Math Finance - Columbia University
A Simulation of Covered Call Strategy
Jiong Chen, Yu Xiang, Zhangpu Luo
May 14, 2014
Abstract Covered call is a trading strategy that is commonly used in stock market, which can be realized by shorting the call option while taking a long position at the underlying stock. This article analyze the performance of covered call by comparing BXM and S&P 500 then build up our own portfolio to simulate this strategy. The results of both methods agree in that: First, covered call can lower volatility and reduce uncertainty of the returns; Second, Covered call can provide cushions and generate more income while market goes down
1. Introduction
1.1 Covered Call Strategy Overview
A covered call strategy is an income-generating strategy achieved by shorting the call option and longing the underlying stock at the same time. The goal here is to collect premium paid by the option buyer. If the stock price does not exceed the strike price, then the covered call strategy will outperform the equivalent long position.
In this case, the long position in underlying stock is said to provide a "cover" since the shares are guaranteed to be able to deliver to the option buyer if the buyer decides to exercise. In short, investors who utilize covered call strategy give up the chance of unlimited capital gain for a higher probability of total return.
1.2 Applications and Illustration
To be more explicit, we draw a simple straightforward chart below:
Here, the blue line is the payoff resulting from shorting a call option; the solid grey line is the payoff from longing the stock; and the top dotted line represents the net payoff with premium, which is higher than just longing the stock.
Example: Pay 527.4 to long one share of Google stock today, and short 530 strike call, collect 10.6 premium from the call option sold. Net cost: 527.4 ? 10.6 = 516.8
Scenario 1: stock price S > K, net return is capped at (530-527.4+10.6)/516.8=2.55% Scenario 2: stock price stayed flat, net return is 10.6/516.8=2.05% Scenario 3: stock price S < K, the investor is in the risk of losing money, however, the call premium collected will provide a cushion to the downside risk
As we can see form the example above, we have the following possible outcomes: Assume call strike > initial stock price, 1. If the stock stats flat, the call won't be exercised, the strategy generates income from the call premium. 2. If the stock price declines, the call won't be exercised either. The strategy is in risk of loss from long stock position, but the option premium acts as a cushion. 3. If the stock rises above the strike, call will be exercised. The strategy will lose the potential gain from stock appreciation. The total return is capped.
2. Stock Covered Call Strategy Performance
2.1 Data selection and explanations
In order to analyze the performance of covered call strategy, we choose the S&P 500 Index and COBE S&P 500 Buy Write Index (!") to make a comparison. The COBE S&P 500 Buy
Write Index (BXM) is a benchmark index designed to track the performance of a hypothetical buy-write strategy on the S&P 500 Index, it is a passive total return index based on (1) buying an S&P 500 stock index portfolio, and (2) selling the near-term S&P 500 Index "covered" call option. Therefore, we can regard BXM as the S&P 500 Stock Index after using the covered call strategy, then we can compare the performance of those two index in order to see what will happen after using the strategy. We choose the range of the data from 01/01/08 to 12/31/12 because there can be bear market and bull market during these days, therefore, we can see in more detailed how the strategy performs. In addition, we choose to use the adjusted stock price in order to take into account the effect of dividends.
2.2 Some statistics that will be used in comparison
(1) Annualized Return
! !
= [ (1 + !)]! - 1
!
Where ! is the annual return in !! year (2) Standard Deviation
(!) =
!!!!(! - )! - 1
Where
!
is the daily return of a index and
= !
!
! !!!
!
(3) 90 days rolling volatility for 1 day
!" = (!)!" Where (!)!" is the standard deviation of the daily returns in 90 days (4) Annualized Volatility
= 1 250
2.3 Comparison of the two indexes
2.3.1 Covered call can lower volatility and reduce uncertainty of the returns
We can use the formula above to calculate the 1-day volatility and annual volatility to compare how volatile those two indexes are. We plot the 1-day volatility and annual volatility for both of the index. (Figure 1)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1/4/08
1/4/09
1/4/10
1/4/11
1/4/12
1--day
vol
for
S&P
Annual
vol
for
S&P
1--day
vol
for
BXM
Annual
vol
for
BXM
Average Volatility: S&P 23.3% 500 BXM 17.4% Covered call is almost 1/4 less volatile
Figure 1
As we can see from the plot above, the annual volatility of BXM is lower than that of S&P 500, which means by using covered call, we can reduce the uncertainty of the returns provided by the stock. To further explore this, we can also derive the histogram of the returns of those two indexes and see how they are distributed. (Figure 2)
Figure 2: The histogram returns of S&P 500 and BXM
We can see from the plot the returns of BXM is more concentrated in its center than the returns of S&P 500, which means we can say the probability of achieving the returns in the center is high and we can have more stable returns.
2.3.2 Covered call can provide cushions and generate more income while market goes down
We can firstly calculate the annual returns of S&P 500 Indexes and BXM then compare them.(Table 1 and Figure 3)
2012 2011 2010 2009 2008
Table 1: The Annual returns
Annual return of S&P 500 Annual return of
BXM
0.116776032
0.045949957
-0.0112197
0.051246843
0.110018623
0.052708771
0.196716033
0.241621832
-0.375846486
-0.280455502
0.3
0.2
0.1
0
--0.1
2012
--0.2
--0.3
--0.4
--0.5
2011
2010
2009
2008
annual
return
of
S&P
500
annual
return
of
BXM
Figure 3: The Annual Returns of year from 2008 to 2012 0.8
0.6
0.4
0.2
0
Bear
Bull
Market
Slight
Bull
Bull
Market
Bear
Bull
Market
--0.2
Market
Market
Market
S&P
500
BXM
excess
return
--0.4
--0.6
Figure 4:The returns and excess returns for S&P 500 and BXM
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- s p 500 financial ratios yardeni research
- using artificial neural networks to forecast financial
- how to get data an introduction into quantmod wu
- estimating a market model step by step
- dryden s p 500 index fund prudential financial
- math finance columbia university
- s p 500 trailing p e ratios yardeni research
- stock market volatility during the 2008 financial crisis
- byjeff rey heer michael bostock and vadim ogievetsky aur
- s p u s indices s p global
Related searches
- columbia university graduate programs
- columbia university career fairs
- columbia university graduate tuition
- columbia university costs
- columbia university cost per year
- columbia university tuition and fees
- columbia university book cost
- columbia university cost of attendance
- columbia university graduate school tuition
- columbia university tuition 2019
- columbia university tuition 2020 2021
- columbia university neuroscience