(MoneyWatch) A call option contract gives the holder the right, but not the obligation, to buy a security at a predetermined price (the strike price) on a specific date (European call) or during a specific period (American call). A call is "in the money" when the current price of the stock is trading above the strike price and "out of the money" when the reverse is true.

**You make the call**

Many investors buy call options as part of their investment strategy. Unfortunately, it's likely they do so without knowing the returns to such a strategy. This is an all-too-common problem that isn't limited to options trading -- individuals don't know the returns on their investments. For example, the authors of the study "Why Inexperienced Investors Do Not Learn: They Don't Know Their Past Portfolio Performance" found that not only do individual investors dramatically overstate their performance, but performance is negatively related with the absolute difference between return estimates and realized returns.

In other words, the lower the returns, the worse investors were when judging their realized returns. They noted that while just 5 percent of investors believed they had experienced negative returns, the reality was that 25 percent did so!

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With this in mind, Ryan McKeon, the author of the study "Returns from Trading Call Options," analyzed the performance of a strategy of buying calls. He used the bid-offer spreads to take into account trading costs (though commissions and other fees were not considered). This is important not so much because the spread is wide, but because the spread can be wide compared to the price of the option. The following is a summary of his findings:

- Call option returns are generally low and decrease as the strike price increases.
- Deep in-the-money calls generally deliver positive returns if held for a month, while all other calls deliver returns that are negative or not statistically significant from zero.
- Deep out-of-the-money calls deliver lottery-like returns -- very large losses on average, with occasional, but rare, large and positive returns. Of the 709 options that fell into this category, 706 expired worthless, with the average return being -91 percent. The three that did produce a profit provided returns of 1,092 percent, 2,414 percent and 2,600 percent. Such returns provide the hope that leads to mostly very poor results.
- The holding period didn't matter.

These findings are consistent with studies that show that individuals are risk seekers in that they have a preference for investments that have lottery-like distributions (such as "penny stocks," stocks in bankruptcy, IPOs and small growth stocks). They produce very poor results on average, but on rare occasions they provide outsized returns. The other explanation is that investors don't realize how bad such strategies are in terms of expected returns. If you've been buying call options, you no longer have that excuse.

The poor results of a buying calls strategy raises the question about the results of the other side of the trade -- selling calls and earning the premium. There are many investors who engage in this strategy by selling what is referred to as covered calls.

**Covered Calls**

A covered-call strategy requires the investor to write (sell) a call option on stocks that are in the portfolio. Essentially, the covered-call investor is trading off the upside potential (above the strike price) of the equity investment for an up-front fee and reduced (by the size of the call premium) exposure to downside risk.

Marketers of covered-call strategies demonstrate the efficiency of the strategy through the "Sharpe ratio," a measure of the return earned above the rate of return on riskless short-term U.S. Treasury bills relative to the risk taken, with risk being measured by the standard deviation of returns. While the Sharpe ratio is a useful risk-reward measurement tool, it defines standard deviation as the measure of risk. While standard deviation does measure the volatility of returns, volatility is not the only measure of risk. Investors care not only about volatility, but also about other characteristics of the distribution of returns, such as skewness.

Skewness measures the asymmetry of a distribution. Negative skewness occurs when the values to the left of (less than) the mean are fewer but farther from the mean than are values to the right of the mean. For example, the return series of -30 percent, 5 percent, 10 percent, and 15 percent has a mean of 0 percent. There is only one return less than zero percent, and three higher; but the one that is negative is much further from zero than the positive ones. Positive skewness occurs when the values to the right of (more than) the mean are fewer but farther from the mean than are values to the left of the mean. As we have already mentioned, the evidence suggests that investors prefer assets with positive skewness, like the lottery ticket. They generally try to avoid assets with negative skewness.

This leads us to the question of what impact does a covered-call writing strategy have on the potential distribution of returns. Does it shift the distribution away from a normal one, rendering the use of measures such as the Sharpe ratio less meaningful? The study, "Covered Calls: A Lose/Lose Investment," covering the nine-year period of February 1987 to December 1995, found that that while covered-call strategies did produce a lower standard deviation than did an indexing strategy, because the covered-call strategy eliminates the upside potential it produces negative skewness of returns (the kind investors dislike). For example, using a strategy of one-month covered calls produced a negative skewness of 4.6 versus a negative skewness of just 1.1 for a buy-and-hold indexing strategy. The negative skewness calls into question the relevance of the Sharpe ratio for this strategy.

**Trim the fat**

While it is true that a covered-call strategy does reduce kurtosis ("fat tails"), the problem is that it eliminates the potential for the good fat tail (the one to the right), while having no impact on the risk of the bad fat tail (the one to the left) occurring. Risk-averse investors would much prefer to eliminate the risk of the left fat tail (bear market) while accepting a smaller right fat tail (bull market).

Unfortunately, there are other negative features of covered-call writing strategies which include tax inefficiency and high transactions costs. As an alternative, I recommend investors consider lowering their equity allocation while increasing their exposure to small and value stocks.*Image courtesy of Flickr user 401(K) 2013*