Quant Principle Strategies: Buy Write

Quant Principle Strategies: Buy Write

Q. Boiler

February 5, 2010

February 2009 Vol 2 No. 1
Also Known as ‘Covered Call Option’


This article discusses a form of Financial Derivative investment strategy called a ‘Buy-Write.’ A ‘Buy-Write’ is also referred to as a ‘Covered Call Option’ in some literature.

This article will do the following:

  • Present a simple definition of the ‘Buy-Write’ or ‘Covered-Call’strategy.
  • Present the structure, explaining in detail how to set this up.
  • Present the benefits.
  • A bit of history, specifically looking at BXM from the CBOE.
  • The Bull Market problem with this strategy

If you would like to contact the author, send a message to q.boiler@QuantP rinciple.com  . If there are any errors, typos, or defects with this article please make the effort to contact the author.

1 Buy-Write

First a quick refresher on buying and selling call and put options. With options there are basically 4 positions that you can take:

  • long the call option - in this case you are buying a contract that gives you the right to purchase an underlying on or before a future date at a predetermined ‘strike ’ price. You give up some money so that you can hold this right.
  • short the call option - in this case you are the party that sells a contract which gives someone else the right to purchase (from you) an underlying on or before a future date at the strike price.
  • long the put option - in this case you are buying a contract that gives you the right, but not the obligation, to sell an underlying on or before a future date at the strike price.
  • short the put option - in this case you are selling to someone else a contract that gives them the right, but not the obligation, to sell an underlying (to you) on or before a future date at the strike price.

Each of the four options mentioned above can be either in or out of the money.

2 Creating the Position

In order to create this position, the investor first must find a stock or commodity that he or she feels would be good to own long term, and has generally stable market outlooks. It is beyond the scope of this artical to discuss how to select the stock or ETF for investing in, however, any broad index ETF would tend to be a good candidate.

2.1 The Structure

Once you have selected the stock or ETF you are interested in, you will do 2 simple actions:

  1. Buy N 100 share blocks of the stock where N is some integer 1 or more. This will obviously depend on how much money you have to invest. Some stocks that trade for 5 dollars will only cost you 500 dollars per block, while other stocks like Berkshire Hathaway will cost 11,000,010.00 per 100 share block as it is trading at 110,000.10 per share at the time of this writing. Also, just for completness BRK-A does not have exchange traded options written against it.
  2. Sell N Call contracts against the stock or ETF you just purchased, where N is the number of blocks you bought. The selling of the call will generate cash (put money into your account). However, if the call expires in the money you will be forced to sell the N blocks of stock you just bought.

While the structure above sounds very simple, there is actually lots of important details yet to discuss. We have to discuss whether to sell in the money or out of the money calls, what expiry to choose for the calls, how to handle the transactions as expiry aproaches, implications of an il-liquid stock, and the implications of dealling with stocks below 10 dollars.

Taking as an example Freeport-MacMoRan (FCX), we will explore writing covered calls.


The Figure above shows a 3-Dimensional plot of expiry value versus stock price for FCX on expiry saturday versus the option purchased. Please take a few moments to study the chart making careful note of the yaxis which represents the option purchased in the format of (Strike Price)-(Days to Expiry), e.g. 70-10 would be 70 dollars and 10 days to expiry, and 85-101 would be an 85 dollar strike price with 101 days to expiry.

Studying this figure carefully, you will make several observations, the first observation might be that the graph looks like roofing tin (I did some roofing several years back). The more important observations will be to understand how to use this information to choose a good covered call strategy to enter into. When analyzing data it is some times best to look at the data from more than one prespective, so to that end this data will be presented in multiple views as we drive on this investment strategy. The table below presents the same data in a tabular format:

StrikePriceAsk Call To sell 65 70 75 80 85 90

70 2.81 Feb-70 Call 67.81 72.81 72.81 72.81 72.81 72.81

75 0.78 Feb-75 Call 65.7870.7875.7875.7875.7875.78

80 0.17 Feb-80 Call 65.17 70.17 75.17 80.17 80.17 80.17

70 5 Mar-70 Call70 75 75 75 75 75

75 2.64 Mar-75 Call 67.64 72.64 77.64 77.64 77.64 77.64

80 1.2 Mar-80 Call66.2 71.2 76.2 81.2 81.2 81.2

70 7.65 May-70 Call 72.65 77.65 77.65 77.65 77.65 77.65

75 5.3 May-75 Call70.3 75.3 80.3 80.3 80.3 80.3

80 3.5 May-80 Call68.5 73.5 78.5 83.5 83.5 83.5

70 9.9 Aug-70 Call74.9 79.9 79.9 79.9 79.9 79.9

75 7.6 Aug-75 Call72.6 77.6 82.6 82.6 82.6 82.6

80 5.7 Aug-80 Call70.7 75.7 80.7 85.7 85.7 85.7

70 12.752011-70Leap77.7582.7582.7582.7582.7582.75

75 10.4 2011-75Leap75.4 80.4 85.4 85.4 85.4 85.4

80 8.45 2011-80Leap73.4578.4583.4588.4588.4588.45

70 17.052012-70Leap82.0587.0587.0587.0587.0587.05

75 14.752012-75Leap79.7584.7589.7589.7589.7589.75

80 12.852012-80Leap77.8582.8587.8592.8592.8592.85

Now taking a look at one slice of the above data, namely what is the portfolio value if the stock price is $85 at expiry. This plot shows the Strike Price - Days to expiry vs the portfolio’s value at expiry. It is worth taking a couple of minutes to choke down what this plot is really presenting. Steping through the data, the bottom axis shows various call options which an investor could write ( AKA sell or short). Each of the options indicates the number of days to expiry. It is worth noting that the plot does note show the portfolio value of each of the options on the same day, instead the plot is showing the portfolio value at expiry. However, for some of the options expiry is 710 days away, and for other options expiry is only 10 days away. The implication of this is that for some of the positions you will have to wait along time to realize the profit. Finally this chart makes the other assumption that the stock price is $85 at expiry. This is the case of being called for all the options. What this boundary condition presents is the maximum profit that this portfolio could have.


Now taking a slice the ”other” way through the data will allow us to look at the value of the portfolio as a function of the Stock Price at expiry for a fixed option. Understanding this picture is very important to the Covered-Call investor, because it shows what your option payout will look like as a function of stock price at expiry. Notice that once the stock price has exceeded your contract stike price, your portfolio will no longer increase in price. There are techniques to get out of these ”undesireable” covered call postions. We are currently not ready to discuss them here, because we need to understand delta, and time depreciation. However, before you get actively involved in covered call stategies it is best that you understand some of the defensive options stategies. Finally, it is important to note that the time value depreciation effect is significantly amplified expiry week. This is important because it allows for significant profit opportunities for the savy options trader.


3 BXM the CBOE Monthly Buy-Write Index

The CBOE created a hypothetical buy-write index which they called the BXM. This index has been tracking against the S&P 500 for some time. The Chart below was crated with yahoo finance, and shows how the BXM has compared to the performance of the S&P 500 for the past several years. The important thing to note is that the BXM significantly out performs the S&P during neutral and bear markets, but gets easily beaten by the S&P 500 during bull markets. Armed with the knowlege above, you can understand why.

BXM vs SP500

4 Bull Market Problem

As you can see from the data above, the Buy-Write stategy has a problem in bull markets. The specific problem is that it under performs the stock or index it is covering. There are some defensive techniques which can be used to minimize this effect. At this point it is best just to be aware of the fact that the Buy-Write underperforms the market during a bull run. We will be discusing the bull market stategies in other articles.

5 Summary and Conclusion

This document discusses the Buy-Write, or covered call strategies. These stategies are effective at reducing volatility, generating cash flow, and improving the rate of return durring neutral and bear markets. Buy-Write stategies will not maximize profits during bull runs, and infact will not typically beat the market during bull runs. However, the stategies are a very important derivatives stategy to be familiar with.

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