Risk Management Framework for Hedge Funds Role of Funding and Redemption Options on Leverage
by John Dai of Capula Investment Management, LLP., and
March 21, 2010
Abstract: We develop a model of hedge fund returns, which reflect the contractual relationships between a hedge fund, its investors and its prime brokers. These relationships are modelled as short option positions held by the hedge fund, wherein the "funding option" reflects the short option position with prime brokers and the "redemption option" reflects the short option position with the investors. Given an alpha producing human capital, the hedge fund's ability to deploy leverage is shown to be sharply constrained by the presence of these short options. We show that the hedge funds typically have an optimal level of leverage. Optimal leverage is shown to differ across hedge funds reflecting their de-levering costs, Sharpe ratios, correlation of assets, secondary market liquidity of their assets, and the volatility of the assets. Using a minimum level of unencumbered cash level as a risk limit, we show how a hedge fund can optimally allocate its risk capital across different risk-taking units to maximize alpha in the presence of these short option positions. Implications of our analysis for hedge fund investors and policy makers are summarized.