Exam #1



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Homework Assignment #2 – (210 points total) Econ 351 –Fall 2018 –PLEASE STAPLE, DUE, Wednesday, September 19 AT THE BEGINNING OF CLASS: NO LATE HWS ACCEPTED.

YOU MUST USE THIS AS A TEMPLATE – THAT IS – MAKE MORE SPACE FOR YOUR ANSWERS IF YOU NEED TO BY HITTING ENTER (you certainly don’t need to type this assignment)– LEAVE THE QUESTIONS AS THEY ARE – AND PLEASE STAPLE! NOTEBOOK PAPER (OR ANY PAPER) STAPLED TO THE BACK IS NOT ACCEPTABLE (GETS A ZERO). ALSO, PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME IN THE TOP RIGHT HAND CORNER OF THIS PAGE SO THAT WE CAN ALPHABETIZE THESE EASILY. THANKS IN ADVANCE!

1) (110) points total) So when you found out that Florence, the hurricane, was heading for a direct hit on North Carolina, you decided to go long on hogs since North Carolina has many hog farms and disruptions in the supply of hogs will surely raise the price of hogs.

The specs on hog futures are as follows - the margin

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requirement is $1200 and the multiplier is 40,000 (lbs).

So you open up your long position at point A by buying ten hog futures contracts at a price of $.53 / lb.

a)(5 points) What is the leverage ratio when you open up your position?

40,000 x .53 = 21,200/1200 = 17.6666

b)(5 points) Interpret your answer in part a)

For every one percent change in the futures price of hogs, my return will be plus or minus 17.66%

c)(5 points) What is your profit/loss if you closed at point B, where the futures price of hogs is $.56 / lb?

10 x 40,000 x (.56 - .53) = $12,000

d)(10 points) Now calculate your rate of return in two ways:

i) calculate rate of return using leverage ratio

%Δ in hog price = .03/.53 = 5.66%

5.66 x 17.666 = 100%

ii) calculate your rate of return using the margin requirement

profit as above = $12,000 .... the margin requirement for 10 contract is 10 x $1200 = $12,000 so your return is $12,000/$12,000 = 100%

So you are feeling very well about your bet and decide to remain bullish on hog futures believing that the hurricane will result in even higher hog futures prices. So you are walking along and stumble into a hedgehog who happens to be a hurricane forecaster. The hedgehog tells you that "you need to hedge your hog position!" And you say what??? The hedgehog repeats: " I meant to say that you need to hedge your long hog position since you never know... the hurricane might not do as much damage as you think - hurricanes are hard to predict..... you need to buy insurance."." He gives you two choices: hedge #1) buy 10 futures options puts or hedge #2) write ten futures options calls.

So you look into hedge #1 and you are considering buying 10 FO puts with a strike price of $.54. The premium on each FO put (see graphic) is $1540 (ignore the commission of $10).

So you look into hedge #2 and you are considering writing 10 FO calls with a strike price of $.54. The premium on each FO call (see graphic) is $1928 (ignore the commission of $10).

e)(5 points) Why are the FO calls more expensive than the FO puts?

The calls are in the money and the puts are not

Consider the following two scenarios:

Scenario #1: The hurricane does no more / no less damage than expected so the futures hog prices stay at $.56 /lb and expire that way.

Scenario #2: The hurricane does less damage than expected so the futures hog prices fall to $.45 /lb and expire that way.

f)(10 points) Given scenario #1, calculate the profit or loss with each hedge - that is, calculate the profit or loss when buying the 10 futures with the futures price of $.53 as above along with the FO puts hedge (Hedge #1) and then calculate the profit or loss when buying the 10 futures with the futures price of $.53 along with the FO calls hedge (Hedge #2). Please show all work.

Hedge #1: $12,000 profit minus $15,400 (need to eat the puts premium) = - $3,400 = loss

Hedge #2: $12,000 profit plus...... the writing the calls - each call is 2 cents in the money times 40,000 == $ 800, buying the ten calls back = $ 8000..... collected $19,280 in the first place so you make $11,280 with call hedge plus $12,000 = $23,280 = profit

g)(10 points) Given scenario #2, calculate the profit or loss with each hedge - that is, calculate the profit or loss when buying the 10 futures with the futures price of $.53 as above along with the FO puts hedge (Hedge #1) and then calculate the profit or loss when buying the 10 futures with the futures price of $.53 along with the FO calls hedge (Hedge #2). Please show all work.

Hedge #1: lose 10 x 40,000 x (.45 - .53) = - $32,000 (futures bet) but FO put is 9 cents in the money so is worth 10 x 40,000 x .09 = $36,000 minus the cost (premium) 15,400 - profit on hedge 20,600... loss = 20,600 - 32,000 = - 11,400

Hedge #2: lose 10 x 40,000 x (.45 - .53) = - $32,000 (futures bet), the FO calls are out of money and thus you keep the entire premium = $19,280 = profit off of hedge #2..... loss = 19,280 - 32,000 = -12,720

(30 points) We are now going to graph all three of these bets on the SAME graph - recall we went long by buying ten hog futures contracts at a futures price of $.53 / lb and conducted 2 different hedges: the FO puts (hedge 1) and the FO calls (hedge 2) both with a strike price of $.54. On your graph be sure to identify as point(s) #1 consistent with scenario #1 when the futures price of hogs expire at $ .56... there are three points #1.

Then move onto scenario #2 where the futures price of hogs expire at $.45 / lb. There are three points #2.

Be sure to label everything including the two breakeven points.

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h)(10 points) Consider the case where the hog futures spot at expiration is $.56. Suppose that the futures price got there (=.56) and stayed there shortly after the hurricane until the expiration date in December. Consider the long bet with Hedge #1 (the put hedge). Would it have been better to close both positions as soon as the futures price got to .56 (remember it stays there until exp) or would it have been better to wait to expiration. Explain.

CLOSE IMMEDIATELY SO YOU CAN SELL BACK PUTS WITH TERM PREMIUMS ATTACHED!

i) (10 points) ) Consider the case where the hog futures spot at expiration is $.56. Suppose that the futures price got there (=.56) and stayed there shortly after the hurricane until the expiration date in December. Consider the long bet with Hedge #2 (the call hedge). Would it have been better to close both positions as soon as the futures price got to .56 (remember it stays there until exp) or would it have been better to wait to expiration. Explain

WAIT UNTIL EXPIRATION - YOU HAVE TO BUY BACK CALLS TO CLOSE - BEST TO BUY BACK WITHOUT A TERM PREMIUM ATTACHED!

j)(10 points) If you drew your two hedge profit functions correctly (the put hedge, the call hedge) they cross twice. Consider the larger of the two crossings - at what price at expiration would you be indifferent to either hedge. Label this point as indiff. Please show all work.

10 x 40000 x ( .54 - z) = - 19,280 + - 15,400 + - ..... z = .6267

2) (100 points) Consider the graphic below from the election of 2016 (Nov.9, 2016)

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a) (5 points) Suppose you opened up a long position on gold by buying one futures contract when the price of gold is $1270 per oz (point A) and closed when the futures price is 1,330 (point B). Click Here for the contract specs on gold and here for the margin requirement. What is the leverage ratio when you opened up your position? THE MARGIN USED IS $3100 - ITS A LITTLE DIFFERENT NOW

100 x 1270 = 127,000/3100 = 40.9677

b)(5 points) Calculate your rate of return using the leverage ratio.

%Δ in gold = 60/1270 = 4.724%

4.724 x 40.9677 = 193.53%

c) (5 points) Now calculate the rate of return using the margin requirement.

Profit = 100 (1330 - 1270) = 6000/3100 = 193.54%

d)(5 points) Suppose you were greedy and didn't close at point B and held onto your position until point C, where the futures price of gold is 1300. What did your greed cost you? (compare profits closing at B vs. profit closing at point C)

Profit = 100 (1330 - 1300) = 3000 - your greed cost you $3000

e)(10 points) Suppose that once the futures price of gold hit $1330 you hedged your long position by buying a FO put with a strike price = $1330 for $3000. Suppose that the futures price of gold at expiration is 1300 as above. Did your hedge work, why or why not? Assume that you exercised the put at expiration. Show all work!

No, it did not - the put is $30 in the money so you can sell it for $3000. Exercise: Buy put = $3000. Buy 100 oz at spot = 100 x 1300 = $130,000. TC = $133,000. Then exercise - sell 100 x 1330 = $133,000 = TR = TC...you breakeven on hedge, so it did not work!

f)(10 points) Suppose instead that you hedged by writing an FO call (strike price = $1330) and collected the premium = $3000. Suppose that the futures price of gold at expiration is 1300. Did this hedge work?

Yes! The call is out of money and we collect and keep the entire $3,000.

(30 points) We are now going to graph all three of these bets on the SAME graph - recall we went long by buying one futures contract on gold with the futures price at $1270, went short (first hedge) by buying an FO put with a strike price = $1330 for $3000 and went short (hedge 2) by writing a FO call with a strike price of $1330 with a premium = $3000.

Consider 2 scenarios:

Scenario #1: These gold futures expire at a price of $1330 (point B above). On your graph label these three points #1 (for scenario #1)

Scenario #2: These gold futures expire at a price of $1300 (points C above). On your graph label these three points #2 (for scenario #2)

Be sure to label both break even points

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g)(10 points) Your put hedge and your call hedge cross at two different points. Consider the smaller of the two (on left side of graph). What is the price at expiration such that you are indifferent between the two hedges. Please provide all the math. Label point as Indiff.

the call make a profit of 3000 since it is out of money - put is 60 in the money and is worth 60 x 100 = 6000 .. minus the cost = 3000 means a profit of 3000, same as call hedge.

alternative for put: TC = 3000, buy low at spot 100 x1270 = 127,000...TC = 130,000...Sell high at strike 100 x 1330 = 133,000.... profit = 3000 - same as call

h)(10 points) Suppose you had a crystal ball and knew ahead of time that when you hedged, the futures price of gold would expire at $1300. Would it have been better to write a FO call with a strike price of $1300 instead of writing a call with a strike price of $1330 as you did above? Explain in detail.

yes, writing a call that is already in the money...strike price = 1300 - you would collect a larger premium and still keep it since the call will expire at the money

i)(10 points) Same type of questions as above. If you knew ahead of time, would it have been better to buy a FO put with a strike price of $1300 instead of buying a FO put with a strike price of $1330 as you did above? Explain in detail!

no - the 1330 put is the better option - you break even on this hedge - if you bought the 1300 put, it would expire at the money and you would lose the entire premium, which is worse than breaking even!

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