# Calculating The Return On Options

Accountancy Resources

#### Calculating The Return On Options

The return on your options trades can be complicated. When you consider the various elements, including your basis and profit in stock, dividends you earn, and the time your stock and option positions remain open, this is no easy matter.

In Opening, Closing, Tracking: How It All Works, you found a useful summary for calculating return on various option positions. There are several potential methods for return calculations, and the most important points to remember are: the method you pick has to be realistic, and annualization is a means for comparing similar risks, not to establish likely returns from options trades.

## Finding a Realistic Method

Among the many methods available to you, some are exceptionally complex and involve theoretical valuation.

The small increments of difference in these incremental returns versus the easier, faster, and more logical methods make them impractical. The options market is fast-moving, and traders have to make decisions in the moment and based on return calculations and risk that are readily comprehended. Some of the methods used by academics do not have practical applications in the real world of options trading.

#### Smart Investor Tip

You can expand return and valuation calculations infinitely, but the more obscure the method, the less practical it becomes. It is useful to know about complex methods for valuation of options, but in the real world of trading, you will most likely prefer a simple method over a complex one.

Two of the best-known modeling calculations are worth a brief explanation. The Black-Scholes model is named for Fischer Black and Myron Scholes, who together published a scholarly paper in 1973 explaining their theory. The calculation is beyond the scope of this book; however, it is designed to take into account the elements of time value, stock price variation, an assumed market rate of interest, and time remaining until expiration. The formula sets a fair price for options, and several variations of the original formula have evolved since 1973.

#### Smart Investor Tip

Black-Scholes is a well-known model, but it is based on assumptions about interest rates and fixed expiration. Even with its variations, this model is too obscure for most applications.

One problem with the original Black-Scholes model is that it was based on European-style option expiration. Under the European rule, options can be exercised only immediately before expiration and not whenever the owner wants, as is the case with American-style options.

An alternative calculation is known as the binomial model. This calculation was developed in 1979 and allows for possible exercise at different moments in an option’s life. These times are selected between the current date and expiration to demonstrate how time valuation adjustment would be made. One major flaw in the binomial model, however, is that it assumes the stock’s price is always reasonable; in other words, this model succeeds only if you also accept the premise of the efficient market theory. Clearly, in the volatile and emotional market environment, highly volatile stocks will not behave in an efficient manner, so that the binomial model is just that — a model. It is instructive, however, because it also assumes a risk-neutral posture in valuation of the underlying stock. If such efficiency worked in the real world, option valuation, risk analysis, and return calculations would be quite simple.

#### Smart Investor Tip

The binomial model would be excellent if the efficient market theory were realistic. But as anyone who has tracked the market knows, it is far from efficient.

Neither the Black-Scholes nor the binomial model will be able to provide a practical, realistic method for determining option values. However, in reviewing options for any trade you have in mind, the apparent value of an option at any time is best made in comparisons between other options on the same stock. You will consider time until expiration, the level of intrinsic versus time value, proximity between a stock’s current value and the option’s striking price, and then dollar value of the option itself. This process applies whether you are considering long or short positions; using calls, puts, or combinations of both; and willing to take high risks or only very conservative risks. The process is the same in any case.

In evaluating risk, you will also want to make a judgment call about the level of exposure versus the premium value of an option. For example, you might not be willing to enter a covered call for only \$200 over the next two months. However, if the stock’s current market value is \$20, that is a 10 percent return (60 percent annualized). If the stock is worth \$60, the same option yields only 3.33 percent (20 percent annualized). All of the elements have to be brought into the decision, including the yield itself, dollar value of the option, time to expiration, and your risk profile.