Options and the Volatility Surface
The price of equity and index options are largely determined by their implied or forecasted volatility. As most investors are aware, call options are a bet on the upside performance of a stock while put options are a bet on the downside. Each has a different strike price- or trigger price which is tied to the stock price that represents the point at which they begin to pay profits. There are multiple strike prices for both calls and puts. The strike prices closest to the current stock price are called “at the money” or “ATM” while the strike prices furthest away from the stock price are called “out of the money.” Options also have different expirations (reflecting the length of time that you can exercise the contract for a profit) ranging from one week to more than one year. If we compute the implied volatility for each option across the entire range of strike prices and expirations across both calls and puts we can plot the “volatility surface.” By looking at this volatility surface, it is possible to derive a lot of useful information.
Figure 1: The Volatility Surface
If we isolate one expiration date, we can plot the volatility surface on a 2-dimensional plot. Finance theory would predict that all implied volatilities would be the same regardless of strike price. In other words, we would expect to see a flat line. However, options reflect forward looking estimates and also the demand for hedging against tail risk. As a result, the shape of the volatility surface can have curvature depending on the shape of the estimated probability distribution. The demand for hedging or tail risk protection is reflected in the relative volatility of out of the money put options. Higher demand for tail protection would increase the relative implied volatility of out-of-the-money puts versus at-the-money puts. Conversely, the demand to speculate on a large upside move in the market would be reflected in the relative volatility of out-of-the-money calls versus at-the-money. We can see this effect on the 2-D volatility surface which shows a “volatility smile” on the chart below:
Before 1987, investors didn’t estimate a high probability of price black swan events. They also assigned a higher probability to upside moves. After the crash of 1987, the implied volatility of out-of-the-money puts or “the price of tail risk” was considerably higher while the probability of a large upside move or the “price of upside risk” was considerably lower.
Skew or asymmetry are fancy words that measure the relationship between upside and downside volatility. More upside (call option) relative to downside volatility (put option) would represent positive skew, while more downside relative to upside would represent negative skew. In the chart above we can see that the S&P500 exhibits negative skew since the volatility of out of the money calls is much lower than out of the money puts. This means that a black swan event is a lot more likely than a massive up spike in returns. Intuitively most investors understand this to be true- it would be a lot more likely that the market could fall 10% tomorrow than go up 10%. In contrast, individual stocks can have positive skew. If a company announced good earnings or gets taken over, the stock price could easily go up 20% or move in one day. As it turns out, using skew is an excellent tool for stock selection which is the subject for another post.
To measure index skew one of the interesting tools available to investors is the CBOE Skew Index. This is an indicator that typically ranges from 100-150, with higher values reflecting higher probabilities of a tail risk or black swan event. Values below 100 have not occurred since the S&P500 has exhibited negative skew on average. The chart below taken from the CBOE Skew Whitepaper shows the estimated probability of a tail risk event as a function of the value of the skew index:
The current value of the skew index sits at 152.93 (as of March 21, 2017) which is a new all time high. According to the table above this would reflect a greater than 3% chance of a large downside move. On the surface this makes sense given the renewed geopolitical uncertainty that has emerged since the election. The real question however is whether or not the fact that the CBOE Skew Index has hit new highs is predictive. Given that we only have data going back to 1990 for the index, it is difficult to make any conclusions about the ability for the CBOE Skew Index to predict tail events over 30-day periods (which are inherently rare). However, we can look at the distribution of returns after the index hits certain levels. As a basic test, we look at the S&P500 (SPY) returns n-days forward (1 through 50 days after) after the CBOE Skew Index hits new highs using various lookbacks versus the average return.
As we can see, it seems that when the CBOE Skew index hits new highs the market tends to underperform up to 35 days later for longer lookbacks and up to 50 days later for shorter lookbacks. This underperformance doesn’t happen immediately after hitting new highs, but rather develops starting roughly two weeks following a new high. It is important to point out however, that new highs in the CBOE Skew Index do not portent negative returns but rather a period of market consolidation or a brief pullback/ market correction. The situation is far more positive when the skew index hits new lows (more positive skew- or less negative):
In this case, we can see that outperformance is strong and positive up to 50 days after the CBOE Skew Index hits new lows. Investors are well-rewarded for waiting for such situations to crop up.
Skew is a measure of the upside versus downside potential for a given market. Mathematically, negative skew is associated with higher tail risk while positive (or less negative skew) is associated with lower tail risk. One robust way to estimate skew is to look at the index options market. This gives a forward versus backward looking estimate of where skew will be 30-days into the future. The CBOE Skew Index uses a sophisticated calculation to estimate this skew and tail risk with an indicator that tends to range from 100-150. Our analysis shows that the CBOE Skew Index is a useful indicator for assessing market potential for up to two and a half months following new highs or new lows. New highs tend to predict below-market returns while new lows tend to predict above-average returns for up to 50-days later. However, more data is needed to determine whether the CBOE Skew Index is an effective predictor of tail risk events.
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