Coming to Terms with Options Trading and its Higher Moments

Gamblers commonly think in terms of hot and cold streaks: Of having a lucky run, of probability pointing to a sudden and likely success at the tables or slot machines because they’ve been losing lately, or because they have been winning lately, or because today is Thursday, or because today is November 6 and 6 is the gambler’s lucky number.

Casino operators gain from gamblers’ irrationality. They know wheels and dice and decks of cards have no memory. Every wager has the same statistical probability of success as the previous attempt. The only predictable outcome is that 98% of gamblers will leave the casino with less money than when they walked in.

When a seemingly random set of values is plotted from just about any statistical source—income, obesity, winnings at blackjack tables, you name it— the random, jumbled set of values tend toward a predictable shape – a bell curve or normal distribution. Yet, options are unique in that prices are the collective effort of buyers and sellers struggling to express the grand notion of randomness that surrounds them. The current options bid/ask spread is an attempt to establish value in a world that’s not well-charted; where markets have wrinkles, jumps, and fat tails.

One option pricing phenomenon is what the industry calls “negative skew” and is most common in equity options. Skew is the contour, or the unevenness, in a distribution, the dent in the bell curve. A negative skew suggests the left half of the normal distribution (the left side of the mean) is twisted in such a way the prospect of achieving negative returns is superior to that of achieving large positive returns.

Recall in a theoretically precise, ideal normal distribution, positive returns and negative returns of equivalent magnitudes have more or less equivalent probabilities. Hence the distribution is symmetrical, or balanced. Of course, a distribution can possess positive skew as well (e.g. agricultural options), which signifies the prospect of a large positive return. When dealing with skew, traders strive to resolve how frequently in the trading time horizon they will obtain negative returns rather than positive returns. A skew demonstrates the relationship between the movement of an underlying asset and its volatility.

A current example of “negative skew” can be found in the SPDR S&P 500 ETF (SPY) reference: 202.34– where I’m once again reminded an options “fair value” is more art than science – it simply does not square with the arithmetic of a probability distribution.

Consider SPY options expiring on December 10. The SPY December 212 calls are currently .0477% out-of-the money and settled at .33 with a 10.23% implied volatility, while the SPY December 192 puts, currently .051% out-of-the-money, settled at 1.34 with 17.64% implied volatility. Simply put, there is a $1.01 price differential between basically equidistant calls and puts.

SPDR Gold Shares (GLD) reference: 109.79 is another case-in-point. Looking at February 2015 options prices, the 121 call (10.21% out-of-the-money) closed at .97 (implied volatility 18.43%) while the 99 put (9.90% out-of-the-money) closed at 1.34 (implied volatility 22.41%). In the GLD example there is a .37 premium in the out-of-the-money put versus its equally distanced out-of-the-money call.

Currently SPY skew is trading in the 70percentile while GLD skew is in the 85% percentile. For SPY this indicates that equidistant puts vs. calls have been higher 30% (relative to one another) of the time and lower 70% of the time as measured over the last year. For GLD this indicates equidistant puts vs. calls have been higher 15% of the time and lower 85% of the time over the last year. In short, the negative skews for both SPY & GLD are trading relatively high according to recent history. Puts are trading a little higher than calls both on a relative and realistic basis.

We must admit we live in a predominately long biased world. Pensions, mutual funds, and individual investors own equities and thus there is an overwhelming demand to sell out-of-the money calls (recall the covered call) and purchase downside protection via. out-of-the-money puts. This order flow creates a situation where participants are literally willing to buy puts above and sell calls below their actuarial value – thus negative skew is born.

Analyzing skew involves a variety of components that more often than not can only be described with the benefit of hindsight. Changes in skew can be produced by ordinary supply and demand, the opinions of options market makers, or from a hedge resulting from a large off-floor trade. There have been periods (e.g. early summer 2014) where skew was so cheap that a trader’s chief concern became how many puts the market makers could actually afford to finance. With that quantity of long (skew) supply being held by market makers, the skew became as flat as anyone had seen in modern memory. In that scenario, would a flat skew necessarily imply anything? Perhaps.

Keep in mind human frailty. Skew is all about possible loss that you can’t predict and can’t control. It’s the result of living in an imperfect world with imperfect people who become greedy and short-sighted, who panic, who make blunders and then try to hide them, who try to protect their jobs, who lack experience, or who have too much experience and grow complacent. Skew rises from an unpredictable world with too many human factors to count. And nothing is more unpredictable in markets and trading than the humans who are behind it all.