Thursday, July 06, 2006

Reply to Dan McCarthy in re Covered Calls.

Dan McCarthy writes up an interesting reply to my fisking of a spam from Bernie Schaeffer promoting buy-write.

I'll begin by pointing out that core of my critique is of the buy-write strategy. That is the strategy of buying stocks for the purpose of writing calls on them. This is bad idea for two reasons. The first reason is that you end up chasing volatile stocks while limiting (censoring) the possible reward and keeping almost all of the downside risk.

The big problem with a buy-write strategy is that it generates plenty of trading costs which become an unbeatable hurdle. That combination of limited upside, downside risk, and a high hurdle rate, ensure that a buy-write strategy is going to be a long term loser.

Dan McCarthy's first point is if you are very confident about a stocks intrinsic value, then you can quickly monetize that portion of the return distribution beyond the intrinsic value via covered calls. Since you plan to sell the stock once its price moves past intrinsic value, you are effectively clawing back some of return that you would have given up. If the stock takes longer than expected to reach full value, then you get some extra return via the option premium.

My response is that at least for me, I am rarely very very confident about a stock's intrinsic value, certainly not enough to make point estimates, and then back up my guess with covered calls. My personal style is to have a big margin of safety by buying stocks that are trading about 30% below my guess of the range of intrinsic value. I think that it's super important to recognize the limits of our knowledge, by being conservative, three times careful, and then admitting that we don't know.

A secondary point is that just because a stock reaches intrinsic value, doesn't mean its time to sell. Often a stock that gets up to full value attracts momentum investors and other stupid money. These folks can bid up the stock far past its intrinsic value. When I own a stock that I think is at intrinsic value, I become somewhat indifferent to owning it.

Dan's second point, has something to do with problems of shorting volatility which is what happens when you write calls. I think that's a bad thing to do in volatile markets simply because we don't know the direction of future volatility, and we probably aren’t getting enough compensation for taking it on that risk. I'm not a huge fan of making directional bets on "squishy" things like volatility or interest rates.

Dan's final argument involves some portfolio theory math, that I'm not afraid to admit I don't understand. I've never believed that investing is particularly complex. It mostly boils down to being price sensitive and diversified. The main difference between a portfolio with covered calls and one without covered calls is that the return distributions are different. Specifically the covered call portfolio has a constrained positive return, which is not a good thing, unless you have a constrained negative return as well.

My personal guess is that after taking into account the censoring of the right tail (positive returns) and the small positive skew (from the options premium) the mean value of the covered call portfolio is less than doing nothing.

I did a quick experiment in SPSS to test this hypothesis. I generated 500 normally distributed random numbers with a mean value of 38 and standard deviation of 14.87. This roughly equal to the value and implied volatility (39.45%) of (GDX) the Gold Miners ETF, as taken from iVolatility.com. I then priced a 40 August 2006 Call with underlying price of 38, strike = $40, IV 39.15%, and Risk rate %5.4. This call was worth $1.9754.

Using the set of 500 numbers, I then calculated the effect of writing a call by adding the option premium of $1.9754 and censoring the results to a maximum of 41.97 and minimum of zero. Unsurprisingly the mean of the covered calls was $35.41 with a standard deviation of 9.0, compared to the mean of $38.43 and SD of 14.37. As is typical for censored distributions, the covered call distribution has a strong negative skew which affects the mean but not the median.

If you compare medians a different picture emerges. The median of the covered calls is 40.61 vs. 38.70 for the unencumbered. What this means is that that the typical outcome for writing a covered calls is small and positive. So far so good, But, when you calculate returns [(final outcome-$38)/$38], the futility of the covered call strategy becomes obvious.

The mean return for writing covered calls is -6.8% vs +1.04% for doing nothing. Again the typical return for writing covered calls is positive, but the total return is negative. The small positive returns from writing covered calls do not offset the occasional big losses. Taken as a whole, the strategy has a negative return. Ultimately this goes back to Benjamin Graham's observation in Security Analysis [1962ed] that the individual investor should not turn himself into insurance company by accepting a fixed and limited return while suffering occasional catastrophic losses of principal.

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