80833 |
|Sum squared resid |1.84E+09 | Schwarz criterion |16.82528 |
|Log likelihood |-13298.79 | Hannan-Quinn criter. |16.81463 |
|F-statistic |789.9790 | Durbin-Watson stat |0.053805 |
|Prob(F-statistic) |0.000000 | | | |
SO THESE RHS VARIABLES ARE ALL PART OF THE INFORMATION SET
[pic]
LET'S ADD THE OBVIOUS - a lagged DJIA term
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:23 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1582 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |26.39219 |59.36265 |0.444593 |0.6567 |
|CORPSPREAD(-1) |-17.51524 |13.44292 |-1.302935 |0.1928 |
|VIXCLS(-1) |1.845633 |1.176906 |1.568207 |0.1170 |
|PAPERBILLSPREAD(-1) |-28.88434 |14.17016 |-2.038392 |0.0417 |
|SLOPEYC(-1) |-6.238820 |3.475534 |-1.795068 |0.0728 |
|DJIA(-1) |0.998321 |0.003233 |308.8019 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.994691 | Mean dependent var |11933.10 |
|Adjusted R-squared |0.994674 | S.D. dependent var |1867.416 |
|S.E. of regression |136.2845 | Akaike info criterion |12.67115 |
|Sum squared resid |29271790 | Schwarz criterion |12.69151 |
|Log likelihood |-10016.88 | Hannan-Quinn criter. |12.67871 |
|F-statistic |59052.57 | Durbin-Watson stat |2.144099 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
CHECK OUT THE POWER OF YESTERDAY'S DJIA IN THE MODEL!
[pic]
LET'S
TESTING THE EFFICIENT MARKET THEORY
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/10/13 Time: 12:55 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1639 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |27.80542 |26.44765 |1.051338 |0.2933 |
|DJIA(-1) |0.997742 |0.002098 |475.6008 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.994459 | Mean dependent var |11850.64 |
|Adjusted R-squared |0.994456 | S.D. dependent var |1910.876 |
|S.E. of regression |142.2824 | Akaike info criterion |12.75472 |
|Sum squared resid |33139872 | Schwarz criterion |12.76132 |
|Log likelihood |-10450.50 | Hannan-Quinn criter. |12.75717 |
|F-statistic |293808.2 | Durbin-Watson stat |2.218066 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
[pic]
ADD LAGS
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/10/13 Time: 12:56 | | |
|Sample (adjusted): 1/30/2007 10/04/2013 | |
|Included observations: 1114 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |41.65038 |30.70866 |1.356308 |0.1753 |
|DJIA(-1) |0.874143 |0.043242 |20.21502 |0.0000 |
|DJIA(-2) |0.081718 |0.067250 |1.215134 |0.2246 |
|DJIA(-3) |0.047933 |0.065094 |0.736358 |0.4617 |
|DJIA(-4) |-0.013973 |0.061607 |-0.226812 |0.8206 |
|DJIA(-5) |-0.020373 |0.063273 |-0.321994 |0.7475 |
|DJIA(-6) |0.023064 |0.072414 |0.318501 |0.7502 |
|DJIA(-7) |-0.036536 |0.067062 |-0.544818 |0.5860 |
|DJIA(-8) |0.102430 |0.070459 |1.453754 |0.1463 |
|DJIA(-9) |-0.074870 |0.069470 |-1.077729 |0.2814 |
|DJIA(-10) |0.012848 |0.049960 |0.257175 |0.7971 |
| | | | | |
| | | | | |
|R-squared |0.994211 | Mean dependent var |11839.00 |
|Adjusted R-squared |0.994158 | S.D. dependent var |1929.595 |
|S.E. of regression |147.4832 | Akaike info criterion |12.83513 |
|Sum squared resid |23991675 | Schwarz criterion |12.88466 |
|Log likelihood |-7138.168 | Hannan-Quinn criter. |12.85386 |
|F-statistic |18941.78 | Durbin-Watson stat |2.026282 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
NOTE - NONE OF THE ADDED LAGS ARE SIGNIFICANT - THE FIT HAS NOT CHANGED
LET'S CHECK OUT THE RESIDUALS - THE FORECAST ERRORS - SAME AS PREDICTING THE CHANGE IN THE DJIA FROM ONE DAY TO THE NEXT"
|Dependent Variable: FE | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:46 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1582 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |60.86573 |44.64669 |1.363275 |0.1730 |
|DJIA(-1) |-0.003049 |0.002490 |-1.224893 |0.2208 |
|CORPSPREAD(-1) |-3.948232 |12.29165 |-0.321213 |0.7481 |
|PAPERBILLSPREAD(-1) |-18.76430 |13.35854 |-1.404667 |0.1603 |
|SLOPEYC(-1) |-5.431679 |3.444850 |-1.576753 |0.1151 |
| | | | | |
| | | | | |
|R-squared |0.005825 | Mean dependent var |0.688103 |
|Adjusted R-squared |0.003303 | S.D. dependent var |136.7859 |
|S.E. of regression |136.5597 | Akaike info criterion |12.67456 |
|Sum squared resid |29408787 | Schwarz criterion |12.69152 |
|Log likelihood |-10020.57 | Hannan-Quinn criter. |12.68086 |
|F-statistic |2.309998 | Durbin-Watson stat |2.176839 |
|Prob(F-statistic) |0.055856 | | | |
| | | | | |
| | | | | |
AS YOU CAN SEE, YOU CANNOT PREDICT THE FORECAST ERROR TODAY, WITH INFORMATION YESTERDAY! HERE WE SAY TODAY'S FORECAST ERROR IS ORTHOGONAL TO YESTERDAY'S INFORMATION SET - WE DID THE BEST WE COULD - THIS NEWS IS UNPREDICTABLE!
LET'S CHECK TO SEE IF THE FORECAST ERRORS ARE AUTO-CORRELATED - THAT IS, DO THEY HAVE A PATTERN
|Dependent Variable: FE | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:52 | | |
|Sample (adjusted): 1/05/2007 10/04/2013 | |
|Included observations: 1577 after adjustments | |
|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |0.310619 |3.417839 |0.090882 |0.9276 |
|FE(-1) |-0.104658 |0.032695 |-3.200989 |0.0014 |
| | | | | |
| | | | | |
|R-squared |0.011214 | Mean dependent var |0.366532 |
|Adjusted R-squared |0.010586 | S.D. dependent var |141.6477 |
|S.E. of regression |140.8960 | Akaike info criterion |12.73519 |
|Sum squared resid |31266408 | Schwarz criterion |12.74199 |
|Log likelihood |-10039.70 | Hannan-Quinn criter. |12.73772 |
|F-statistic |17.86160 | Durbin-Watson stat |2.031995 |
|Prob(F-statistic) |0.000025 | | | |
| | | | | |
| | | | | |
HERE WE HAVE A SLIGHT VIOLATION OF THE EMT - INTERPRET??
ADD MORE LAGS - NOT MUCH HELP
|Dependent Variable: FE | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:54 | | |
|Sample (adjusted): 1/11/2007 10/04/2013 | |
|Included observations: 1339 after adjustments | |
|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |-0.334619 |3.864469 |-0.086589 |0.9310 |
|FE(-1) |-0.111541 |0.038642 |-2.886483 |0.0040 |
|FE(-2) |-0.042194 |0.052573 |-0.802573 |0.4224 |
|FE(-3) |0.011283 |0.041409 |0.272488 |0.7853 |
|FE(-4) |-0.016290 |0.040956 |-0.397734 |0.6909 |
|FE(-5) |-0.026073 |0.046839 |-0.556660 |0.5779 |
| | | | | |
| | | | | |
|R-squared |0.014599 | Mean dependent var |-0.302586 |
|Adjusted R-squared |0.010903 | S.D. dependent var |144.2587 |
|S.E. of regression |143.4701 | Akaike info criterion |12.77460 |
|Sum squared resid |27438023 | Schwarz criterion |12.79790 |
|Log likelihood |-8546.595 | Hannan-Quinn criter. |12.78333 |
|F-statistic |3.949889 | Durbin-Watson stat |2.049769 |
|Prob(F-statistic) |0.001468 | | | |
| | | | | |
| | | | | |
LET'S CHECK OUT THE ERRORS FROM THE MODEL WITHOUT DJIA - I COPY AND PASTE FROM ABOVE
|Dependent Variable: DJIA | | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 07:20 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1583 after adjustments | |
|White Heteroskedasticity-Consistent Standard Errors & Covariance |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |16168.56 |103.1214 |156.7915 |0.0000 |
|CORPSPREAD(-1) |-1247.905 |57.17984 |-21.82422 |0.0000 |
|VIXCLS(-1) |-86.68247 |5.108776 |-16.96737 |0.0000 |
|PAPERBILLSPREAD(-1) |674.9472 |40.23692 |16.77433 |0.0000 |
|SLOPEYC(-1) |-449.4423 |28.91532 |-15.54340 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.666942 | Mean dependent var |11933.80 |
|Adjusted R-squared |0.666098 | S.D. dependent var |1867.028 |
|S.E. of regression |1078.849 | Akaike info criterion |16.80833 |
|Sum squared resid |1.84E+09 | Schwarz criterion |16.82528 |
|Log likelihood |-13298.79 | Hannan-Quinn criter. |16.81463 |
|F-statistic |789.9790 | Durbin-Watson stat |0.053805 |
|Prob(F-statistic) |0.000000 | | | |
SO THESE RHS VARIABLES ARE ALL PART OF THE INFORMATION SET
[pic]
I LABELED THESE ERRORS AS WITHOUTDJIARESIDS
|Dependent Variable: WITHOUTDJIARESIDS | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 08:01 | | |
|Sample (adjusted): 1/04/2007 10/04/2013 | |
|Included observations: 1582 after adjustments | |
|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |-3919.148 |494.1908 |-7.930436 |0.0000 |
|DJIA(-1) |0.328474 |0.040920 |8.027284 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.323801 | Mean dependent var |0.057241 |
|Adjusted R-squared |0.323373 | S.D. dependent var |1077.822 |
|S.E. of regression |886.5876 | Akaike info criterion |16.41390 |
|Sum squared resid |1.24E+09 | Schwarz criterion |16.42068 |
|Log likelihood |-12981.40 | Hannan-Quinn criter. |16.41642 |
|F-statistic |756.5915 | Durbin-Watson stat |0.099424 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
SO THERE IS INFORMATION AVAILABLE IN YESTERDAY'S INFORMATION SET THAT IS NOT BEING USED - VIOLATION OF THE EMT
DO THESE ERRORS HAVE A PATTERN?
|Dependent Variable: WITHOUTDJIARESIDS | |
|Method: Least Squares | | |
|Date: 10/11/13 Time: 08:04 | | |
|Sample (adjusted): 1/05/2007 10/04/2013 | |
|Included observations: 1494 after adjustments | |
|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |
| | | | | |
| | | | | |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
| | | | | |
| | | | | |
|C |1.787490 |3.933498 |0.454428 |0.6496 |
|WITHOUTDJIARESIDS(-1) |0.976777 |0.005286 |184.7729 |0.0000 |
| | | | | |
| | | | | |
|R-squared |0.946850 | Mean dependent var |-8.203185 |
|Adjusted R-squared |0.946815 | S.D. dependent var |1079.034 |
|S.E. of regression |248.8461 | Akaike info criterion |13.87288 |
|Sum squared resid |92391176 | Schwarz criterion |13.87999 |
|Log likelihood |-10361.04 | Hannan-Quinn criter. |13.87553 |
|F-statistic |26579.66 | Durbin-Watson stat |2.849583 |
|Prob(F-statistic) |0.000000 | | | |
| | | | | |
| | | | | |
YES!!! THE ERRORS FROM THE INCOMPLETE MODEL ARE HIGHLY AUTOCORRELATED - IF POSITIVE TODAY, POSITIVE TOMORROW AND VICA VERSA
The Wall Street Journal tested this random walk proposition by comparing the return of professional investors against a portfolio that was chosen by throwing darts. For more information, see:
Journal's Dartboard Retires
After 14 Years of Stock Picks
By GEORGETTE JASEN
Staff Reporter of THE WALL STREET JOURNAL
Below is a graphic summarizing the results:
[pic]
Most economists believe that all three of the asset markets; stocks, bonds, and foreign exchange are quite efficient.
|This article contains a discussion among two very prominent economists from the University of Chicago about how efficient the |
|‘market’ may or may not be.. |
| |
| |[pic] |[pic][pic] |[p|
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| |October 18, 2004 | | |
| |
|[pi|PAGE ONE |
|c] | |
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[pic]Stock Characters
As Two Economists
Debate Markets,
The Tide Shifts
Belief in Efficient Valuation
Yields Ground to Role
Of Irrational Investors
Mr. Thaler Takes On Mr. Fama
By JON E. HILSENRATH
Staff Reporter of THE WALL STREET JOURNAL
October 18, 2004; Page A1
For forty years, economist Eugene Fama argued that financial markets were highly efficient in reflecting the underlying value of stocks. His long-time intellectual nemesis, Richard Thaler, a member of the "behaviorist" school of economic thought, contended that markets can veer off course when individuals make stupid decisions.
In May, 116 eminent economists and business executives gathered at the University of Chicago Graduate School of Business for a conference in Mr. Fama's honor. There, Mr. Fama surprised some in the audience. A paper he presented, co-authored with a colleague, made the case that poorly informed investors could theoretically lead the market astray. Stock prices, the paper said, could become "somewhat irrational."
Coming from the 65-year-old Mr. Fama, the intellectual father of the theory known as the "efficient-market hypothesis," it struck some as an unexpected concession. For years, efficient market theories were dominant, but here was a suggestion that the behaviorists' ideas had become mainstream.
"I guess we're all behaviorists now," Mr. Thaler, 59, recalls saying after he heard Mr. Fama's presentation.
Roger Ibbotson, a Yale University professor and founder of Ibbotson Associates Inc., an investment advisory firm, says his reaction was that Mr. Fama had "changed his thinking on the subject" and adds: "There is a shift that is taking place. People are recognizing that markets are less efficient than we thought." Mr. Fama says he has been consistent.
The shift in this long-running argument has big implications for real-life problems, ranging from the privatization of Social Security to the regulation of financial markets to the way corporate boards are run. Mr. Fama's ideas helped foster the free-market theories of the 1980s and spawned the $1 trillion index-fund industry. Mr. Thaler's theory suggests policy makers have an important role to play in guiding markets and individuals where they're prone to fail.
Take, for example, the debate about Social Security. Amid a tight election battle, President Bush has set a goal of partially privatizing Social Security by allowing younger workers to put some of their payroll taxes into private savings accounts for their retirements.
In a study of Sweden's efforts to privatize its retirement system, Mr. Thaler found that Swedish investors tended to pile into risky technology stocks and invested too heavily in domestic stocks. Investors had too many options, which limited their ability to make good decisions, Mr. Thaler concluded. He thinks U.S. reform, if it happens, should be less flexible. "If you give people 456 mutual funds to choose from, they're not going to make great choices," he says.
If markets are sometimes inefficient, and stock prices a flawed measure of value, corporate boards and management teams would have to rethink the way they compensate executives and judge their performance. Michael Jensen, a retired Harvard economist who worked on efficient-market theory earlier in his career, notes a big lesson from the 1990s was that overpriced stocks could lead executives into bad decisions, such as massive overinvestment in telecommunications during the technology boom.
Even in an efficient market, bad investments occur. But in an inefficient market where prices can be driven way out of whack, the problem is acute. The solution, Mr. Jensen says, is "a major shift in the belief systems" of corporate boards and changes in compensation that would make executives less focused on stock price movements.
Few think the swing toward the behaviorist camp will reverse the global emphasis on open economies and free markets, despite the increasing academic focus on market breakdowns. Moreover, while Mr. Fama seems to have softened his thinking over time, he says his essential views haven't changed.
A product of Milton Friedman's Chicago School of thought, which stresses the virtues of unfettered markets, Mr. Fama rose to prominence at the University of Chicago's Graduate School of Business. He's an avid tennis player, known for his disciplined style of play. Mr. Thaler, a Chicago professor whose office is on the same floor as Mr. Fama's, also plays tennis but takes riskier shots that sometimes land him in trouble. The two men have stakes in investment funds that run according to their rival economic theories.
Highbrow Insults
Neither shies from tossing about highbrow insults. Mr. Fama says behavioral economists like Mr. Thaler "haven't really established anything" in more than 20 years of research. Mr. Thaler says Mr. Fama "is the only guy on earth who doesn't think there was a bubble in Nasdaq in 2000."
In its purest form, efficient-market theory holds that markets distill new information with lightning speed and provide the best possible estimate of the underlying value of listed companies (IT’S THE FUNDAMENTALS – RECALL THE EQUATION). As a result, trying to beat the market, even in the long term, is an exercise in futility because it adjusts so quickly to new information.
Behavioral economists argue that markets are imperfect because people often stray from rational decisions. They believe this behavior creates market breakdowns and also buying opportunities for savvy investors(THIS IN A SENSE IS ARGUING THAT YOU CAN BEAT THE MARKET AT CERTAIN TIMES!) Mr. Thaler, for example, says stocks can under-react to good news because investors are wedded to old views about struggling companies.
For Messrs. Thaler and Fama, this is more than just an academic debate (WHAT DOES MORE THAN ACADEMIC MEAN??). Mr. Fama's research helped to spawn the idea of passive money management and index funds. He's a director at Dimensional Fund Advisers, a private investment management company with $56 billion in assets under management. Assuming the market can't be beaten, it invests in broad areas rather than picking individual stocks. Average annual returns over the past decade for its biggest fund -- one that invests in small, undervalued stocks -- have been about 16%, four percentage points better than the S&P 500, according to Morningstar Inc., a mutual-fund research company.
Mr. Thaler, meanwhile, is a principal at Fuller & Thaler, a fund management company with $2.4 billion under management. Its asset managers spend their time trying to pick stocks and outfox the market (TRYING TO PICK WINNERS!) The company's main growth fund, which invests in stocks that are expected to produce strong earnings growth, has delivered average annual returns of 6% since its inception in 1997, three percentage points better than the S&P 500.
Mr. Fama came to his views as an undergraduate student in the late 1950s at Tufts University when a professor hired him to work on a market-forecasting newsletter. There, he discovered that strategies designed to beat the market didn't work well in practice. By the time he enrolled at Chicago in 1960, economists were viewing individuals as rational, calculating machines whose behavior could be predicted with mathematical models. Markets distilled these differing views with unique precision, they argued.
"In an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value," Mr. Fama wrote in a 1965 paper titled "Random Walks in Stock Market Prices." Stock movements were like "random walks" because investors could never predict what new information might arise to change a stock's price. In 1973, Princeton economist Burton Malkiel published a popularized discussion of the hypothesis, "A Random Walk Down Wall Street," which sold more than one million copies.
Mr. Fama's writings underpinned the Chicago School's faith in the functioning of markets. Its approach, which opposed government intervention in markets, helped reshape the 1980s and 1990s by encouraging policy makers to open their economies to market forces. Ronald Reagan and Margaret Thatcher ushered in an era of deregulation and later Bill Clinton declared an end to big government. After the collapse of Communist central planning in Russia and Eastern Europe, many countries embraced these ideas.
As a young assistant professor in Rochester in the mid-1970s, Mr. Thaler had his doubts about market efficiency. People, he suspected, were not nearly as rational as economists assumed.
Mr. Thaler started collecting evidence to demonstrate his point, which he published in a series of papers. One associate kept playing tennis even though he had a bad elbow because he didn't want to waste $300 on tennis club fees. Another wouldn't part with an expensive bottle of wine even though he wasn't an avid drinker. Mr. Thaler says he caught economists bingeing on cashews in his office and asking for the nuts to be taken away because they couldn't control their own appetites (THESE ARE SUPPOSEDLY EXAMPLES OF IRRATIONAL BEHAVIOR)
Mr. Thaler decided that people had systematic biases that weren't rational, such as a lack of self-control (LACK OF SELF CONTROL – THALER WANTS TO EXPLOIT THIS!!). Most economists dismissed his writings as a collection of quirky anecdotes, so Mr. Thaler decided the best approach was to debunk the most efficient market of them all -- the stock market.
Small Anomalies
Even before the late 1990s, Mr. Thaler and a growing legion of behavioral finance experts were finding small anomalies that seemed to fly in the face of efficient-market theory. For example, researchers found that value stocks, companies that appear undervalued relative to their profits or assets, tended to outperform growth stocks, ones that are perceived as likely to increase profits rapidly. If the market was efficient and impossible to beat, why would one asset class outperform another? (Mr. Fama says there's a rational explanation: Value stocks come with hidden risks and investors are rewarded for those risks with higher returns.)
Moreover, in a rational world, share prices should move only when new information hit the market. But with more than one billion shares a day changing hands on the New York Stock Exchange, the market appears overrun with traders making bets all the time.
Robert Shiller, a Yale University economist, has long argued that efficient-market theorists made one huge mistake: Just because markets are unpredictable doesn't mean they are efficient. The leap in logic, he wrote in the 1980s, was one of "the most remarkable errors in the history of economic thought." Mr. Fama says behavioral economists made the same mistake in reverse: The fact that some individuals might be irrational doesn't mean the market is inefficient (IN OTHER WORDS, AS LONG AS THE MAJORITY OF INVESTORS ARE RATIONAL THEN MARKETS WILL BE EFFICIENT – ADD IN THE FOOTBALL BETTING THESIS)
Shortly after the stock market swooned, Mr. Thaler presented a new paper at the University of Chicago's business school. Shares of handheld-device maker Palm Inc. -- which later split into two separate companies -- soared after some of its shares were sold in an initial public offering by its parent, 3Com Corp., in 2000, he noted. The market gave Palm a value nearly twice that of its parent even though 3Com still owned 94% of Palm. That in effect assigned a negative value to 3Com's other assets. Mr. Thaler titled the paper, "Can the Market Add and Subtract?" It was an unsubtle shot across Mr. Fama's bow. Mr. Fama dismissed Mr. Thaler's paper, suggesting it was just an isolated anomaly. "Is this the tip of an iceberg, or the whole iceberg?" he asked Mr. Thaler in an open discussion after the presentation, both men recall (HIGH BROW INSULT FOR SURE!!)
Mr. Thaler's views have seeped into the mainstream through the support of a number of prominent economists who have devised similar theories about how markets operate. In 2001, the American Economics Association awarded its highest honor for young economists -- the John Bates Clark Medal -- to an economist named Matthew Rabin who devised mathematical models for behavioral theories (I WONDER IF THESE MATHEMATICAL MODELS FAILED RECENTLY??) . In 2002, Daniel Kahneman won a Nobel Prize for pioneering research in the field of behavioral economics. Even Federal Reserve Chairman Alan Greenspan, a firm believer in the benefits of free markets, famously adopted the term "irrational exuberance" in 1996 (PARSE THIS TERM! RECALL THALER ARGUES THAT AT TIMES, PEOPLE EXPERIENCE LACK OF CONTROL!)
Andrew Lo, an economist at the Massachusetts Institute of Technology's Sloan School of Management, says efficient-market theory was the norm when he was a doctoral student at Harvard and MIT in the 1980s (OF COURSE IT WAS THE NORM!!! )"It was drilled into us that markets are efficient. It took me five to 10 years to change my views." In 1999, he wrote a book titled, "A Non-Random Walk Down Wall Street."
In 1991, Mr. Fama's theories seemed to soften. In a paper called "Efficient Capital Markets: II," he said that market efficiency in its most extreme form -- the idea that markets reflect all available information so that not even corporate insiders can beat it -- was "surely false." Mr. Fama's more recent paper also tips its hand to what behavioral economists have been arguing for years -- that poorly informed investors could distort stock prices.
But Mr. Fama says his views haven't changed. He says he's never believed in the pure form of the efficient-market theory. As for the recent paper, co-authored with longtime collaborator Kenneth French, it "just provides a framework" for thinking about some of the issues raised by behaviorists, he says in an e-mail. "It takes no stance on the empirical importance of these issues."
The 1990s Internet investment craze, Mr. Fama argues, wouldn't have looked so crazy if it had produced just one or two blockbuster companies, which he says was a reasonable expectation at the time. Moreover, he says, market crashes confirm a central tenet of efficient market theory -- that stock-price movements are unpredictable. Findings of other less significant anomalies, he says, have grown out of "shoddy" research.
Defending efficient markets has gotten harder, but it's probably too soon for Mr. Thaler to declare victory. He concedes that most of his retirement assets are held in index funds, the very industry that Mr. Fama's research helped to launch. And despite his research on market inefficiencies, he also concedes that "it is not easy to beat the market, and most people don't." (PUT YOUR MONEY WHERE YOUR MOUTH IS AND NO KIDDING, IT IS TOUGH TO BEAT THE MARKET!)
Write to Jon E. Hilsenrath at jon.hilsenrath@1
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Using technical analysis
Although there are many, these Bollinger Bands examples will give us a good feel for the notion of technical analysis. Note that technical analysis is completely removed from the fundamentals, which are based on expected profits and interest rates. As such, “technical analysts” are often referred to as “chart watchers,” as the following, as the following analysis demonstrates.
Bollinger bands are a very useful and popular technique in predicting stock movements. They provide many useful signals, such as whether a price is relatively high or low, whether a current trend is likely to continue or reverse, and market volatility. What separates Bollinger bands from most other price channeling techniques is in the way the bands are derived. Rather than setting the channels at a fixed percentage above and below the moving average, Bollinger bands are plotted two standard deviations above and below the moving average. This is done to ensure that 95% of price data will fall between the bands. It also ensures that the bands are sensitive to volatility.
When speaking of market trends, Bollinger bands can provide a signal based on both penetrations of the bands, as well as width of the bands. A penetration of either band, high or low, implies a continuation of the current trend. When the bands move far apart relative to the norm, the current trend may be ending. If the bands are unusually tight, it may be a sign of a new trend beginning.
Price targets can also be achieved through the use of Bollinger bands. For example, if a price is moving along the lower band and proceeds to cross above the moving average, the upper band will become a price target. Of course, the opposite also applies.
Finally, momentum can also be checked through the use of Bollinger bands. If a price is seen to move above or below a band, and on a subsequent move, fails to reach the band for a second time, there is a good chance that momentum is being lost and a reversal may be in the works. It is important to note that even if the subsequent move reaches a
higher or lower price, it must still penetrate the respective band in order to indicate lasting momentum.
Bollinger Bands – Test One
[pic]
Above we see a current six-month chart of Dell Inc. (DELL) The standard set up for use of Bollinger bands includes a six-month chart, along with a 20-day moving average. Starting from the left portion of the graph, you can see the sell signals, indicated by red arrows. As you can see, as the price bars pass through the bottom band during mid-March, a trend may be starting. In addition, the bands are fairly tight during this time period. As we progress into the early and middle of April, the lower band continues to be penetrated by the price, confirming the downtrend. As the bands widen into May, the price begins to stabilize and then rise. Dell’s price then crosses through the moving average and continues up through the upper band. However, it does not continue to hug the band, so no uptrend can be confirmed. As the bands become very wide through late May and early June, the price evens out. Two more potential buy signals are seen in June and July, but once again, only for a couple of days at a time. During this time, attention should also be focused on the bands, which are once again becoming tighter.
Looking back on what was just covered; it is safe to say that the rules regarding Bollinger bands seem to work just as described. For each change in price, the bands properly adjusted and did not provide any erratic signals. That being said, the buy and sell signals shown on the graph should not be immediately followed as soon as a band is penetrated. While each instance would provide a profit if followed, most would be minimal.
Using the rules provided by Bollinger bands, it would seem quite easy to predict the short-term future for Dell’s stock price. However, there are no definitive movements currently in progress. We can still take a look at what the chart is showing us and try to make an educated guess. The bands are beginning to widen once again, implying less volatility. The price has recently dropped below the moving average and seems to be staying somewhat near the lower band. The price drop does not appear to look
dramatically sharp, and looking at similar trends and price levels throughout the past six months, it seems as though there will be no drastic price changes in the near future. But, if the price continues to descend throughout the following week and eventually hugs the bottom band, there is a good chance we may be seeing the start of a downtrend worth moving in on with a short-position.
Bollinger Bands – Test Two
To get a better view of the accuracy and potential gains associated with Bollinger bands, let’s take a look at some more examples and see how they fare. The chart below depicts the current state of Ford Motor Company’s (F) stock. It provides a good look at a consistent downtrend beginning in late February through mid-April. Taking a short position at first sign of a downtrend on February 25 at a price of 13.00 and riding it out through April 22 at 9.89 would provide a change of 23.92%. Comparing this change to
the S&P 500 rate of 4.89%, we can undoubtedly say that we would have beaten the market. Also interesting to point out is the single buy signal, which if followed would provide a false signal, and thus a loss.
[pic]
Bollinger Bands – Test Three
The next chart shows the previous six months of International Business Machines (IBM) stock and a good opportunity to profit from both the drop and rise in price during this time. If a short position was taken at the first sell signal on March 22 at a price of 89.50 and held onto until it was clear that the trend was over on, say, April 26 at 74.65, then it would clearly show a market beating opportunity (-16.59% change). During the same time period, the S&P 500 was growing at a rate of -1.70%, so it is clear that following the bands would have paid off.
In the second part, taking a long position at the sign of an uptrend starting July 11 at a price of 78.96 and selling off on July 22 (84.44) once it appears the trend is over, another profitable opportunity is seen. A change of 6.94% is seen, as compared to the S&P 500 of 1.17%.
[pic]
Bollinger bands can provide information about the market that many other technical strategies cannot. When seeking information regarding volatility, the bands are second to none. Furthermore, once locked into a trend, Bollinger bands can give us a very good idea of what to expect in the near future. One needs to use caution when studying Bollinger bands however, as prices movements which penetrate the outer bands do not always send the correct signal. Instead, it is the movement that occurs near the outer bands that is most important, especially when the movements are consistent. That is where the real strength of Bollinger bands shines through.
Key Terms
1. Stock price determination formula.
2. The efficient market theory.
3. Autoregressive properties.
4. Technical analysis.
5. Jawboning.
6. Price to earnings ratio.
7. Earnings per share.
8. Inside information.
9. Random walk.
10. Two Crystal Balls
11. Bollinger bands
Exam #1
Econ 351
Spring 2015
Good Luck!
Name ______________________________________ Last 4 PSU ID __________
Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!
GOOD LUCK!!!
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1. (30 points total)
a) (10 points) The Table below is from January 31, 2015 so that these Jan 30 options have already expired. The ‘last’ column for all the 8 options is wrong. Please enter the correct last sale price to the left of the existing and wrong last sale price for all 8 options.
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b) (20 points total) We are going to evaluate two of the futures bets I made on Stock Trak using the boardofdart account.... I went short on Platinum and short on Feeder Cattle by selling March 2015 futures contracts. The pertinent information is below, please answer the following questions: (for full credit, please show all work).
Prices in table were those that prevailed on Feb 3, when I made the bets.
|Contract |Margin Requirement (each |# of Contracts |Contract Size (each |Price |
| |contract) | |contract) | |
|Platinum |$3,465 |15 |50 troy ounces |$1,200 per troy ounce |
|Feeder cattle |$2,025 |10 |50,000 lbs. |$ 2.00 per pound |
As of Friday, February 13, 2015, the (March) futures price of Platinum was $1,212 per troy ounce and the (March) futures price of feeder cattle was $2.04 per pound. I am closing both positions since my ‘fur is burning.’
(5 points) Considering the bet on Platinum, what is the $ value of each Platinum futures contract when I initially made the bet and what is the leverage ratio (please take the leverage ratio to three decimal spaces)?
b) (5 points) Calculate the rate of return when I close using the leverage ratio and the percent change in the price of platinum. What is my profit or loss?
c) (5 points) Now consider the bet on feeder cattle. What is the $ value of each feeder cattle futures contract when I initially made the bet and what is the leverage ratio (please take the leverage ratio to three decimal spaces)?
d) (5 points) Calculate the rate of return when I close using the leverage ratio and the percent change in the price of feeder cattle. What is my profit or loss?
3. (35 poits total)
Use the three tables below to answer the following questions
Table 1
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Table 2
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Table 3
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a) (5 points) Suppose we play a long straddle by purchasing one 535 call option and one 535 put option at Table 1 and close both positions on Table 2. Calculate the profit or loss AND rate of return.
b) (5 points) Suppose instead that we waited and closed on Table 3, calculate the profit or loss and rate of return. How much money did we make (+) or lose (-) by waiting until Table 3 to close as compared to closing on Table 2.
c) (5 points) Suppose we play a strangle by buying a 545 call and a 525 put on Table 1 and close at Table 2. How much money did we make (+) or lose (-) by waiting until Table 3 to close as compared to closing on Table 2.
d) (5 points) Name two reasons why each of the options (2 reasons for call and put) in the strangle above are so cheap on Table 3! Be very specific
e) (5 points) Suppose your friend plays a short straddle by writing one 535 call and writing one 535 put on Table 1 and closes on Table 3. How much does your friend make (+) or lose (-)? Does your answer relate to one of your answers above – why or why not? Explain.
.
f) (5 points) Suppose we gave your friend who played the short straddle a choice to close as above at Table 3 (choice 1) or to close at expiration assuming the spot price of Google remains as it is at Table 3 until expiration (choice 2). Compare the difference in losses or profits if they close at Table 3 vs. waiting until expiration (again, assume price is frozen until expiration as in Table 3).
g) (5 points) Considering your answer in part f), explain what would determine the magnitude of the difference between closing at Table 3 or waiting until expiration with the spot price frozen at Table 3.
3) (40 points total)
a) (20 points) We are now going to graph the profit functions for the long and short straddle as above where we opened up the positions at Table 1. We are only going to plot the profit / loss for both players for one point, let's call it point B, with the spot at expiration as it is in Table 2: spot = $510.66 (there are two points B's, one for player of short straddle and one for player of long straddle). Be sure to include the math as to how you calculated the payoffs for each player and prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!).
b) (20 points) We are now going to graph the profit functions for the strangle for both the buyer and writer of the strangle above where both players opened up the positions at Table 1. We are only going to plot the profit / loss for both players for one point, let's call them points B, with the spot at expiration as it is in Table 2: spot = $510.66 (there are two points B's, one for buyer of the strangle and one for the writer of the strangle). Be sure to include the math as to how you calculated the payoffs for each player and prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!).
4. (25 points total)
a) (5 points) Suppose you purchased the 540 put at Table 1 and close the position on Table 2. Calculate the profit/loss and rate of return (please show work).
b) (5 points) Plot the evolution of the premium of the 540 put that you purchased on Table 1 assuming that the spot price of Google is frozen as it is in Table 1.
c) (15 points) In the space below, graph the profit function of the 540 put that you purchased on Table 1 given the following three scenarios:
Scenario 1): the option expires with the spot price of GOOG as it is on Table 1 and your position is closed. Locate this point on your diagram as point A, clear labeling the profit or loss associated with this scenario.
Scenario 2): the option expires with the spot price of GOOG as it is on Table 2 and your position is closed. Locate the specific profit or loss on your diagram and label as point B.
Scenario 3): the option expires with the spot price of GOOG as it is on Table 3 and your position is closed. Locate the specific profit or loss on your diagram and label as point C.
5. (30 points) Let’s pretend that you graduated in December of 2014 and you scored a job as chief financial officer for a golf resort in New York. Your ‘season’ ended in the fall and the person that you replaced 'parked' all the cash made during the 2014 golf season in ten year Government securities. In particular, they purchased 10 ten year Treasury contracts during the fall of 2014. The CEO, let's call her Betty, tells you that you need to use those 10 ten year Treasury contracts to pay taxes in April of this year (2014).
a) (5 points) So Betty comes to you and tells you that she can't sleep because of this stress and asks you to buy insurance (make a hedge) against bad things happening (in terms of paying the tax bill). What are the bad things happening and how can you make the hedge? I am looking for 3 different hedges.
So here we are in the January of 2015 and you are considering three different hedges:
Scenario #1: You sell 10 March futures contracts for 132 and the price at expiration is 135.
Scenario #2: You buy 10 March futures option puts with a strike price at 132 for a price of $3,000 per put and the price at expiration is 135.
Scenario #3: You write 10 March futures option calls with a strike price of 132 for a price of $3,000 per call and the price at expiration is 135.
b) (10 points) Compare the revenue obtained to pay the tax bill under each scenario and rank them accordingly from highest to lowest. Please show all work.
c) (15 points) Given that these March futures contracts expire at 135, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.
6. (30 points) So the next day, Betty comes to you and tells you that she plans to do some renovations to the resort next winter (in December 2015) and wants to do some more hedging since she really trusts you and your excellent education at Penn State University. The resort makes some serious cash beginning in May and ending in early September. She wants you to 'park' half of the seasons money in Treasuries by buying 10 June Treasury contracts and then wants you to sell these Treasuries in December to pay for the renovations. So it is Jan 2015 and you need to do some more hedging by playing the futures market.
a) (5 points) What is your natural position in June and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'
The June hedge - consider the following 3 scenarios
So it is still in January of 2015 and there are futures options, both calls and puts available with a strike price of 123 for $3,000 each. Consider the following 3 scenarios.
Scenario #1: You buy 10 June futures contracts for 123 and the price at expiration is 127.
Scenario #2: You buy 10 June futures option calls with a strike price at 123 for a price of $3,000 per call and the price at expiration is 127.
Scenario #3: You write 10 June futures option puts with a strike price of 123 for a price of $3,000 per put and the price at expiration is 127.
b) (10 points) Compare the costs of acquiring the 10 Treasury contracts in June for each scenario and rank them accordingly from lowest cost to highest cost. Please show all work.
c) (15 points) Given that these June futures contracts expire at 127, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option calls profit function and the profit function for writing the puts all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.
7. (50 points total) Now on to the December Hedges:
a) (5 points) What is your natural position in December and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'
Scenario #1: You sell 10 December futures contracts for 125 and the price at expiration is 128.
Scenario #2: You buy 10 December futures option puts with a strike price at 125 for a price of $3,000 per put and the price at expiration is 128.
Scenario #3: You write 10 December futures option calls with a strike price of 125 for a price of $3,000 per call and the price at expiration is 128.
b) (10 points) Compare the revenue obtained to pay for the new equipment under each scenario and rank them accordingly from highest to lowest. Please show all work.
c) (15 points) Given that these December futures contracts expire at 128, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.
d) (10 points) So let us pretend your are at the paving company's Holiday party in December of 2015 and the CEO, Lee, wants to give you a Holiday bonus. Lee gives you an envelope and tells you that he decided to give you 20% of the money you saved the paving company given all the hedging. We assume, importantly, that you had a crystal ball the whole time and played the best hedge for each of the three hedges (March, June and December). Compare the total revenue left for buying the equipment assuming you played the best hedge to the total revenue that you would have left for the new equipment if you went naked and didn't hedge at all. How much is the check for or is the envelope empty? Please show all work.
Exam #1
Econ 351
Fall 2014
Good Luck!
Name ______________________________________ Last 4 PSU ID __________
Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!
GOOD LUCK!!!
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1. (30 points total) We are going to evaluate two of the bets I made on Stock Trak.... I went long on gold by buying 10 Dec 2014 futures contracts and I went short on heating oil by selling 10 Dec 2014 contracts. The pertinent information is below, please answer the following questions: (for full credit, please show all work).
Prices in table were those that prevailed when I made the bets.
|Contract |Margin Requirement (each |# of Contracts |Contract Size (each |Price |
| |contract) | |contract) | |
|Gold |$8,800 |10 |100 oz |$1,290 per oz |
|Heating Oil |$4,290 |10 |42,000 gallons |$ 2.70 per gallon |
As of Friday, September 26, the Dec 2014 futures price of gold was $1,250 per oz and the Dec 2014 price of heating oil was $2.50 per gallon. I close both of my positions on this day at these prices.
a) (5 points) Considering the bet on gold, what is the $ value of each gold futures contract when I initially made the bet and what is the leverage ratio?
b) (5 points) When I close my position on gold, what is my profit/loss rate of return?.
c) (5 points)What was the percent change in the futures price of gold and how does my rate of return on the gold bet relate to the percent change in the futures price of gold? Be very specific.
d) (5 points) Considering the bet on heating oil, what is the $ value of each heating oil futures contract when I initially made the bet and what is the leverage ratio?
e) (5 points) When I close my position on heating oil, what is my profit/loss rate of return.
f) (5 points)What was the percent change in the futures price of heating oil and how does my rate of return on the heating oil bet relate to the percent change in the futures price of heating oil? Be very specific.
2. (112 points total) Let’s pretend that you graduated in Spring of 2014 and you scored a job as chief financial officer for a large paving company in the Pittsburgh area. Your ‘season’ ended in the fall and the person you replaced 'parked' all the cash in ten year Government securities. In particular, they purchased 10 ten year Treasury contracts during the fall of 2014. The CEO, let's call him Lee, tells you that you need to use those 10 ten year Treasury contracts to pay taxes in April of next year (2015). The CEO is worried about bad things happening and thus wants you to hedge against bad things happening.
a) (5 points) What is the CEO worried about and how can you hedge against these bad things happening?
So here we are in the fall of 2014 and you are considering three different hedges:
Scenario #1: You sell ten March 2015 futures contracts for 135 and the price at expiration is 133.
Scenario #2: You buy ten March 2015 futures option puts with a strike price at 135 for a price of $2,000 per put and the price at expiration is 133.
Scenario #3: You write ten March 2015 futures option calls with a strike price of 135 for a price of $2,000 per call and the price at expiration is 133.
b) (9 points) Compare the revenue obtained to pay the tax bill under each scenario and rank them accordingly from highest to lowest. Please show all work.
c) (20 points) Given that these 10 March futures contracts expire at 133, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).
So the next day, Lee comes to you and tells you that he plans to buy some new equipment next winter (in December 2015) and wants to do some more hedging since he really trusts you and your excellent education at Penn State University. The paving company makes some serious cash beginning in May and ending in early September. He wants you to 'park' half of the season's money in Treasuries by buying 10 June 2015 Treasury contracts and then wants you to sell these Treasuries in December to pay for the new equipment. So it the fall of 2014 and you need to do some more hedging by playing the futures market.
d) (5 points) What is your natural position in June 2015 and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'
e) (5 points) What is your natural position in December 2015 and how could you hedge against bad things happening? Name the three hedges and make sure you explain what we mean by 'bad things happening.'
The June hedge - consider the following 3 scenarios:
Scenario #1: You buy 10 June futures contracts for 133 and the price at expiration is 130.
Scenario #2: You buy 10 June futures option calls with a strike price at 133 for a price of $2,000 per call and the price at expiration is 130.
Scenario #3: You write 10 June futures option puts with a strike price of 133 for a price of $2,000 per put and the price at expiration is 130.
f) (9 points) Compare the costs of acquiring the 10 Treasury contracts under each scenario and rank them accordingly from lowest to highest.
g) (20 points) Given that these June futures contracts expire at 130, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option calls profit function and the profit function for writing the puts all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).
Now on to the December Hedges:
Scenario #1: You sell 10 December futures contracts for 134 and the price at expiration is 130.
Scenario #2: You buy 10 December futures option puts with a strike price at 134 for a price of $2,000 per put and the price at expiration is 130.
Scenario #3: You write 10 December futures option calls with a strike price of 134 for a price of $2,000 per call and the price at expiration is 130.
h) (9 points) Compare the revenue obtained to pay for the new equipment under each scenario and rank them accordingly from highest to lowest. Please show all work.
i) (20 points) Given that these December futures contracts expire at 130, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points. (20 points for completely labeled graph).
j) (10 points) So let us pretend your are at the paving company's Holiday party in December of 2015 and the CEO, Lee, wants to give you a Holiday bonus. Lee gives you an envelope and tells you that he decided to give you 50% of the money you saved the paving company given all the hedging. We assume, importantly, that you had a crystal ball the whole time and played the best hedge for each of the three hedges (March, June and December). Compare the total revenue left for buying the equipment assuming you played the best hedge to the total revenue that you would have left for the new equipment if you went naked and didn't hedge at all. How much is the check for or is the envelope empty? Please show all work.
3. (70 points total) Use the following 3 Tables to answer the questions that follow:
TABLE 1
|C (CITIGROUP INC) | |14.35 -0.89 |
|Sep 16, 2008 @ 10:14 ET |Bid 14.35 Ask 14.36 Size 13x40 Vol 33660766 |
|Calls |
|08 Sep 10.00 (C IB-E) |
|C (CITIGROUP INC) | |15.66 +0.42 |
|Sep 16, 2008 @ 12:32 ET |Bid 15.63 Ask 15.64 Size 15x114 Vol 130134024 |
|Calls |
|08 Sep 12.50 (C IZ-E) |
|C (CITIGROUP INC) | |13.20 -2.55 |
|Sep 17, 2008 @ 12:41 ET |Bid 13.21 Ask 13.22 Size 41x99 Vol 152391812 |
|Calls |
08 Sep 10.00 (C IB-E) |4.10 |-1.50 |3.45 |3.55 |20 |1311 |08 Sep 10.00 (C UB-E) |0.23 |+0.19 |0.22 |0.25 |9833 |69074 | |08 Sep 12.50 (C IZ-E) |1.50 |-2.00 |1.42 |1.48 |2336 |3621 |08 Sep 12.50 (C UZ-E) |0.70 |+0.61 |0.70 |0.71 |5172 |62467 | |08 Sep 15.00 (C IC-E) |0.35 |-0.95 |0.30 |0.38 |4316 |14178 |08 Sep 15.00 (C UC-E) |2.00 |+1.62 |1.98 |2.11 |7942 |159794 | |08 Sep 17.50 (C IR-E) |0.08 |-0.13 |0.07 |0.09 |1880 |66836 |08 Sep 17.50 (C UR-E) |4.25 |+2.49 |4.25 |4.40 |1650 |109581 | |08 Oct 10.00 (C JB-E) |4.36 |-1.77 |4.30 |4.45 |34 |1346 |08 Oct 10.00 (C VB-E) |1.11 |+0.52 |1.07 |1.13 |7645 |38018 | |08 Oct 12.50 (C JZ-E) |2.60 |-1.90 |2.57 |2.67 |182 |624 |08 Oct 12.50 (C VZ-E) |1.85 |+0.78 |1.83 |1.88 |2442 |33215 | |08 Oct 15.00 (C JC-E) |1.41 |-1.28 |1.35 |1.43 |3997 |5269 |08 Oct 15.00 (C VC-E) |3.05 |+1.29 |3.05 |3.15 |10526 |49708 | |08 Oct 17.50 (C JR-E) |0.69 |-0.72 |0.65 |0.70 |2655 |27398 |08 Oct 17.50 (C VR-E) |5.00 |+2.00 |4.75 |4.95 |736 |49221 | |
a) (5 points) Use Table 1 to answer this question. Assume that we freeze the spot of Citigroup as it is in Table 1, On the same diagram, plot the evolution of the term premium for the Oct 12.50 and Oct 15 put. Please label your diagram completely making sure you clearly indicate which option each line represents.
You and a friend are not sure of the direction Citigroup is going to go so you both decide to play what is known in option talk as straddle(s). You decide to play a short straddle by writing a Sept 15 call and Sept 15 put at Table 1: Your friend plays a long straddle by buying a Sept 15 call and Sept 15 put at Table 1.
b) (10 points - 5 for correct calculations and 5 for intuition) Given your short straddle bet as above, would it be better to close your position in Table 2 or Table 3? Show all work. Explain the intuition.
c) (10 points - 5 for correct calculations and 5 for intuition) Given the long straddle played by your friend, would it be better to close his/her position in Table 2 or Table 3? Show all work. Explain the intuition.
d) (5 points) How your answers in b) and c) are related. What characteristic of options markets applies here? Explain.
(30 points total) In the space below, we are going to plot two profit functions on the same graph: one for the buyer of one Sept 15 put and one for the writer of one Sept 15 put. We open these positions on Table 1.
Scenario 1): the spot price of Citigroup stays the same as in Table 1 and the option expires. Locate these two points (one for buyer of put and one for writer of put) and label as points A, clearly labeling the profit or loss for each. Show all work.
Scenario 2): the spot price of Citigroup stays the same as in Table 2 and the option expires. Locate these two points (one for buyer of put and one for writer of put) and label as points B, clearly labeling the profit or loss for each. Show all work.
Scenario 3): the spot price of Citigroup stays the same as in Table 3 and the option expires. Locate these two points (one for buyer of put and one for writer of put) and label as points C, clearly labeling the profit or loss for each. Show all work.
Be sure to label the break even point.
e) (10 points) Prove that we have a zero sum game with Scenario 3). That is, go through the math with you, the buyer of the Sept 15 put and someone else, the writer of the Sept 15 put. Recall that you bought the puts in Table 1 and the spot at expiration is that on Table 3.
Exam #2
Econ 351
Spring 2015
Good Luck!
Name ______________________________________ Last 4 PSU ID __________
Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!
GOOD LUCK!!!
Total Points for exam = 240
Test time = 120 minutes
One minute for every two points - if you keep this pace you will have 10 minutes left over
To help with time management if spreading time evenly
Question #1 = 40 points..... 20 minutes
Question #2 = 45 points ......22 minutes
Question #3 = 30 points.... 15 minutes
Question #4 = 40 points ....20 minutes
Question #5 = 35 points..... 17 minutes
Question #6 = 25 points.... 12 minutes
Question #7 = 25 points.... 12 minutes
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1. a) (40 points total) In the space below, draw a reserve market diagram depicting points A, B, and C. Assume that the Fed held reserve supply constant and that the volatility in the effective (actual) federal funds originated entirely from the volatility in reserve demand. Note, this period is well before the Fed obtained the authority to pay interest on reserves. The period we are considering is where the target for the federal funds rate is 7%. During this time, the discount rate was set below the target as was not used by banks since there was such a stigma associated with borrowing from the Fed - so the discount rate is irrelevant for this part of problem.
(10 points for correct and completely labeled diagram)
b) (10 points) In hindsight the Fed could have done a better job in terms of hitting their federal funds target = 7%. Explain in words what they should have done to avoid point A and what they should have done differently to avoid point C. Be sure to be clear on two things in your explanation: 1) when we say 'what THEY should have done differently,' who exactly is 'THEY?' and 2) what is the operational aspect of avoiding points A and C - ie., what do 'THEY' have to do and how do they do it and who do they do it with? Please refer to each of the two cases (i.e., avoiding both points A and C). Recall, this is before the Fed had the authority to pay interest on reserves.
c) (20 points total: 10 points for diagram and 10 points for explanation) Now let's pretend that we were in a new regime (as they are now) where the Fed sets the interest rate they pay on reserves at 25 basis points below the federal funds target and the discount rate set 25 basis points above the federal funds target = 7% In the space below, redraw the reserve market diagram accounting for this new regime. Make sure you label the new points A, B, and C under this new and current regime. Explain why the old points A and C do not exist anymore - the word arbitrage should be in your answer numerous times - be sure you convey to us you know exactly what is going on here. Note, the shocks to reserve demand occur just as before and the Fed does not respond (i.e., they do not conduct any open market operations). Note also that we are assuming zero transactions costs, that is, there is no cost of arbitrage.
(10 points for correct and completely labeled diagram)
Write your essay for part 1.c) in the space below.
2. (45 points) As we know, the Fed recently finished up a two day FOMC meeting on Wednesday March 18. The Table below provides data on selected interest rates. What we want to do in this problem is to explain why the rates changed as a result of the meeting. In particluar, we are comparing interest rates on Tuesday, 3/17 (the day before the FOMC statement and press conference) to Wednesday, 3/18 which is after the announcement and press conference. Please answer the questions below.
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a) (5 points) In general, what happened to all the interest rates above and why between Tuesday, 3/17 and Wednesday, 3/18? Be sure to use an equation in your answer.
b) (10 points) Now calculate what has happened to the one year interest rate expected one year from now between Tuesday, 3/17 and Wednesday, 3/18. Please show all work. Are your results consistent with your answer from part a)?
c) (10 points) Now calculate what has happened to the one year interest rate expected two years from now between Tuesday, 3/17 and Wednesday, 3/18. Please show all work. Are your results consistent with your answer from part a)?
d) (10 points) The two graphics below show the reaction of the federal funds futures contract for Dec. of 2015 from two events - one event is the reaction of this federal funds futures contract as a result of the FOMC meeting as above and the other is the reaction of this federal funds futures contract from the employment report Friday, March 6, 2015. Identify which graph applies to the FOMC meeting (graphic A or B) and which graph applies to the employment report (graphic A or B). Make sure you explain exactly why this federal funds futures contract reacted the way it did and whether, with perfect hindsight, you should have been a bear or a bull on this futures contract for each event. Please identify on each graphic when the news came out , what the news was exactly, and whether the reaction of the fed futures contract is consistent with the efficient market theory.
Graphic A
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Graphic B
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Write your answer to part d) here:
e) (10 points) Now explain what happened in the stock market after most recent FOMC meeting and why. Please use the stock price determination expression we used in class to support your explanation. Finish your essay commenting on the following: A Fed watcher, commenting on the results of the FOMC meeting was quoted as saying: "on one hand, there was no news, on the other hand, there was plenty of news." What was this Fed watcher talking about? Please refer to each of the Fed watcher's hands.
3) (30 points, 10 points for each explanation) Explain the three reasons why the Fed wanted to pay interest on reserves. Please be as specific as possible and feel free to refer to question #1 on this exam for one of the reasons (you already did this work!). For reason #3, use the balance sheet below and identify, by CLEARLY marking on the graph below when the Fed got the authority to pay interest on reserves. Also locate on the graph the period of sterlization and be sure to explain what exactly sterilized intervention means.
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write your answer to question #3 here:
4) (40 points) The table below contain some money supply data - we are going to compare and contrast the information in the last row of each table (2008-01-01 and 2014-08-01). The target for the federal funds rate at the end of January of 2008 was 3% (this is the rate we use) and was a range or 0 - .25% in August of 2014. All numbers are in billions of dollars except for the ratios and money multiplier (MM).
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a) Let's return to January 2008 (2008-01-01), the beginning of the year that will go down in history as one of the worst years ever for the global economy. Recall that this was before the Fed obtained the authority to pay interest on reserves that happened in October of 2008. In the space below, draw a reserve market diagram depicting these conditions and label as point A (assume that the Fed does perfect in terms of predicting reserve demand so that the actual funds rate is equal to its target rate = 3%). The discount rate was 3.5% at the end of January 2008.
(10 points for correct and completely labeled diagram)
b) Let us update to August of 2014. As you know, since the Fed has hit the 'zero bound' in December of 2008, where the official target for the federal funds rate is now and has been a range: 0% - .25% or in words, zero to 25 basis points. In the space below, redraw the diagram as above with point A (from January 2008) and add a point B, that corresponds to the conditions in August of 2014. Assume importantly and for simplicity, that the position of reserve demand remains constant from January 2008 to August 2014. Assume also that the actual funds rate is at its upper bound of the target range. The discount rate was set at .75% (75 basis points) in August of 2014.
(10 points for correct and completely labeled diagram)
c. (10 points) If the Fed wants to raise the federal funds rate to 3.00% like it was at the end of January, 2008, what type and how many open market operations would they need to conduct? What are the implications on the economy if the Fed pursued such a strategy?
d) (10 points) Given that the Fed preferred not to conduct the open market operations as above in part c), what else could they do to raise the federal funds rate to 3%. Be very specific and explain exactly how this 'alternative' policy would work in terms of influencing the federal funds rate and why. The word arbitrage needs to be in your answer.
5. (35 points) We discussed the important results from a research paper on forward guidance.
a) (10 points) Fill in the blank below.
[pic]
The authors of this paper argue that the FED could have done better in their forward guidance. Write an essay explaining how forward guidance is supposed to work in terms of influencing the economy and what the Fed should have done differently and why (according to the authors). Use the two graphics (below) to support your answer. That is, mark the period where the Fed achieved maximum 'bite' on their forward guidance as 'maximum bite' on both diagrams identifying the date and what the Fed did exactly to achieve this 'maximum bite.'
[pic]
[pic]
b) (10 points) Now explain how we can use the diagrams to identify the period of maximum bite. That is, on the first graph, how exactly can we tell, by viewing the graph, the period of maximum bite. Be sure to comment on the similarities or differences in the movement of the various interest rates before the period of maximum bite as well as during the period of maximum bite.
c) (10 points) Similarly, using the second graphic, how can we identify the period of maximum bite in the Fed's forward guidance? Be sure to comment on what exactly the vertical axis represents in the second graph and how we should interpret it before the period of maximum bite as well as during the period of maximum bite. How does all of this relate to the pure expectations theory of the term structure (PET)?
d) (5 points) Let’s go back to question #2 on this exam - How would the graphics A and B in question #2 of this exam be different , if at all, if we were still in a period of maximum bite in the Fed’s forward guidance? – explain.
6. Merck Problem. (50 points total) Pretend that you are hired by Merck to do some research on the behavior of their stock price. The CEO wants you to develop a report investigating two rumors that she has been hearing about Merck stock: 1) The behavior of Merck stock is consistent with the efficient market theory and 2) Changes in Merck stock, just like any other stock, are impossible to predict. That is, Merck stock follows a random walk.
In this problem, you are going to prepare the report. I will help!
To begin, I went to Yahoo finance and copied a picture depicting the behavior of Merck’s stock for the week of (10/31/05 – 11/04/05). I also went to the WSJ online and copied and pasted an excerpt from “Merck and Qualcomm Gain, But ImClone, Guidant Decline”
By KAREN TALLEY, DOW JONES NEWSWIRES November 4, 2005.
Excerpt
“Merck was the best percentage gainer among the Dow industrials, rising $1.07, or 3.8%, to $29.48. The drug maker scored a court victory in its second Vioxx liability case; thousands of cases lie ahead.”
Answer the following questions:
[pic]
a) (5 POINTS) To begin this “make believe” report (the CEO treasures completeness), explain exactly what determines stock prices. Write out our general formula of stock price determination, explaining exactly what each term means, and the intuition underlying the formula itself.
Now discuss some of the factors that could influence the terms of your expression above.
b) (5 POINTS) Now use your expression above to explain the movement in Merck stock on Thursday, November 3. Be specific as to the cause of the movement as well as well the movement itself, i.e., the duration.
c) (5 POINTS) Use the expression in a) above to explain the behavior of Merck stock on Tuesday, November 1, the day the FOMC raised their target for the federal funds rate. Again, be very specific as to the cause of this behavior, using your expression in a). Below is an excerpt fromthe official statement from the 11/1 meeting.
[pic]
Release Date: November 1, 2005
For immediate release
The Federal Open Market Committee decided today to raise its target for the federal funds rate by 25 basis points to 4 percent.
Write your answer for part c) here.
d) (10 POINTS) Are your results consistent with the efficient market theory? Begin your answer with explaining exactly what the efficient market theory is making sure you refer to the best investment advice assuming that markets are efficient. Apply your definition of the efficient market theory to your answers on both b) and c) above. Be very specific and be sure to use the term NEWS numerous times in your explanations.
NEW GRADER) We now move on to addressing whether or not changes in Merck stock are predictable. Begin with a little notation. Let MRKt be the current spot price of Merck at time t (right now; today) and let MRKet+1 be the spot price of Merck expected tomorrow.
Of course the information set available to you is Ωt and includes all information, relevant or not, that is available up until time t (right now!).
e) (10 POINTS) According to the efficient market theory (along with our class discussion), what is the best forecasting model that you can come up with to predict MRKt+1 (the price of Merck stock tomorrow)? Be very specific and justify the choice of your forecasting model (i.e., justify why your model is the best of all the possible choices, being sure to identify some of the other possible forecasting models! (hint – redundant variables everywhere!!)).
f) (15 POINTS TOTAL, 5 FOR EACH EQUATION WITH SOLID ACCOMPANYING DISCUSSION) We are now ready to test whether or not Merck (stock) follows a random walk. Using the forecasting model above, explain exactly how we would test whether or not Merck follows a random walk. Be sure to identify the expected empirical results using all the equations that we set up in class. There are a minimum of three equations to set up and discuss. Be sure to continuously refer to the efficient market theory and the random walk properties of Merck throughout your discussion.
Exam #2
Econ 351
Fall 2014
Good Luck!
Name ______________________________________ Last 4 PSU ID __________
Please put the first two letters of your last name on the top right hand corner of this cover sheet. Also, ONLY NON-PROGRAMMABLE CALCULATORS ARE ALLOWED - THERE ARE NO SUBSTITUTES. THANKS FOR YOUR COOPERATION!
GOOD LUCK!!!
Total Points for exam = 240
Test time = 120 minutes
Approximately one minute for every two points - if you keep this pace you will have 10 minutes left over
To help with time management if spreading time evenly
Question #1 = 50 points..... 25 minutes
Question #2 = 40 points ......20 minutes
Question #3 = 30 points.... 15 minutes
Question #4 = 40 points ....20 minutes
Question #5 = 30 points..... 15 minutes
Question #6 = 50 points..... 25 minutes
1. (50 points) Leading up to and during the Lehman Brothers collapse, overnight lending markets became quite volatile, as shown by the figure below.
[pic]
1. a) In the space below, draw a reserve market diagram depicting points A, B, and C. Assume that the Fed held reserve supply constant and that the volatility in the effective federal funds came originated from the volatility in reserve demand. Note, this is the period before the Fed obtained the authority to pay interest on reserves.
(10 points for correct and completely labeled diagram)
b) (10 points) In hindsight the Fed could have done a better job in terms of hitting their federal funds target = 2%. Explain in words what they should have done to avoid point B and what they should have done differently to avoid point C. Note that we are still in the period before the Fed obtained the authority to pay interest on reserves.
c) (10 points) Draw a reserve market diagram depicting your answer for part b) above. Be sure to label points A, B and C. Note that we are still in the period before the Fed obtained the authority to pay interest on reserves.
d) (20 points total: 10 points for diagram and 10 points for explanation) Now let's pretend that we were in a new regime (as they are now) where the Fed sets the interest rate they pay on reserves at 25 basis points below the federal funds target and the discount rate set 25 basis points above the federal funds target. In the space below, redraw the reserve market diagram accounting for this new regime. Make sure you label points A, B, and C under this new and current regime. Explain in detail as to why the implied (actual) funds rate is different in this new regime relative to the old regime as in 1.a).
(10 points for correct and completely labeled diagram)
2. (40 points total) Use the Sept 17, 2014 FOMC Statement at the back of exam to answer the question below.
2.a) (10 points) List the three policy alternatives and prove, by using excerpts from the FOMC statement provided at the end of exam, that the Fed has been pursuing these 3 policy alternatives. Simply circle the excerpts that refer to each of the three policy alternatives at the zero bound (label the excerpts with the policy alternative that applies).
b) (30 points, 10 points for each explanation) Explain how these three policy alternatives (aka unconventional policy) are supposed to work in terms on influencing the economy. Be very specific in explaining how each of these are supposed to influence the economy. In your answer you should use the equation that we used in class, as well as any diagrams that you deem appropriate.
continue your answer for 2)b. here
3. (30 points, 10 points for each explanation) Explain the three reasons why the Fed wanted to pay interest on reserves. Please be as specific as possible. The terms sterilization, balance sheet capacity, tax, and control should be part of your answer(s).
continue your answer to 3. here
4. (40 points total)) We discussed how federal funds market operated during more normal times (before the Fed obtained the authority to pay interest on reserves) with a picture just like the one below. To review, there are two phones on the desk.
[pic]
a) (10 points) Discuss how this federal funds market worked in more normal times - feel free to use one of the examples we used in class as in finding cash outside the classroom / me getting mad at PNC bank and moving my money (deposit) to M & T bank. Be sure to refer to how the federal funds rate is determined.
b) (10 points) Let us fast forward to the present. Using the graph below, explain how things have changed in the federal funds market. Are the phones still ringing? Why or why not? Explain.
[pic]
Now consider the graph below. Note that the federal funds is hypothetical and remains between the upper bound (the discount rate) and the lower bound (the interest paid on reserves).
[pic]
c) (10 points). Explain why this federal funds rate would not prevail given the current conditions in reserve markets. Be sure to explain what would happen to the federal funds rate and why. Be sure to refer to the desk with the phones on it.
d) (10 points) Under what conditions would the federal funds rate lie between its upper bound (the discount rate) and its lower bound (the interest paid on reserves) as it does in the graph. How could the Fed make this hypothetical federal funds rate a reality in the sense of the actual federal funds rate remaining between its lower bound and upper bound?
5. (30 points total) Us the table below to answer the following questions.
[pic]
a) Let's return to January 2008 (2008-01-01), the beginning of the year that will go down in history as one of the worst years ever for the global economy. Recall that this was before the Fed obtained the authority to pay interest on reserves that happened in October of 2008. The numbers above are in $ billion. The target for the federal funds rate at the beginning of January, 2008, was 4.25% (those were the days!). In the space below, draw a reserve market diagram depicting these conditions and label as point A (assume that the Fed does perfect in terms of predicting reserve demand so that the actual funds rate is equal to its target rate). The discount rate in January 2008 was set at 4.5%.
(10 points for correct and completely labeled diagram)
b) (10 points) Let us update to January 2009. As you know, since the Fed has hit the 'zero bound' in December of 2008 where the official target for the federal funds rate is now and has been since December of 2008, a range: 0% - .25% or in words, zero to 25 basis points. In the space below, redraw the diagram as above with point A (from January 2008) and add a point B, that corresponds to the conditions on January 2009 (2009-01-01). Assume importantly and for simplicity, that the position of the reserve demand remains constant from January 2008 to January 2009. Assume also that the actual funds rate is at its upper bound of the target range. The discount rate was set at 50 basis points in January of 2009.
(10 points for correct and completely labeled diagram)
c. (10 points) If the Fed wants to raise the federal funds rate to 4.25% like it was in January, 2008, what type and how many open market operations would they need to conduct? What are the implications on the economy if the Fed pursued such a strategy.
6. Merck Problem. (50 points total) - same as in previous exam 2.
-----------------------
[1] For those of you familiar with finance, this concept is known as the efficient market theory.
[2] When state the word financial markets, we are typically referring to three very large markets:1) the Bond market; 2) the Stock (equity) market, and 3) the Foreign Exchange market.
[3] Throughout this course, we will typically ‘assume away’ transactions costs in our numerical calculations and analyses.
[4] For example, If I short 100 shares when the price is $10 and the price subsequently rises (triples) to $30, it would cost me $3000 (buying 100 shares at $30 and returning them to my creditor) to close my position. The initial value of my ‘investment’ was $1000 (100 shares times $10) so the loss is 200% (($1000 - $3000)/$1000) x 100. You will be required to calculate rates of return throughout this course.
[5] Hawkish refers to the Fed aggressively fighting inflation by raising interest rates to slow down aggregate demand. The opposite of hawkish is dovish and refers to the Fed being soft on inflation. An inflation dove typically worries more about employment and economic growth and less about inflation; the opposite can be said about an inflation hawk. These terms will be used throughout the semester, especially when we consider the Fed’s loss function and the Taylor rule.
[6] One major difference between options and futures is that futures contract require you to close your position where as options do not (i.e., options can expire without any action between the buyer and seller).
[7] As in at harvest time. In the real world, the standardized quantity for a futures wheat contract is 5,000 bushels!
[8]"')*+-8 ................
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