Classic Computer Magazine Archive CREATIVE COMPUTING VOL. 9, NO. 2 / FEBRUARY 1983 / PAGE 208

Naked call writing. (computer programs for stock option investing) Jonathan Richards.

It has been said that stock market investing and the computer go together like Brie and Chablis. In this article I hope to show you that this aphorism is true and that by using computer power you can tilt the investment odds significantly in your favor.

We will begin by discussing a deliciously complicated field of investing called stock options using call options. Next, I will outline a specific strategy, called naked call writing, that allows you to make a profit without directly investing any money. Finally, I will present a computer program that will help you find the best possible stock option on which to implement that strategy.

Before describing naked call writing, I want to issue two major caveats. First, it is very important to understand the concepts of stock option investing; they are complex. No one should invest without fully understanding the implications of his investment; yet the temptation is great to jump into option investing without being completely aware of all the risks.

Second, naked call writing has a statistically good chance of making a profit, and in fact is recommended by several respected writers, including the Value Line Advisory service but it can be very risky, and while there is no initial cash investment, your losses can be very large.

There are many types of investment strategies using options. There are spreads, straddles, naked puts, naked calls, covered writes, butterfly spreads, alligator spreads, and many others. The possibilities are limited only by the imagination of the investor. Naked call writing is one possibility that has a high mathematical chance of success. What Is a Naked Call Write

A call option is a contract to sell a stock at a stated price, called the strike price, within a certain specified time. If you own the stock, your position is said to be covered. If you do not own the underlying stock, your position is said to be naked. In both covered and naked call writing you are the one who sells the option for the call option, and in return you agree to deliver the stock to the buyer of your option for the strike price.

The most money you can make is the amount of the premium you receive. You hope the price of the stock will go down so that the buyer of your call option will not exercise it and you can keep the premium.

If Ashland Oil common stock is currently selling for $32.25 per share, you might be able to sell someone the right to buy 100 shares from you at a price of $35 per share. In return he would give you a premium of $275, and the option might be good until October. You would say you had sold an October-35 call for $2.75. (Options are sold in round lots of 100, but quoted in single option prices.)

You hope the price of Ashland Oil does not go above $35 per share before the October expiration date. If the price of Ashland goes to $40, you are obligated to buy it for that price and deliver it to the holder of the call option for $35 per share. Since Options are always sold in round lots of 100 shares, you must buy the stock for $4000 and sell it for $3500, for a $500 loss.

But you did receive a $275 premium, so your actual loss is only $225. Your losses could be even greater if you were unlucky enough to pick a stock that went to $50 a share or more.

Why would anyone invest in something that has a profit limited to the premium received and a loss that may be unlimited? First, you do not have to hold the call option until expiration; you can buy it back on the open market whenever you want to close out your position. Losing positions can be closed out at almost any time.

You have two ways of satisfying your obligation to deliver 100 shares of Ashland Oil at $35 per share to the call buyer. You can buy the stock on the open market; or you can buy the call option that you previously sold.

The call option price, like the stock market price, is quoted in the paper daily, it fluctuates up and down, and is very liquid. It is usually more profitable to buy back the call option and close out your position than to buy and deliver the stock, since the commission is smaller on option transactions than on stock transactions.

The second reason people sell naked call options is that as time goes by the $2.75 premium you receivd, and for which you have an obligation to buy back or deliver 100 shares of Ashland Oil, is decaying. That is, as the expiration date of October 21, 1983 draws closer, you can purchase the October-35 call for, perhaps, $1.75, then $1, then maybe $0.25.

The less you pay to purchae the call option the greater your profit; and you hope the call will expire, so you won't even have to purchase it to close the position. In other words, for you to lose money, the stock must make a dramatic move upward. If it goes down in price or remains at the same price you will make a profit. In And Out Of The Money Calls

Let's consider it another way. There are three types of calls.

There are in-the-money calls, at-the-money calls, and out-of-the-money calls. These concepts are sometimes difficult for the new investor; yet once they are understood all the strategies and positions become clear.

To explain these three types of call option we need to explain two more terms, time value and intrinsic value of the call premium. The intrinsic value of a call option premium is the value in the call premium if the call wre immediately exercised. Or to put it another way, the intrinsic value is the market price of the stock less the strike price of the option.

The time value part of the call option premium is the value that the buyers and sellers of options place on the time remaining until the option expires, and for the hope that the stock price will rise between now and the expiration date. Therefore, option premiums have been called a wasting asset. As time goes by, and the call option gets closer to expiration it will get cheaper and cheaper. Time is on the side of the call seller.

A call option seller is really only selling time value. An in-the-money call option has a premium that is made up partly of time value and partly of intrinsic value. For example, if the price of Ashland is $36 a share and you are selling an October-35 call, the premium would probably be $3.75 rather than $2.75 per Call, as in the above example, since there is $1 of intrinsic value in the call. That is, the stock can be called away for $35 with the stock at $36; so the call premium has $1 of instrinsic value, and the rest of the premium, in this case $2.75, reflects merely the time value of the option.

In the first example, with the strike price at $35 and Ashland Oil selling of only $32.25 per share, the October-35 call is said to be out-of-the-money. An out-of-the-money call option occurs when the strike price is higher than the stock price. The premium you received, in this case $2.75, consists entirely of time value. If the stock does not change in price between now and the expiration date, that time value will decay to zero, and you will keep the premium.

At-the-money calls are those that have strike prices that are close to or equal to the stock price. An example of an at-the-money call is one where the strike price is $35 and the stock is selling for $35.

In summary, if you write a call option for which the price of the underlying stock is higher than the strike price of the call, then the premium must include the intrinsic value and the time value, and the call is said to be in-the-money.

An out-of-the-money call has a strike price that is higher than the stock price, and the premium is made up only of time value. These concepts are essential in making good options investments, because writing out-of-the-money calls has different risks and profits than writing in-the-money calls. Later, I will, in fact, recommend writing at-the-money calls. Collateral

Besides an understanding of in-the-money and out-of-the-money call options and time value and intrinsic value, we must consider the collateral required to write naked calls. As mentioned, you receive a premium from the call buyer. This premium goes into your account as cash and earns interest. You have no cash outlay for your naked write investment, and you earn interest on money you did not previously have.

You broker, however, wants to be sure you will deliver should the stock, in this case Ashland Oil, be called away. That is, if the holder of your call option decides he wants to buy the stock from you at the strike price, you must deliver it to him. To insure your performance, the broker requires that you have cash or other securities in your account.

First, he may require equity in your portfolio which may vary from $2000 to $25,000 on deposit with him. This amount depends on your broker. In addition, each naked call position requires a certain amount of collateral or margin, which also varies with each broker. Generally, the requirement is 30% of the price of the stock plus the amount the stock is in-the-money or minus the amount it is out-of-the-money. There is a minimum of $250 per call. The premium received is used to offset this collateral requirement.

If you sell six October-35 calls on Ashland Oil with Ashland selling for $32.25 per share your collateral or margin requirement is $2505. This amount can be in other stocks or in a money market account with the broker.

The $2505 was arrived at in the followinmg way: The stock is at $32.25 and 30% of that is $9.675. It is $2.75 out-of-the-money--$35 strike less the $32.25 price. So $2.75 from $9.675 is $6.925; less the $2.75 premium per call you received is $4.175. Since calls are always written on 100 shares, you must multiply $4.175 times the 600 calls you sold which gives you $2505.

Figure 1 gives us this figure plus $36 in commissions or $2541. We can always subtract the premium we receive, but if the call were in-the-money we would have had to add the difference between the stock price and the strike price. For a more detailed description of collateral requirements you can write to the Chicago Board of Options Exchange for any of their several excellent booklets. Collateral is important to understand since in these strategies it is used to figure your return on investment and to compare difference naked writes one with another. CHoosing A Naked Write

There are five factors to consider in choosing an option to sell or write. First, we need to find a stock that we feel will not rise in price. The program presented here does not really deal with choosing a poor stock, it concentrates on finding a good call option. But in choosing a poor stock it is usually best to use an advisory service or your broker. It seems much easier to pick a stock that will not rise in price than to pick one that will rise. Of course, if you make a mistake and pick a stock that takes off, the consequences, as discussed above, can be disastrous.

Next we need to consider whether to write an option on a stock that is in-the-money, at-the-money, or out-of-the-money. As mentioned, call options that are at-the-money have the greatest time value, and it is time value that we want to sell. Writing far out-of-the-money calls with the stock at, say, $25 and the strike price at $40, and receiving a correspondingly small option premium, appears attractive since the chance of a stock rising that much is remote. That is one way of earning small profits, with a very large risk should the stock rise.

Or you can write deeply in-the-money calls, with the strike price at, say, $25 and the stock selling for $15. In this case, the premium you receive might be $10.125 ($10 of intrinsic value and $0.125 of time value). So the time premium you earn is only 0.125 of a point, or $12.50. The only way you could earn a large profit would be if the stock dropped in price. Selling deeply in-the-money calls is much like selling a stock short.

A third factor to consider in choosing a naked write is whether the call is over-valued. If it is, it may be a good candidate for selling. Although supply and demand set option premiums, they are influenced by the price of the stock, the volatility of the stock, the time to expiration of the option, risk-free interest rates, dividends on the stock, and other factors.

While these are difficult to objectify, several attempts have been made to do so by several theoreticians, most notably Fisher Black and Myron Scholes. The Black-Scholes mathematical model allows the input of the 90-day T-bill interest rate, time to expiration of the option, and the volatility of the underlying stock, and then predicts a theoretical value for the call premium. The formula is so widely used that you can even buy calculators with the functions built in. So if we calculate what a premium should be and determine what that figure is more than the actual premium, we might consider the call over-priced and sell it. If it is under-priced, we would not want to sell it.

A fourth factor in considering which option to sell has to do with the concept of the volatility of the underlayer stock mentioned above. Volatility is a statistical term and is determined by the annual standard deviation of stock price movements. You can get the volatility of a stock from your broker, and advisory service, a simple computer program, or even a pocket calculator.

A volatility of 33% means that the stock will fluctuate about 33% from its current price about two thirds of the time. While this is only a probability measure, it is a most useful tool in deciding what position to invest in.

Using this concept, we can predict the statistical chance that the stock will rise above the breakeven point. We look for those that have a good chance of not rising past that breakeven point. If Ashland Oil had a volatility figure of 33% and a breakeven point of 37.69, it is possible statistically to say that there is a 79% change that Ashland Oil will not rise above 37.69.

This figure is deduced by assuming that stock prices on a single stock have a log normal distribution, which seems to be empirically true.

Finally, we want to locate stock and option positions that offer a good annualized return on the collateral required. All returns must be annualized for easy comparison with other potential investments.

In summary, we want to locate naked writing positions that allow us to sell over-valved calls on stocks that will perform poorly, that have a good statistical chance of not rising past the point at which we will lose money, and the offer an excellent annual percentage return on our collateral. The Computer And Naked Calls

Figure 1 is the printout from the Naked Call Writing program. It shows the calculations on all of the items discussed above.

The first section is a summary of a position on Ashland Oil with the stock at $32.25 per share. We sold six October-35s and received a premium of $2.75 per call or $1614 in premiums deducting a commission of $36.

The second section has computed the theoretical value of the option at $1.91 per call. The call, thus, appears to be overvalued by $0.84 or 30.52%--perhaps a good candidate for selling.

The third section shows the maximum profit to be realized if Ashland Oil is at $32.25 at the expiration date on October 21, 1983. It also shows the annualized percentage return based on the collateral required on the day the naked option was writen. Item 3 in the third section gives the statistical probability of the stock moving past the breakeven point of $37.69.

With a 79% chance of the stock staying below the breakeven point, and an overprice call that gives us a potential profit of $1614 on $2541 worth of collateral this looks like a good investment. The Index is an arbitrary number composed of the amount by which the call is over-priced, the days to expiration, the percent of return, and the chance of making a profit. I have never lost money on a position that had an Index over 30. The higher the Index, the better the investment. But, you must always realize that losses can be great; overconfidence has hurt many an investor.

The fourth section of the output has additional facts to help you choose an investment. If the call was originally out-of-the-money, then the maximum possible return is the same as the return unchanged, i.e. the stock is at the same price at expiration as it is today. While this is unlikely, it offers the best way to compare between investments. If the call was in-the-money, then the two figures would be different. The best comparison between positions is available only if the stock price at the call expiration is the same as the stock price when you established the naked write position.

Item 3 in this section indicates the point to which the stock can rise before a loss occurs. The next three items are various collaterals that may be required should the stock price rise to the strike price or increase by 15%. It is a good idea to have extra collateral in you account, in cast the stock does not move against you and you still want to maintain the position.

The program is written so that you can enter up to 30 different possible naked write investments at one time and compare each. a printer is not necessary, but is helpful.

In summary, naked call writing is an effective strategy for adding extra income to your porfolio and should repay diligent study and close monitoring.

The program is written for an Apple computer, but should be easily translatable to other Basics. If you would like a copy of this program, and a Black-Scholes program to find the volatility or fair value of calls for other option strategies, and a follow-up program to Naked Call Writing called Rolling for Credits send $6.50 and I will mail you all three programs.