Equity Volatility as an Asset Class

May, 2006

Investing in volatility is clearly not an easy subject. Could you please explain the difference between futures contracts on implied and realized volatility?

We agree that this is a complicated subject, and we stress that we too look forward to the introduction of a retail futures-based fund (like commodity index funds) that will make it easier for individual investors to access this asset class. To address your question, there are two futures contracts traded on the Chicago Board Options Exchange. On is on the "implied volatility" of the S&P 500 (as measured by traded options contracts), which is known as the VIX index. The other futures contract is on the actual "realized variance" of the S&P 500, which is known as the VT. Note that volatility is another name for standard deviation, which is the square root of the variance. So, despite the different names, we're still talking about the same statistic. Though both started in 2004, the market for VIX (as measured by outstanding futures contracts) is about one hundred times as big as the market for VT. In the construction of our model portfolios, we used the VIX as our proxy for equity market volatility as an asset class, since it is the deeper market.

As we have noted in our writing, over different time periods, the standard deviation of returns on the S&P 500 (or any analogous equity index in another currency zone) is not stable over time. In addition, historical data shows an inverse relationship between realized volatility and returns. When volatility is high, returns are typically low, and vice versa. However, VIX futures contracts are a biased predictor of future spot values of the VIX index. Futures prices are typically lower than the eventual spot price. The reason for this is economically logical: since the returns on holding equity (as measured by the S&P 500 Index) are negatively correlated with investors want to invest in VIX futures to offset some of the risk of owning equity. However, the party on the other side of that trade -- the one selling the VIX futures -- is taking on a lot of risk, since probability suggests that he or she will be losing money on the futures contract at the same time that he or she will be losing money on they equities they own. Hence, the seller of a VIX futures contract requires a substantial risk premium. The form this risk premium takes is a VIX futures contract price that is lower than it otherwise would be if it was an unbiased predictor of the future spot VIX index value.

So, to sum up, one set of our model portfolios allows allocations to equity market volatility as an asset class. As we have noted, until retail volatility products are introduced, these portfolios are very much experimental. An investor implementing this allocation today would have to continuously buy and rollover VIX futures contracts. Because of the risk premium required by the sellers of those contracts, they tend to underestimate the final spot price of the VIX at their expiration date.

On its own, this would cause the investors returns on the VIX contracts to be less than the returns on the spot VIX index that we used in the calculation of our model portfolios. However, as is the case with commodity index futures, VIX futures contracts can be purchased "on margin" at less than their full face value. This enables an investor to invest the difference in some other asset class. In the case of retail commodity index funds, this is typically government bonds. In practice, the earnings on these bond investments usually come close to offsetting the risk premium on the futures contract, so that the realized return by the investor in the commodity index fund is close to the realized return on the spot index. We believe that, in the case of VIX futures, this also would usually be the case.

June, 2005

We have long believed that equity volatility (i.e., the standard deviation of returns on a broad equity index) was a potentially attractive asset class. . First, volatility is not stable over time. Second, equity returns tend to be negatively correlated with volatility. When volatility (which is not constant over time) goes up, returns tend to go down. Third, since changes in equity volatility tend to track changes in credit spreads in the debt markets (i.e., the yield on risky debt instruments less the yield on default-risk free government bonds), the potential diversification benefits of adding this asset class to a portfolio appeared to be significant. However, until last year, it was hard to invest in equity volatility. That changed when a future contract based on the "VIX" index was introduced in the United States. The VIX tracks the volatility implied by the price of options contracts on the Standard and Poor's 500 Index. A similar contract had also been introduced in Germany (the "VOLAX" on the "DAX" equity index), but had not generated the same investor interest and liquidity as the VIX and its associated futures contract.

The underlying payoff on the VIX is easy to understand. Rising uncertainty and risk typically lead to increases in implied volatility and the value of the VIX. These increases in perceived risk are often associated with declining returns on the equity asset class. In theory, these can be offset by increased returns on a futures contract tied to the VIX. A second benefit of investing in VIX futures is more subtle. Returns on many hedge fund strategies are not normally distributed -- they have significant skewness (i.e., they are more tilted than normal) and kurtosis (i.e., they have fatter tails -- more extreme returns -- than normal). Statistically, these are related to the fact that volatility is not constant over time, and instead varies between high and low regimes. To some extent, investing in VIX futures can offset the negative impact of changes in equity market volatility, and in so doing make "more normal" the distribution of returns in a portfolio that includes hedge funds (for more on this, see "How the VIX Ate My Kurtosis" by Keith Black).

The interesting question is whether non-U.S. dollar based investors could benefit from adding U.S. equity volatility as an asset class to their portfolios. The following table shows the impact this would have, as well as the average real returns from holding the VIX between 1990 and 2004.

As you can see, there appears to be a strong case for including U.S. equity market volatility, as measured by the VIX index, as a new asset class when we update our model portfolios later this year. We also hope that at some point, a retail index product will be introduced, based on continuously rolled over VIX futures (i.e., one similar to current commodity index fund products). In the meantime, we are also including year-to-date nominal returns for volatility in our global asset class returns summary.