Where's the Logic?

"A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations." Henri Poincare

While there are many books on options, few of the authors advocate selling naked options. Most authors are quick to point out that selling naked options involves "unlimited risk". Traders are urged to consider combining short and long option positions ("spreads") to take advantage of the trader's market outlook, while at the same time limiting risk. Other authors stress the risk-reward advantages of selling calls on long stock positions (covered calls). Many of the same authors who warn against selling naked options correctly point out that covered call writing is a more conservative strategy than owning stock outright. What you are seldom told is that a covered call position is the equivalent of a naked put (assuming adequate capitalization in your brokerage account). How then could a covered call be a conservative investment strategy when its equivalent position, a short put, is risky? The authors usually don't explain. Each of the two strategies theoretically involves substantial risk. If the stock price goes to zero, a person would lose the amount paid to purchase the stock less the call premium collected. The holder of a short-put position would incur the exact same loss. While it is true that a covered call and its synthetic equivalent, a naked put, can result in a substantial loss if the stock rapidly declines in value, either strategy is less risky than simply owning the stock outright due to the premium collected.

If covered call writing is a conservative strategy and naked put writing is an equivalent strategy, why should we be encouraged to do the former and discouraged from the latter? Well we are told that the reason lies in leverage. In other words, you can generally sell more naked puts than purchase covered calls due to the different margin requirements imposed by your brokerage firm. While that may be true, having the ability to leverage more investment with your dollars is a good thing not a bad one at least so long as you do not overextend. It can also be less costly since you are paying only one commission when selling a put versus two separate commissions when establishing a covered call position. In addition, you are typically paid interest on the cash proceeds realized from the sale of the puts. Once you realize the illogic of the paradoxical claims that covered call writing is conservative whereas naked put writing is risky, you can begin to open your mind to the exciting new possibilities of the POWER strategy, a strategy that features selling equal numbers of puts and calls. If selling a naked put is the equivalent of a covered call position, is it possible that selling the same number of short calls and short puts with the same strike (a straddle) or with different strikes (a strangle) can not only be made less risky but potentially more profitable at the same time? You bet! Utilizing these strategies has enabled me to earn consistently high rates of returns over many years and achieve an alpha, which would be the envy of most money managers (more on alpha later).

One of my favorite subjects in college was a course in logic which has guided me throughout my career both as a lawyer, judge and financial advisor. Aristotle is credited with developing the concept of the syllogism from the Greek word syllogismos meaning "conclusion" or "inference". Syllogistic reasoning applies logic to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. A categorical syllogism is an argument consisting of two premises and a conclusion, in which there appear a total of exactly three categorical terms, each of which is used exactly twice. The most common example involves the following argument:

"All men are mortal (major premise). Socrates is a man (minor premise). Socrates is mortal (conclusion)." Socrates further proved the validity of the syllogism by dying in Athens in 399 B. C. at the age of 71. Applying logic to the main thesis of this book, I would make the following argument: admonitions warning you against the practice. Furthermore, you will discover that when you simultaneously sell puts and calls with the same strikes (straddle) or different strikes (strangle) with the same expiration, you extend the range of profitable expiration outcomes.

When you sell options, you are selling time premium. The price of an option is made up of two components, the intrinsic value plus time premium (option price = intrinsic value + time premium). The intrinsic value for an in-the-money call option is the difference between the stock price and the strike price, where stock price > strike price. For out-of-the money call options (i.e. where strike price > stock price), the option has no intrinsic value. In such instances, the entire premium represents time premium. Conversely, a put option has no intrinsic value if the stock price exceeds the strike price (stock price > strike price). No rationale investor would exercise the right to put (sell) a stock for less than it is worth nor to call (buy) a stock for more than it is worth. The price of an out-of-the money option, whether a call or put, is entirely made up of the time premium.

Time premium is greatest for at-the-money options. Since we are sellers of options, it only makes sense to capture as much time premium as possible. As we shall see, we best accomplish our objective by selling at-the-money (or near-the-money) puts and calls.

It has been my observation that most advocates of option writing, suggest selling far out-of-the money options since those options have the best chance of expiring worthless. While that may be true, by selling far out-of-the money options, the seller is leaving a lot of time premium on the table. I prefer to put that time premium in my pocket. The POWER strategy allows me to do just that.

Do You Have An Edge?

"May the odds be ever in your favor."

The Hunger Games

Most investment books on options offer strategies for profiting if you know which way the market is headed. If you are bullish on the market or a stock, you are presented with various ways of placing winning trades with options (the simplest involving the purchase of call options). Conversely, if you are bearish, you can profit from a short position (the simplest involving the purchase of put options). More complex option strategies, such as calendar spreads, butterflies, and condors, are offered to further take advantage of the decay in time premium and to limit losses. That's all fine and well but unfortunately, for most investors, market outlook is little more than guesswork. We may think that the market is over or undervalued or that a stock is poised to rally or fade. We may even have good reasons for those beliefs based on fundamentals or technical indicators. While there may well be some professional traders with the skill and foresight to predict what the market will do, most predictions are little more than educated guesses or hunches. I don't recall reading many predictions of the market implosions of 2000-01, 2003 or 2008-09. Unfortunately, for the average investor, predictions of market direction are amateurish and as likely to be wrong as right. At any given moment, the market and each stock in it are fairly priced with an equal number of investors believing it will move in either direction. Price itself is the actual indicator of where the equilibrium is on the supply-demand curve. So, if XYZ stock is selling for $100 share, an equal number of market participants expect the stock to rise in value as to decline. If there are rumors of a favorable event affecting the company's bottom line, such as FDA approval of a cancer treating drug, that news and the probability of it being accurate have been factored into the current price of the stock. Thus, you will hear traders talk about a stock being discounted for potential bad news and vice versa.

Moreover, by the time the average investor obtains relevant information, more sophisticated investors and professional money managers have already processed and acted upon it. Thus, at any given time, there is essentially an equal probability that a stock will increase or decrease in price, and that is generally true of options as well. I say "generally" because there are instances where supply-demand is not fully reflected in the price of an option resulting in an option being under or over-priced. Why is that? It is for the same reason that consumers willingly purchase insurance policies, or extended warranties on products, knowing that the insurer and not the consumer will likely profit from the transaction. We know the probability of our house burning to the ground or being struck by lightning is remote. However, what homeowner would sleep at night knowing their home was uninsured? We purchase insurance for the protection it affords us. We do the same with life and medical insurance. We aren't hoping to make a profit from the insurance. Rather, we hope that we don't. So, what if the insurance company is getting the better end of the bargain? It's worth it to us for the peace of mind. The same is true of extended warranties on expensive electronic products. We know when we purchase a new widescreen television or laptop computer at Best Buy that the three-year extended warranty is unlikely to be needed and that the $179 or so required to purchase the warranty is most likely not a good investment. Yet, we don't want to be the one consumer out of 100 whose product is defective. So, for our peace of mind we willingly shell out the money for the warranty.

The same is true for portfolio managers who purchase puts to hedge their bets and protect against a potential market implosion. It's much easier to justify the added expense of purchasing overpriced puts than to explain to investors significant losses due to the failure to utilize risk management procedures. Just like purchasing traditional insurance, portfolio insurance is a legitimate cost of doing business. And just as the insurance carriers and warranty companies are happy to profit from customers willing to pay for protection, so too are option writers like me.

We talked about the inflated price of puts. What about the calls? The purchaser of a call option is anticipating that the underlying stock will rise in value more rapidly than the call will lose time value. In other words, the investor is speculating. History is full of examples where speculators have paid exorbitant prices, thereby driving up the prices of a commodity or call option. Perhaps you've heard of tulip mania, a period in the seventeenth century during which prices for tulip bulbs in the Netherlands reached ridiculously high levels and then collapsed. The story of tulip mania is often used by educators to dramatize malfunctioning markets, imbalances in supply and demand, and irrational consumer behavior. So too there are market distortions resulting from speculation on call options. Perhaps there are rumors of a merger or acquisition, a good earnings report, or of an impending FDA approval for that cancer curing drug. Just as the price of puts is inflated by fear, the price of calls is inflated by the greed of speculators.

Moreover, as we will learn there is a relationship between puts and calls on any given stock. If the price of the puts is inflated due to an increase in the fear index (VIX) or the price of calls is inflated as a result of speculation, the corresponding increase in the premium will be reflected in both the calls and puts. This is due to the put-call parity relationship explained in Chapter Six.

As previously noted, the price of an option is comprised of two components, intrinsic value and time premium. Expressed mathematically, option price = intrinsic value + time premium. Intrinsic value is the in-the-money (ITM) portion of the option's price. Time premium is the amount of the option price that exceeds intrinsic value. For example, with XYZ Stock trading for $101.00 on June 1, the July 100 XYZ call may have a value of $3.00. The $3.00 call consists of $1.00 of intrinsic value plus $2.00 of time premium. Because out-of-the money (OTM) options have no intrinsic value, the entire price of the option consists of time premium. As an option goes deeper in-the-money, the time premium shrinks and may even eventually disappear, especially near expiration. At such times, the option price = intrinsic value. As option sellers, we are not interested in buying and selling stocks. That would require us to be either bullish or bearish on the stock. But we don't wish to forecast the direction of the price of the stock. Rather, we are sellers of time premium. We know with certainty that time marches on and that the expiration date for the options will eventually and inevitably arrive. At expiration, the time premium goes to zero. Yet, we sold the option at a time when the time premium was maximized. We will profit from selling options so long as the change in stock price does not exceed the amount of the premium collected at the time we sold the option. Time premium is greatest for strike prices that are at-the-money (ATM). Since we want to capture as much time premium as possible, we want to sell only those options that are trading at or near the current strike price. In-the-money options (ITM) have intrinsic value. However, we want to sell time premium, not intrinsic value. Call options that are in-the-money have intrinsic value and therefore a short call position is a directional trade similar to selling short the underlying stock. Conversely, selling in-the-money put options is a directional trade similar to buying stocks. As an option writer, we want to sell options whose price consists primarily of time premium. At the same time, we want to maximize the time premium. The best way to do that is to sell call options with a strike at or just above the current price of the underlying and put options with a strike that is at or just below the current price.

The time premium component of an option is also comprised of two components, the amount of time remaining to expiration and its implied volatility or market expectation of volatility. Because time premium is influenced by expectations of volatility, it is greatest for volatile stocks. While it may therefore seem logical that we would want to sell options only on the most volatile stocks, that may not lead to profits since there may be, and usually are good reasons for the outlook for volatile stock prices. That outlook is based upon historical fluctuations in stock prices as well as current expectations based on fear or greed factors. Being prudent investors, we want to be able to profit from unjustified fear or greed factors but not lose sight of the actual risks of price movements up or down based on historical price movements for the underlying stock. In short, we want to sell options where the implied volatility (IV) exceeds the historical volatility (HV). The difference between those two values can be plotted graphically. Utilizing OptionVue software, we can plot the statistical advantage enjoyed by sellers of at-the-money puts and calls. Historical volatility measures the past actual changes in the price of the underlying stock. Implied volatility measures the expected price changes in the future. With respect to the popular stock market indices, SPX, RUT and NDX, the implied volatility is consistently higher than the historical volatility. Why? Because investors and portfolio managers often need to purchase puts to hedge their long stock positions, while speculators are overpaying for calls in the hopes of hitting a homerun if the market explodes to the upside. These popular indices are used as proxies by hedgers and speculators. Thus, the buying activities of hedgers and speculators create an imbalance in the supply and demand of put and call prices, thereby driving up the costs beyond fair value.

The Chicago Board Options Exchange (CBOE) introduced a volatility index, known as VIX, in 1993. Initially VIX measured the implied volatility of the S&P 100 index (OEX) of at-the-money put and call options. Later, it was changed to the more popular S&P 500 (SPX), to gauge investor expectations of future volatility in the broader market. As an example, when the VIX is at 25, there is a consensus among option traders, based on their buying/selling activity, that the SPX has a 68.3% probability (i.e. one standard deviation) of trading within a range of 25% of its current level (higher or lower), over the next year. VIX values above 30 are generally associated with investor fear or uncertainty, while values below 20 suggest market complacency. For that reason, commentators frequently refer to the VIX as the "fear index".

The VIX rises when put option buying increases and declines when call buying activity picks up. Low VIX readings are believed by most technicians to be bearish, while high readings are bullish indicators. As you know by now, I don't place a lot of stock (no pun intended) in technical analysis or fundamental analysis for that matter. However, there is a high correlation between stock market activity and the VIX. It is an inverse relationship. When stock prices shoot up, most frequently the VIX goes down. When stock prices implode, the VIX can be expected to spike. The following table demonstrates the relationship of the VIX to price movements in the S&P 500 from 2000 to 2012.