Ever since stock options were listed on the Chicago Board Options Exchange in 1973, the most popular and widely practiced option strategy has been “selling covered calls” against stock holdings. On the surface, it can be a very compelling strategy. But it's imperative that this investor fully understand the value of the options he's selling. On a single investment, the investor can profit by selling an undervalued option; but over time, selling options too cheaply will lose money. It's also very important to understand how this strategy impacts the investor's overall portfolio. If he's taking a risk with potential losers yet capping potential winners, his portfolio's expected return will drop. A covered call, then, is a good strategy only if an investor makes sure he's fairly compensated for accepting this lower expected return.

### TERMS DEFINED

A “call option” is, of course, the option to buy a stock at a predetermined price (“strike price”) until a predetermined date (“expiration date”). For example, at press time IBM was trading at $83.50 per share. The option with a strike price of $90 and an expiration on the third Friday of January 2006 costs $3.50. Why buy an option rather than just the stock? The reason is primarily due to risk tolerance. The buyer of the option may have a lower chance of return, but he also takes a much lower level of risk — only $3.50 per share. (For the record, a “put option” is the option to sell a stock at a predetermined price — but we'll save “puts” for another day.)

So how does this “selling covered calls” work? Well, if an owner of IBM sells that January $90 call, he pockets $3.50. By agreeing to be willing to part with IBM at $90 — and foregoing any gain above — this IBM owner effectively gets a “bird in hand” versus some potential appreciation “in the bush.” We might define this relinquished future profit as “opportunity cost.” (See “Opportunity Cost,” this page.)

Despite this opportunity cost, this arrangement sounds awfully attractive. For the owner of the IBM, nothing really changes. An extra $3.50 per share is credited to his brokerage account and the IBM stock is merely segregated as collateral. But things are rarely that simple. And with option puts there are some serious issues for investors to consider.

### LUMPS

First, stock returns are lumpy.

Many investors have the sense that stocks have some “expected return” over time — long-term returns for U.S. large capitalization stocks are around 10 percent to 12 percent. Further, many expect that this 10 percent or 12 percent return comes steadily over time, year in and year out. Perhaps the stock market returns over the last few years have corrected this perception among some investors. Still, though, it's a widely held view. And it is not realistic.

This can be seen clearly by looking at historical stock returns. Assuming no taxes and reinvesting all dividends, a $1,000 investment in the S&P 500 in January 1945 grew to an astounding $850,000 by March of 2005. The annualized return over this period was 11.8 percent a year — or a little less than 1 percent per month.

What if back in 1945 we'd agreed to a cap on our monthly returns? It turns out that if we'd capped the monthly returns during this period at a maximum of 3 percent (over three times the average seems reasonable, no?), the original $1,000 would have grown to only $3,944.

That's because stock returns are not steady. They come in periods of boredom punctuated by great fits and spurts. Capping these unexpected bursts dramatically alters long-term returns.

### DISPERSION

Another notion that many investors have is that stocks all act pretty much the same. But let's analyze this assumption. During the year ending on April 14, the return of an equal weighted portfolio of the stocks in the S&P 100 has been 11.4 percent. But, rather than being made up of similar individual stock returns, the range was quite significant. From a high return of 116.6 percent (Allegheny Technologies) to a low of -50.8 percent (Unisys), the individual stock returns are anything but similar.

So, what if we had agreed to cap each of the 100 stocks at a maximum of 20 percent? It turns out that 26 of the 100 stocks had returns above 20 percent — and if we agreed to this cap, our portfolio return drops from 11.4 percent to 4.6 percent.

If we'd agreed to cap our returns at a maximum of 10 percent, the return drops to nearly zero.

Clearly, to properly induce us to agree to a cap, we need to be paid an appropriate amount.

### PRICING

So what's a fair price?

In 1973, Fisher Black, a PhD in applied math from Harvard, and Myron Scholes, an assistant finance professor at the Massachusetts Institute of Technology, submitted an article on options pricing to the *Journal of Political Economy*. Now known as the Black-Scholes option model, the creation of this model has become one of the most significant in modern financial history. While today there are a variety of option-pricing models, Black and Scholes laid the basic groundwork, and their model gives us some very important metrics for understanding the “fair value” for an option.

While the formula is complex, the inputs are surprisingly intuitive and contain four basic components:

- stock price versus strike price;
- time to expiration;
- interest rates and dividend yields; and
- volatility of stock return.

The first input is the spread between the current stock price and the “strike” price. Not surprisingly, as this distance increases — that is to say, as an option becomes more “out of the money” — the “fair value” declines. For instance, in our example with IBM trading at $83.50, we'd pay less for a call with a strike price of $100 than at $90. Why? Because there is a smaller chance that IBM will get to $100 than $90 (more on this later).

The second input is the time until the expiration of the option; again, quite intuitively, more time equates to a higher price.

The third input is slightly more complex and involves dividends and interest rates. This factor impacts the “forward price” of an asset, but in comparison with the other factors is generally minor. Three down, one to go — so far, so good. Importantly, none of these inputs involve any significant estimate or guesswork.

The fourth input to any option-pricing model is the most important. We need to know how “volatile” the stock is, and the statistic we use for this is known as “standard deviation.” While statistics can be a daunting topic, again, the impact of this is quite intuitive. The more volatile a stock, the more one would expect to pay for an option. Clearly, you'd be willing to pay more for an option on an “exciting” technology stock than a “boring” utility stock.

While the impact of volatility is easily understood, the estimation is not. Option prices tend to be driven by recent market activity. In fact, we can determine this by solving our Black-Scholes formula backward. If we make the assumption that the current option price is indeed “fair,” we can calculate what volatility would be needed in our pricing formula to make this true. This is known as calculating the “implied volatility.” Thus, by doing this, we can get a sense of the volatility that is being implied or predicted by the option price. Importantly, we can compare this with how the actual stock has behaved historically.

It turns out that the implied volatility of our IBM January $90 call is around 17 percent. Without digging too deep into statistics, let's see how this compares with actual IBM price volatility from 1968. What we find is that IBM has rarely had an actual volatility this low. For the bulk of the period, the volatility was much higher and the average during this period was nearly 24 percent. So, with a bit of context, this $3.50 premium now seems too low. (See “How Volatile It Really Was,” p. 30.)

What is interesting is that, while the popular financial media would have one believe that stocks have been very volatile, the truth is that during the last year stocks have been quite the opposite. (See “Stability Over the Past Year,” this page.) And if option prices currently represent this low volatility, then they are only fairly priced if this period of low volatility continues.

### OPPORTUNITY COST

What can we conclude?

The tricky part of any options strategy is to separate the odds from the investor's opinion. For example, an investor may have a strong view that a particular stock won't reach a particular price — and thus may be willing to sell a cheap option. In fact, this investor could well be correct and profit by doing so. But the only rational view is to take the longer-term statistics into consideration.

During the years from the late 1990s through mid-2002, the U.S. stock market saw unprecedented volatility. In fact, during those years, stock options became very expensive and selling them was often a profitable venture. Now, however, the market has become much quieter.

Can covered call writing add incremental income to an equity portfolio? Yes — but only if you are being paid enough for the opportunity cost of doing so.