The Volatility Risk Premium
By Graham Rennison, Niels Pedersen
September 21, 2012
Amid elevated global macroeconomic uncertainty and market turbulence, investors are searching for ways to diversify portfolios with non-traditional asset classes.
Volatility risk premium strategies aim to capture a return premium over time as compensation for the risk of losses during sudden increases in market volatility.
We believe investors seeking to diversify their equity risk exposures should consider adding volatility risk premium strategies to their portfolios, albeit with appropriate diversification across major option markets, active risk management and prudent scaling.
Elevated global macroeconomic uncertainty and bouts of extreme market turbulence have recently plagued financial markets. This environment has prompted a search for diversifying investment opportunities that lie outside the space of traditional asset classes. This article examines the performance of options strategies that aim to capture a return premium over time as compensation for the risk of losses during sudden increases in market volatility. We show that these “volatility risk premium” strategies deliver attractive risk-adjusted returns across 14 options markets from June 1994 to June 2012. Performance furthermore improves significantly after the crisis in 2008 (see Figure 1). We conclude that the risk-return tradeoff for volatility strategies compares favorably to those of traditional investments, such as equities and bonds, and that the strategies exhibit relatively low correlations to equity risk. Investors who want to diversify their portfolio’s equity risk exposures should therefore consider making allocations to volatility risk premium strategies. However, successful implementation would require diversification across major options markets (equities, interest rates, currencies and commodities), active risk management and prudent scaling.
Perspective on the volatility risk premium
The volatility risk premium can be seen as compensation to option sellers for the risk of losses during periods when realized volatility increases suddenly; these periods tend to coincide with general market turmoil, elevated uncertainty and investor stress. The volatility risk premium causes option-implied volatility to exceed realized volatility, on average. Option-implied volatility is consequently a biased estimate of future realized volatility. And, therefore, the volatility risk premium is just another economic risk premium that investors may consider as part of their portfolios. Similar “biases” can be observed in all asset markets that expose investors to important systematic risk factors. In interest rate markets, the term premium, which can be seen as compensation for uncertainty about future inflation and monetary policy, typically causes forward rates to exceed realized interest rates. In credit markets, the credit-risk premium causes market-implied default rates to exceed realized default rates, on average, and compensates investors for the risk of losses on defaults and downgrades. Finally, the currency-carry risk premium typically causes forward exchange rates of low-yielding currencies to exceed realized exchange rates.
In addition, the observed magnitude of the volatility risk premium may be supported structurally by an imbalance in supply and demand. Buyers of options include hedgers, or speculators seeking leverage with capped downside, but there are few natural sellers of options. Imbalances between supply and demand for options may have been especially acute following the 2008 financial crisis and the subsequent sovereign debt crises. While demand for options has increased, fewer market participants are willing or able to supply options, due to increased capital requirements, higher costs and lower tolerance of leverage.
Strategies to capture the volatility premium Our analysis is based on data from 14 options markets, grouped into four categories:
Equities: Equity index options (S&P 500, EURO STOXX, FTSE 100, Nikkei)
As a first indication of the magnitude of the volatility risk premium in these markets, Figure 2 compares average one-month option-implied volatilities to subsequent one-month realized volatilities (options are equally weighted within each broad market). The difference is positive on average and significant – corresponding to roughly one-tenth of the implied volatility.
Of course, these results do not directly correspond to the returns of a tradable strategy. The simplest way to capture the volatility risk premium is to sell one-month at-the-money straddlesi(straddles are comprised of a put and a call at the same strike and maturity). The straddles need to be hedged each day against moves in the underlying instrument (“delta-hedging”), so that they remain exposed primarily to changes in market volatility.
We calculate hypothetical monthly returns of this strategy in each of the 14 options markets, from June 1994 to June 2012. The straddles are sold on the first business day of each month and held till expiry. We include conservative trading costs on both the sale of the option and the rebalancing of the hedgeii.
Figure 3 shows average excess returns, standard deviations of returns, and the associated Sharpe ratios for each option-market category. (The Sharpe ratio measures the excess return per unit of standard deviation in an investment asset or trading strategy.) We find significant positive excess returns in each market with Sharpe ratios of 1.2 for commodities and interest rates, 1.0 for equities, and 0.7 for FX.
These Sharpe ratios compare favorably with other asset classes. However, it is well-known that standard deviation alone is insufficient as a measure of riskiness of a given investment strategy. This is especially true for strategies with embedded tail risks and returns that may be skewed to the downside.
Tail risk analysis
To analyze the left tail risk in the volatility strategies, we calculate the worst returns over one-, three- and 12-month periods (Figure 4), and the number of standard deviationsiii to which these returns correspond. To summarize the right tail of the distributions, we use the same statistics for the highest returns. The last column notes the dates of the worst three-month periods.
Over short horizons, the strategies show significant negative skewed tail risk. All experience at least three- to four-sigma losses over one month vs. two- to three-sigma gains in the right tail. However, over a 12-month period the pattern is reversed: The strategies exhibit positive skew; the right tail of the distribution is more pronounced than the left tail.
These results highlight a consistent empirical characteristic of volatility strategies: they are typically subject to relatively short, sharp losses, but tend to recover quickly. This may be because implied volatility tends to overreact to shocks due to demand from risk-averse hedgers, and remains elevated for some time. Since the strategies sell short-dated options, they monetize this excess risk aversion. To further illustrate this effect, Figure 5 shows the average length of drawdowns of the volatility strategies compared with investments in other classic risk premium strategiesiv. Drawdowns are measured by the average number of months taken for a strategy to recover a previous peak. The volatility strategies exhibit relatively short drawdowns of about five months, compared with an average of more than one year for the U.S. large cap stocks, for example.
Figure 6 highlights the quarter-by-quarter performance during 2008, compared with U.S. large cap stocks and U.S. investment grade credit. As in Figure 4, quarterly returns are expressed as the number of standard deviations. The volatility strategies experience smaller negative shocks than investment grade credit, and comparable or smaller negative shocks than stocks. The third quarter of 2008, which includes the sharp sell-off in September, is the only quarter when all four volatility strategies have negative returns. By the fourth quarter, the volatility strategies start to recover as they monetize the higher implied volatility.
How much return is attributable to equity risk?
Market volatility tends to rise rapidly at times of overall market stress. As such, short-volatility strategies would be expected to lose money when equities sell off, especially during equity tail events. Are returns of these strategies simply due compensation for exposure to equity risk and to equity tail risk in particular? To answer this, we decompose returns into a component attributable to broad equity beta, and a component attributable to exposure to equity tail riskv.
Figure 7 shows the proportion of the return that cannot be attributed to either equity beta or to equity tail risk. Equity volatility strategies, unsurprisingly, contain a substantial component of equity risk. Nearly 60% of returns are attributable to broad-equity and tail-equity risk. Currency volatility strategies also have a significant equity-risk component, contributing nearly 40% of returns. Commodities and interest rate volatility strategies do not have substantial exposure to equity risk.
These results highlight that the majority of the strategy returns (more than 75% on average across asset classes) cannot be explained by their exposure to equity risk. This supports the hypothesis of a distinct volatility risk premium and/or the existence of persistent structural supply-demand imbalances in the options market.
Is there a role for these strategies in portfolios?
The performance of the volatility strategies suggests that they may be attractive on a stand-alone basis. To evaluate their contribution potential in an asset allocation context, we next compare their risk, return and correlation with other risk premiums.
Figure 8 compares realized Sharpe ratios of the volatility strategies with the classic risk premium strategies (see appendix for details) across four historical periods. The four periods cover the pre-crisis era (June 1994 to June 2007), the crisis (July 2007 to March 2009), the sharp recovery (April 2009 to March 2010) and the sovereign-crisis period (April 2010 to June 2012). The volatility strategies perform relatively well across each of these four periods, with notably strong performance during the two most recent periods.
Finally, Figure 9 shows a monthly correlation matrix of the four volatility strategies with each other, and with the other risk premiums. Although the correlations between the volatility strategies in the full sample are positive, they are generally fairly low (around 20%-30%) with the exception of the equity volatility strategies (which are as high as 63%). Correlations do, however, increase across the board during the financial crisis, as shown in the lower part of Figure 9.
This article examines the historical performance of simple tradable strategies that are designed to capture the volatility risk premium over time. The empirical analysis shows that the strategies deliver significant positive risk-adjusted returns across 14 options markets over a sample period from June 1994 to June 2012. The strategies experience drawdowns during spikes in market volatility and exhibit fatter left tails than normal distributions, but rebound fairly rapidly following such episodes. Overall, the risk-return tradeoff for the volatility premium compares favorably to other sources of risk premiums such as equity and credit.
As always, there is a limit to conclusions that can be drawn based solely on historical-return analysis. Some potential risks may not have been realized during the sample period. However, given the economic rationale for the existence of a volatility risk premium, and the supportive supply-demand situation that emerged following the 2008 financial crisis, we believe an allocation to volatility strategies could enhance portfolio efficiency. An allocation should not be sized solely on historical-return statistics, however, but on conservative estimates of potential future returns. Volatility strategies are complex to implement, so both active portfolio and risk management are critical to their successful implementation in portfolios.
iStraddles are comprised of an at-the-money put and call with the same expiry date. On the day the straddle is sold, the value of the option has close to zero sensitivity (“zero delta”) to changes in the price of the underlying. During the month, the delta may become positive or negative as the underlying moves, potentially leading to option gains and losses driven by market direction rather than the volatility premium. To neutralize this we simulate daily delta-hedging – taking an offsetting position in the underlying market – at the market close. The payoff of a delta-hedged straddle is closely related to the difference between initial implied volatility and subsequent realized volatility.
iiA bid-offer of between 0.4% and 1.0% of the implied volatility is assessed on the sale of the option each month, and a bid-offer of between 0 bps and 2 bps is assessed daily on the notional required to rebalance the hedges. These bid-offers are further scaled up in periods of increased volatility, representing a reduction in liquidity in stressed periods. See appendix for additional details.
iiiTo reflect the changing magnitudes of returns through time we measure standard deviations using a 36-month look-back window ending in the same month as the return-observation window, and then scale to match the return-window length. For example, if the worst three-month return is from September 2008 to November 2008, inclusive, the standard deviation is measured by monthly returns from December 2005 to November 2008, inclusive, and multiplied by the square root of three to scale to a three-month standard deviation.
ivClassic risk premium strategies are defined as follows: U.S. large cap stocks, measured as the total return of the S&P 500 minus the total return of the Barclays Capital U.S. 1-3 Month T-Bill Index; U.S. Treasuries, measured as the total return of the Barclays U.S. Treasury Index minus the total return of the Barclays 1-3 Month T-Bill Index; U.S. investment grade credit, measured as the excess return of the Barclays U.S. Corporate Index over duration-matched treasuries; U.S. high yield credit, measured as the excess return of the Barclays U.S. High Yield Index over duration-matched treasuries; emerging market equity, measured as the total return of the MSCI Emerging Markets Index minus the total return of the Barclays Capital 1-3 Month T-Bill Index; emerging market bonds, measured as the excess return of the J.P. Morgan EMBI Global Index over duration-matched treasuries; commodities, measured as the total return of the Dow Jones UBS Commodity Index minus the total return of the Barclays 1-3 Month T-Bill Index; currency carry, measured as the return of investing in the three highest-yielding currencies, and going short the three lowest-yielding currencies each month, as per the Bloomberg function FXFB.
vThe return attributable to equity beta is computed by regressing monthly returns of the volatility strategy on the monthly excess returns of the S&P 500 Index and multiplying the beta of this regression by the average annual excess return of the S&P 500 Index. The return attributable to equity and equity tail risk is computed by regressing monthly returns of the volatility strategy jointly on the monthly excess returns of the S&P 500 Index and the monthly excess returns of a short 5% out-of-the-money one-month S&P 500 Index put. The return is then computed by summing the betas from this regression multiplied by average annual excess returns of the S&P 500 Index and the short puts respectively. All calculations are based on data from June 1994 to June 2012.
Appendix: Transaction Cost Assumptions and Data Sources
Past performance is not a guarantee or a reliable indicator of future results.All investments contain risk and may lose value. Investing in the bond market is subject to certain risks including market, interest-rate, issuer, credit, and inflation risk; investments may be worth more or less than the original cost when redeemed. Equities may decline in value due to both real and perceived general market, economic, and industry conditions. Currency rates may fluctuate significantly over short periods of time and may reduce the returns of a portfolio. Commodities contain heightened risk including market, political, regulatory, and natural conditions, and may not be suitable for all investors. Tail risk hedging may involve entering into financial derivatives that are expected to increase in value during the occurrence of tail events. Investing in a tail event instrument could lose all or a portion of its value even in a period of severe market stress. A tail event is unpredictable; therefore, investments in instruments tied to the occurrence of a tail event are speculative. Derivatives may involve certain costs and risks such as liquidity, interest rate, market, credit, management and the risk that a position could not be closed when most advantageous. Investing in derivatives could lose more than the amount invested.
Hypothetical examples are for illustrative purposes only.No representation is being made that any account, product, or strategy will or is likely to achieve profits, losses, or results similar to those shown. Hypothetical or simulated performance results have several inherent limitations. Unlike an actual performance record, simulated results do not represent actual performance and are generally prepared with the benefit of hindsight. There are frequently sharp differences between simulated performance results and the actual results subsequently achieved by any particular account, product, or strategy. In addition, since trades have not actually been executed, simulated results cannot account for the impact of certain market risks such as lack of liquidity. There are numerous other factors related to the markets in general or the implementation of any specific investment strategy, which cannot be fully accounted for in the preparation of simulated results and all of which can adversely affect actual results. The results shown do not include the effect of management fees or expenses and the results would be different if such fees were included. Results shown may not be attained and should not be construed as the only possibilities that exist.