MaxVaR: LONG-HORIZON VALUE AT RISK IN A MARK-TO-MARKET ENVIRONMENT
Jacob Boudoukh, Matthew Richardson, Richard Stanton and Robert F. Whitelaw
The standard VaR approach considers only terminal risk, completely ignoring the path of the portfolio value prior to this final horizon. This assumption is unrealistic—interim risk may be critical in a mark-to-market environment because interim values of a portfolio may generate margin calls and affect trading strategies. We provide a simple framework for adjusting standard VaR for interim risk. We introduce the notion of MaxVaR, which is analogous to VaR except that it considers the probability of seeing a given low cumulative return on or before the terminal date. Under the standard lognormality assumption and for reasonable parameterizations MaxVaR may exceed VaR by over 40%. We show that adjusting VaR for interim mark-to-market risk is critically important for high Sharpe Ratio portfolios (e.g., for hedge funds).