Maxvar : Long Horizon Value at Risk in a Mark-to-Market Environment

The standard VaR approach considers only terminal risk, completely ignoring the sample path of portfolio values. In reality interim risk may be critical in a mark-to-market environment. Sharp declines in value may generate margin calls and affect trading strategies. In this paper we introduce the notion of MaxVaR, analogous to VaR in every way except it quantifies the probability of seeing a given loss on or before the terminal date rather than at the terminal date. Under standard set of assumptions we provide a simple formula for MaxVaR and examine the ratio of MaxVaR to VaR. For reasonable parameterizations MaxVaR may exceed VaR by over 40%. MaxVaR exceeds VaR by as much as 80% or more for high Sharpe Ratio hedge-fund-like return distributions