Equity volatility short positions are employed mainly in the index space, rather than on single stocks. This strategy tends to be more profitable because, empirically, index volatility often appears to be more expensive. But is there a reliable indicator for the overvaluation of index relative to single-stock volatility? How could a possible mispricing be exploited most efficiently?
With respect to those issues, the implied correlation should guide the investor in his investment decision process. Market participants, for example, may follow the Chicago Board Options Exchange’s (CBOE) S&P 500 Implied Correlation Index. In July 2009, CBOE introduced this index to measure the expected average co-movement of the S&P 500 index components. Investors, however, are not restricted to the American market as option liquidity in Europe, as well as Asia, has increased substantially and thereby now offers good investment alternatives.
Overseas opportunity
When looking at the attractiveness of short volatility positions for three different markets, the Dow Jones Industrial Average, the Euro Stoxx 50 and the Hang Seng index, a comparison of implied volatility versus subsequently realized volatility shows that the Hang Seng offers the best opportunities. The difference of short-term implied to realized volatility since 2008 for the Hang Seng index displays the greatest overvaluation of around two volatility points on average. Due to high realized volatility in the same time period, the Euro Stoxx and Dow Jones reveal a negative spread of -1 and -2 volatility points, respectively.
At this stage, a look into the details of this obvious inefficiency in Hang Seng volatility pricing may be helpful to figure out the best way to profit. We should seek to determine whether the overpriced volatility of the single member stocks or the overpriced implied correlation is the reason for an overvalued implied index volatility.
The latter case would indicate that index volatility often is overvalued not only in comparison to its realized volatility but also versus single-stock volatilities. A closer look at the different indexes reveals that the difference in implied to realized correlation for the Hang Seng index is highest with around 0.1 correlation points on average since 2008 in contrast to only 0.01 and 0.03 for the Dow Jones and the Euro Stoxx 50. Overvaluation is usually quite stable except for times of financial turmoil, as in mid-2008 when realized correlation increased dramatically as equity markets were falling (see "Implied versus realized," below).
There are two ways for a trader to profit from this insight: One is selling index volatility. This could be done through a covered call writing strategy or selling (ideally delta-hedged) plain vanilla index options. Because of usually overvalued implied correlation, the strategy should earn higher profits if implemented solely with indexes instead of single stocks. The second way is by taking a short correlation position through a dispersion strategy. This solution is less sensitive to changes in volatility movements. Different implementation alternatives exist. In an initial delta-neutral strategy, the investor would take a short position in index volatility and an offsetting long position in the index members’ volatilities.
The advantage of a dispersion strategy over a simple volatility short strategy is that it is neutral to volatility valuation so that the profit and loss depends only on the realized correlation. In contrast, even if the expectation of an overvalued correlation proves to be correct, the short volatility strategy can still lose money. If the single-stock volatilities are strongly undervalued, the index volatility still can be too cheap despite expensive correlation.
A market analysis shows that inefficiencies are most significant for the Hang Seng and even persistent in times of financial turmoil, making this market most suitable for such a strategy. Furthermore, overvaluation of correlation is more persistent in different market environments than mispricing of volatility, which makes a dispersion strategy the best way to profit constantly.
Trade setup
Options provide a good vehicle for executing a profitable dispersion strategy on the Hang Seng index. The overvalued index correlation is sold via selling an at-the-money straddle on the index. To offset the exposure to the overall level of volatility, straddles on all the index’s members (the single stocks) are bought.
Obviously the short index straddle positions will win the option premium and lose the final option payoff. The position will earn money if the index does not move too far in one direction. The opposite is the case for the single-stock straddles. Therefore, the strategy will earn money whenever the index members show stronger moves than the index itself in relation to their movements implied by their volatility pricings.
Based on data from July 30, 2010, a straddle on the Hang Seng index would cost 8.79% of the index spot versus 10.46% for the weighted average of the single stock (see "Profits from overvalued correlation," below). If you assume a correlation for the straddle of around 0.6, a value that equals approximately the realized correlation for the index in the past years, the price of the index straddle would drop to 8.03% while the prices for the single-stock positions would stay constant. As the index position would start losing money earlier because of spot movements, the portfolio offers a significantly better risk-return profile than theoretically justified.
The expected payoff of the portfolio is approximated by the difference of the option premium received by the market value of the index straddle and the theoretical value of the straddle based on the fair correlation value. In our example, the market value of the straddle based on a correlation of 0.73 is 1,832 while the value based on a correlation of 0.6 would be 1,674. If our prediction of a correlation of 0.6 turns out to be correct, the investor could expect a profit of 1,832 – 1,674 = 158.
The relationship between realized and implied correlations is an important one for traders to understand. It often reveals unique trading opportunities in fresh markets — in this case, the Hang Seng index — and dispersion strategies offer a perfect way to profit.
Understanding implied correlation
In the same way that market participants often use implied volatility as an estimate of future realised volatility, implied correlation can be interpreted as an estimation of the future co-movement of stocks in an index. One can derive the value by using the formula for the variance of an index of individual stocks:
with 
as the weight for asset i in the index, 
the volatility of asset i and 
as the correlation between assets i and j. Under the (admittedly strong) assumption that the correlation between each asset is equal, the market values for the weights and implied volatilities in the formula determine the value of the average implied correlation:
The realized correlation for the assets in an index can be calculated in the same way by exchanging the implied with realized volatilities.
Marco Erling and Joerg Zimmermann work as portfolio managers for structured products with HSBC Global Asset Management. They manage volatility products. Erling has an MBA from ESADE Business School in Barcelona and can be reached at Marco.Erling@HSBCTrinkaus.de; Zimmermann has a degree in business from the University of Cologne. He can be reached at Joerg.Zimmermann@HSBCTrinkaus.de.
