Wednesday, July 30, 2008

Implied Volatility and Magnitude vs. Direction

Awhile back, a reader posed what sounded like a basic question:

Isn’t implied volatility a function of the size of the move, rather than direction? So why is VIX more commonly referred to as a fear index if high VIX can imply movements in both directions? I mean- HOW and exactly where does the direction get factored into VIX?

This question sounds as if it if might have an easy answer. The problem is that when you scratch the surface of implied volatility. a bunch of other questions have a tendency to pop up and all the tangents make it easy for the questioners eyes to glaze over. So, to make a long story a little shorter, I have decided that it is time to draft some detailed posts that look under the hood at both implied volatility and historical/statistical volatility. Not to worry, this wont happen today; more likely I will tackle these subjects over the course of the next two or three weeks in a series of posts.

Getting back to the questions posed above, to set the context, historical volatility (also known as statistical volatility) looks backward at actual historical price movements and calculates volatility in terms of standard deviations over a given period of time. The result is expressed as an annualized volatility number (the percentage of one standard deviation), just like the VIX. Historical volatility does not care about the direction of the volatility, only the magnitude.

In theory, implied volatility should also be directionally agnostic. Investor psychology and the mechanics of the options marketplace, however, mean that reality diverges from theory as options are transacted. Recall that implied volatility is derived from actual options prices. When the other options pricing variables (strike price; price of the underlying; time to expiration; dividends; and risk free interests rate) of an option are frozen, this leaves implied volatility as the only remaining variable in the options pricing equation. This is how implied volatility is derived.

In the very short term, options prices are largely a function of the price of the underlying and implied volatility, as the other variables tend to change at a slow and/or predictable rate. When the price of the underlying is relatively stable, implied volatility has a tendency to drift down and bring options prices with them. When the price of the underlying (whether it be a stock, ETF, index or whatever) moves sharply, this is when things get interesting. If the underlying moves up quickly, it has a tendency to attract new buyers and sellers. Implied volatility usually rises with the move and so do most options prices. Ultimately, implied volatility becomes a function of supply and demand for options at specific strikes and expirations. If new transactions keep hitting the ask price, then options prices will move quickly and implied volatility will adjust upward to accommodate the new prices. Sellers will also be inclined to keep raising their asking price to account for this demand again stretching prices and pulling implied volatility along for the ride. Generally, this will not result in a panic buying situation, particularly if the underlying is an index or an ETF. Greed is not instantaneous; it tends to build over time. There might be a concern with an individual stock that an acquisition is in the works, a legal matter has been settled, word of an FDA decision has leaked out, etc. but other than these scenarios (which do not apply to an index or an ETF), sharp upward moves tend to be orderly and have a relatively limited short-term psychological impact on the investor.

If you turn this scenario around and think of the move as a sharp selloff, some different dynamics come into play. First consider the maxim that stocks tend to fall faster than they rise. Second, when it comes to portfolio protection, the rush to buy puts to protect an existing position is much more dramatic than any sort of call purchases during a bull spike. Third, the worst case scenario for a bear move includes not only the scenarios noted in the paragraph above, but incorporates any number of potential disasters from a CEO/CFO resignation to accounting irregularities, lowered earnings guidance, new legal challenges, etc. Fourth, as the downward move gathers momentum, investors have a tendency to buy whatever puts they can, at the market, for whatever prices are available. It is this insensitivity to prices during a panic selling situation that tends to overwhelm the ask price and cause market makers to raise the prices of puts dramatically; this, in turn, triggers a sharp jump in implied volatility.

Ultimately, the same aspects of investor psychology and behavioral finance (i.e. loss aversion ) that translate into more panic selling than panic buying also mean that the supply and demand imbalance for options is typically greater in sharp bear moves than in sharp bull moves. The result is that implied volatility tends to spike more with an X% drop than as a result of an X% rise. Statistically, these moves are identical, but psychologically and from a transaction perspective, spikes down will generally move implied volatility more than comparably sized spikes up. Since the VIX is essentially the implied volatility of the SPX, this is one of the reasons why the magnitude and direction of a market move determine the impact the move will have on the VIX.