The implied volatility of a stock index is one of the key descriptive variables of the market’s behavior. Its importance often is underestimated despite its huge impact on the price of the option and, thereby, the profit or loss on a trade.
Studies have analyzed how the volatility implied by option prices relates to the subsequent realized volatility (see "Implied to realized," below). Despite all the statistical problems such as overlapping time intervals, bid/ask spreads of the options, etc., experts usually agree that a volatility premium exists: The implied often is higher than the corresponding realized volatility.
So-called "vola short" strategies enjoyed a great deal of popularity before the financial crisis of 2008-09. Because of significant losses of those strategies during the financial crisis, however, many funds using those strategies were wiped out completely. Constantly shorting volatility can earn a premium but has huge risks in a downturn when realized volatility increases sharply. Similar losses of pure vola short strategies have been seen recently as the European debt crisis has led to higher stock market volatilities.
Some proponents argue that it should be profitable to short implied volatility when it is high because the premium earned for selling options is higher in these situations. However, this approach, as we have seen, has certain risks that must be controlled. So, when should stock investors buy and when should they write options? A closer look at equity market behavior in the last years sheds some light on this question.
Our analysis will classify the stock market as being in an up- or downtrend depending on whether the index spot trades above or below its 100-day simple moving average (SMA). The use of the 100-day SMA leads to an analysis of medium-term trends. If positions are traded whenever the spot crosses the moving average, taking a shorter-term SMA (such as 30 days) leads to more trading and higher turnover of the positions. A 200-day average, on the other hand, will lead to less trading.
Daily data of short-term implied volatilities of one-month at-the-money options and subsequently realized volatility between July 1998 and the end of August 2011 for different indexes generates an implied-to-realized spread for each day. The whole sample forms a distribution of the implied-to-realized spread with the spread on the x-axis and the frequency on the y-axis. "Implied-to-realized" (last page) shows results for the S&P 500 stock index in the United States as well the Eurostoxx 50 in Europe.
The charts illustrate the implied-to-realized spread when markets are trading above (blue line) or below (red line) the 100-day SMA. For the S&P 500 as well as the Eurostoxx 50, the distributions are more skewed to the left for the days when the market is in a downtrend, indicating that there are more days when the realized volatility exceeds the implied volatility.
From a pure volatility standpoint it would have been better to buy options instead of writing them in downtrending markets. Furthermore, there are many more days when the implied-to-realized spread was positive when the market was above its moving average. The numbers in "Crossing the average" (below) illustrate in more detail the spread for various stock market indexes for the two different scenarios when the index is above or below its 100-day SMA.
As expected, the implied and realized volatility both are lower for all indexes when the market trades above its 100-day SMA. In this case, the implied-to-realized spread is, on average, positive for all the indexes.
The difference in the spread between the above and below SMA scenarios is with 0.6% the smallest reading (for the Nikkei225). The Nikkei is the only index that trades more often below the moving average in this time period because of the long-term downturn of Japanese equities (49.4% vs. 50.6%). The values in the table are derived from overlapping daily data for the whole period. However, similar results are obtained when fewer data points with non-overlapping monthly intervals are used.
While this analysis is interesting, what’s truly valuable is how it affects your approach to investing and trading. There are important consequences for derivatives investors when it comes to volatility and how it tends to play out in the markets. Volatility is a key measure in the valuation of many derivatives, and its influence is difficult to overstate.
Here are some key findings from this analysis that can be applied in your investment program:
- Implied volatility, even when low, often is higher when compared to realized volatility. As mentioned, it might seem that options are cheap in a bull market. Investors often do not sell volatility in these low-volatility environments. In the absence of external shocks, however, the bull markets lead to even lower realized volatility. People would profit from writing options in this case.
What’s key, though, is that not only does high realized volatility show up more often in absolute terms, but also relative to previous implied volatility, especially on a short-term basis. The extreme events where one-month realized volatility exceeds the previous implied volatility by more than 10% have a much higher frequency.
- Chances of a bad surprise where, say, realized volatility is far higher than previously assumed, are much higher if the index trades below the moving average. Volatility clustering describes the observation that large moves in a stock price tend to cluster together. In these cases, it seems that those periods of high volatilities stick together when markets are below the moving average.
- Be careful with selling volatility when markets are in panic mode, even when volatilities appear high. It is tempting to sell volatility when market participants are nervous. During these times, options often are trading at relatively high prices, bringing impressive premiums. This often happens as implied volatilities skyrocket after a longer period of low volatilities. It is exceptionally difficult to predict a top correctly during these volatile times, however. As some investors take this opportunity to sell options, the risk of even higher realized volatilities should not be underestimated.
There are many pro-cyclical equity investors using technical analysis and moving averages as a simple tool to follow stock market trends. Given the data we’ve seen here, the equivalent volatility strategy would be to sell short-dated volatility — for example, in the form of short straddles on options with one month maturity with continuous delta hedging or via volatility futures.
Investors betting on continuing upward price trends in the stock market also may consider selling put options. This strategy would allow them to profit from rising stock prices as well as relatively high implied volatilities.
In falling markets, on the other hand, the realized volatility on average does not significantly exceed or fall below the implied volatility. In this case, the data would suggest the investor employ a volatility-neutral strategy, especially considering the skewed distribution and the likelihood of high losses.
Implied vs. realized
Market participants frequently encounter the concepts of implied and realized volatility but often don’t appreciate the difference between the two. Understanding what each describes is critical to fully appreciating a strategy that relies on their comparison.
Implied volatility is a number derived from the Black-Scholes options pricing model. Here’s how it works. The model assumes that a number of factors play a role in determining an option’s price. These include inputs such as the risk-free interest rate, time until expiration, the strike price, the price of the underlying, etc. One of the inputs is volatility. To generate an implied volatility number, we simply solve for volatility instead of the option price, using the current market price of the option as a model input.
Realized volatility, on the other hand, is a measure of volatility actually observed in the marketplace. Realized volatility most often is represented by the standard deviation of price changes over a set period of time. It is a direct statistical calculation using recent changes in the price of a stock index.
Although these two measures of volatility are quite related, they do diverge and their relative value to each other is not constant. These deviations often signal trading or investing opportunities in the underlying market.
Marco Erling works as portfolio manager and quantitative analyst for structured products with HSBC Global Asset Management. He studied mathematics at the University of Dortmund in Germany and earned an MBA from ESADE Business School in Barcelona. He is a CFA Charter holder and a Certified FRM holder. Email him at email@example.com.