**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.**