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Cheap Options

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This article is intended for educational purposes only, and is in no way meant as advice.

Now that the "Big Volatility Crush" is on, I thought it a good time to talk a little about its causes in general terms, but also to talk about the opportunity it presents to me.

There are two primary attributes of option pricing that are relevant to market conditions: nominal prices and skew.

Nominal prices of most options are cheap, both relative to historical measures and to "intrinsic volatility." The first cause of this is the unprecedented liquidity provided by our friends at the Fed. This leads to higher demand for asset prices in nominal terms (in real terms those assets are worth the same because of the decline in the dollar), the process by which we have described in the past and results in increased debt.

As asset prices rise, option prices normally decline as I have also described. Nominal option prices are currently extremely low and indicate complacency, a nap that continues until something does the wakening.

I think the level of prices is indicating very high complacency.

The skew, the relative price between out of the money puts and out of the money calls, is also low and indicates complacency. The skew, however, is not near 1987 levels (nor will it likely ever be again). 1987 as I have described was the result of a confluence of ridiculously stupid events that are unlikely to be repeated (but I can't count it out given human nature).

I think the skew is also signaling high complacency relative to the last few years, but not like just before October 1987. Does anyone remember that Mr. Greenspan took over in August of 1987?

What I want to do now is to give you an idea of the value of a cheap option and how I make money off of it.

UPS(UPS:NYSE) stock price is $74.90 and the January 80 calls are very cheap at $.75, most likely the result of overwriters selling as the stock has rallied. Overwriters are often insensitive to pricing options using calculus; they are income junkies and prefer to price options using a rate of return calculation.

That calculation takes the price of the option plus the dividend as income and the price of the stock less the price of the call as the cost of the investment. The "static" (unchanged stock price) return of this is: ((.75 + .56) / (74.9 - .75)) x 365/205 = 3.5%. So with the stock unchanged, the manager collects the premium and dividends to expiration and risks holding the stock to earn 3%.

Quite frankly, I do not know how a manager can even keep his job if he thinks this is a good risk for reward. To me this calculation shows how desperate managers are for return and re-enforces my opinion on the cheapness of this option.

Pricing the option using a modified Black-Scholes model shows that the option is trading at an implied volatility of 10.5%. This means that over one year's time the option is predicting that the stock will trade in a range of around 10% from its current stock price.

On a day to day basis that means that the stock should trade up or down 10.5/ sq. root(256) = .625% based on 256 trading days in a year. So the stock should trade within a range of .625 x 74.9 = $.47 per day. The stock moving this amount (at least) is what I referred to before as "intrinsic volatility". It is a function mainly of the liquidity of the stock relative to the volatility of the market. It is an amount that we would expect the stock to move daily given no news.

This is a very narrow range, although it has exhibited such for several weeks. But this does not account for possible days where the stock may trade up or down several times this amount or might "trend" to a greater degree. The probability of this is good and has in fact been the case. Just in the last 30 trading days the stock has risen 9%; this implies a 26% volatility for the stock (remember the option prices are telling us that it won't move more than 10.5% over two thirds of a year).

This does not also account for the small probability of a very large move, which could be caused by something specific to the company or dependent on the market itself (systematic risk).

So there are three types of volatility that we incorporate into our decisions: day to day, trending, and tail volatility. Institutional sellers of options know very little of this.

Let me illustrate.

Buying these call options I set up an arbitrage short the stock. The delta today at this price is .23, so for every 1000 calls I buy I will short 23,000 shares. The delta would be higher at a higher implied volatility; at a 15% implied volatility the delta would be .3. So I might be inclined to sell a little more stock than theoretical would dictate at these prices.

By the way, at a 15% implied volatility these options are worth around $1.56; this illustrates the large effect a small change in volatility can have in an option's price (this change would not be as great for a more expensive option).

The gamma or change in delta is currently .05, which means that if the stock drops 1 point today the delta will go from .23 to .18. This is a large relative change in the delta, again because the option price is so cheap.

If the stock traded down $1 tomorrow, the price of the option would go from .75 to .57 and the delta would go from .23 to .18. For every 1000 options I have on I would buy back 5,000 shares of my short stock to adjust the position delta neutral. I would lose .75 - .57 x 1000 x 100 = $18,000 on the option position and make $1 x 23,000 = $23,000 on the stock. The daily profit occurred because the stock moved more than the option price was implying.

If the stock had gone up $1 the delta would increase to .28 and I would sell 5,000 shares of stock to adjust the position neutral. The option price would go to $1.01: I would make $26,000 on the option and lose $23,000 on the stock.

This illustration shows how I set up a delta neutral position with cheap options. I am indifferent on which way the stock moves; I am not indifferent as to how much or how often it moves. I depend on the stock moving more often and to a greater degree than that implied by the option prices. I can also target and price trending and tail volatility as well by the manner of re-hedging.

Lastly, cheap options introduce more gamma into the system. The math shows that cheap options have more gamma than an expensive one, but an illustration can show how it works.

The seller of the UPS option, an over writer, considers the premium not only income but somewhat of a hedge. If he sells the option at $.75, he has that much downside in the stock before he is essentially naked long it again. If instead he had sold the option at an expensive price of $2.00 (I consider fair around $1.50), he would have much more protection on the downside.

If the stock drops, given the little protection he will be more inclined to sell the stock than if he had more downside protection. In the first case he may sell the stock while in the second he may hold off. This inclination may not be much, but it does not take much to cause mistakes.

It is this selling when markets are down that creates much higher volatility that feeds on itself. It is like opening Pandora's Box: once it opens all hell breaks loose.


No positions in stocks mentioned.

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