Optimal Investments in Volatility

Abstract

Volatility has evolved as an attractive new asset class of its own. The most common instruments for trading volatility are variance swaps. Mean returns of DAX and ESX variance swaps over the time period from 1995 to 2004 are strongly negative, and only part of the negative premium can be explained by the negative correlation of variance swap returns with stock market indices. We analyze the implications of this observation for optimal portfolio compositions. Mean-variance efficient portfolios are characterized by sizable short positions in variance swaps. Typically, the stock index is also sold short to achieve a better portfolio diversification. To be able to capture heterogeneous preferences for higher moments, we use a variant of the Polynomial Goal Programming method. We assume that investors strive for a high Sharpe ratio, high skewness and low kurtosis. Our analysis reveals that a balanced trade-off between Sharpe ratio and skewness often does not exist. Investors are advised to hold the extreme portfolios (Sharpe ratio driven, skewness driven or kurtosis driven) and avoid to be stuck in the middle. This 'all-or-nothing' characteristic is reflected in jumps of asset weights when certain thresholds of preference parameters are crossed. These empirical findings can explain why many investors are so reluctant to implement option-based short-selling strategies.

Keywords: Variance Swap, Volatility Risk Premium, Portfolio Analysis, Higher Moments, Polynomial Goal Programming, Hedge Funds

JEL Classification: G10, G12, G13