Dynamic Leverage as a Generalization of Traditional Value-at-Risk Measures and Its Use in Portfolio Construction

We study a concept of dynamic leverage which is a risk measure generalizing traditional value at risk type measures. This measure is suited for hedge funds and can be applied to quantify risk in a fund of hedge funds. Dynamic leverage depends on the level of fund volatility, time horizon and distance in terms of NAV to a pre-defined critical liquidation level for a fund. Thus dynamic leverage incorporates the minimal holding time of investment and the risk associated with it. This reflects the fact that investments in hedge funds have lockups and limited redemption frequency. We present a variety of models for dynamic leverage to illustrate some of the differing structural features of hedge funds. We give examples of historical critical liquidation levels for hedge funds following different strategies. We study the use of dynamic leverage in a fund of funds portfolio. For a single hedge fund we study variety of derivatives of dynamic leverage and demonstrate the existence of a critical NAV below which the efficiency of de-leveraging is compromised. Finally we study a Constant Dynamic Leverage Portfolio insurance that is a modification of the classical portfolio insurance of Black-Jones-Perold