Using positive expected returns

Before getting into this concept, understanding the big difference between “expected return” and “actual return” is important. Expected return is a statistical concept that applies to the return you would expect for a specific strategy over a large number of trials.

We would expect, for example, that a typical coin flip would come up heads half the time. That doesn’t mean heads will come up half the time. In fact, there may be long stretches during which either heads or tails could hit in succession. However, there are only two possible outcomes, so statistically, heads should ultimately hit half the time.

The same theory can be applied to stocks, although with a much wider range of possible outcomes. The volatility of the underlying stock and the profitability of the investment position are incorporated into an expected return calculation resulting in a mathematical expectation of profit. Taken one trade at a time, things could turn out very differently. However in the long run, the same strategy should generate a return that approximates its expected return.

Not that any of us will be around long enough to invest in the same position repeatedly over time. However, if your goal is to focus on a specific option strategy – covered call writing, bull call spreads, calendar spreads, etc. – then look for a strategy with a positive expected return. And be ready to grin and bear it if you run into stretches during which the actual return is significantly different than the expected return.

So, how does this theory work? To use a simple example, let’s calculate an expected return on a bull call spread. To begin, we assume the following prices exist: XYZ trading at $52, the XYZ 90-day call 50 call is at $4.75 (implied volatility: 35%) and the XYZ 90-day 60 call is at $1.25.

The bull call spread involves purchasing the XYZ 50 call and selling the XYZ 60 call for a net debit of $3.50 ($4.75 minus $1.25 = $3.50). The maximum potential profit for the bull call spread is $6.50 (assuming XYZ is above $60 a share at expiration) with a maximum loss of $3.50 (assuming XYZ is below $50 a share at expiration).

The trick is to calculate the probability of XYZ being above or below specific price points. You can download an Excel spreadsheet entitled “Probability of a Successful Option Trade” to assist with this calculation. The free spreadsheet can be downloaded at http://investexcel.net/category/option-pricing-2/.

In the spreadsheet, we begin by entering the current value for XYZ ($52 a share) and the implied volatility on the options. The net cost for the XYZ 50 vs 60 call spread is $3.50, which means that the spread will be profitable if XYZ is trading at any price between $53.50 and $60 a share at the expiration of the options.

So, what is the probability of XYZ being above, say, $54 a share at expiration? According to the model, there is a 41.40% chance that XYZ will be at or above $54 a share at expiration. At a stock price of $54 a share, the bull call spread generates 50¢ a share profit. Multiply 50¢ by the 41.40% probability, and we get an expected profit of 21¢ a share.

The next step is to add up the expected profit at the $2 intervals between $50 and $60 a share. The end-value is an expected profit of 76¢ per share. Finally, divide the expected profit (76¢) by the total outlay of $3.50, which equals 21.6%.

That 21.6% represents the annual potential return of the bull call spread strategy over long periods. Remember, this is a statistical concept that does not necessarily apply in the real world. However, this calculation can be a very useful tool when comparing various option strategies with different expiration dates.

Armed with the expected return calculation, let’s apply some real-world trading techniques to the XYZ example. We begin by looking at the aforementioned trade and, fast-forwarding 30 days, assume that XYZ is trading at $56 a share.

The XYZ 50 call theoretically would be worth $7.15 and the XYZ 60 call about $2. The spread would have widened to $5.15, generating a profit of $1.60 (not counting transaction costs). At this point, the $1.60 profit is greater than the 76¢ total expected return.

Given this scenario, you should think about exiting the position – or, at least, selling a portion of the spread. By taking the profit, you are recognizing that expected return is a statistical concept derived from many transactions. By seeking opportunities to take profits in specific positions, you are using real-world trading to augment statistical certainties.

This options strategy is much like the poker game Texas Hold ‘Em. Assuming you have enough capital to stay in the game long enough, you eventually will get a flop, which is when the statistical probability of winning is better than 50%. The trick is to throw away your losing hands before you run out of money.

Expected return is a useful concept for beginner option traders. It is also useful for financial advisors who want to add value for clients who have a preference for a certain type of strategy.

If nothing else, it may provide you some comfort, knowing that every time you lose money in an options trade, you are one step closer to benefiting from the mathematics of expected return. Or not!

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