Alternative measures to value at risk

The purpose of this article is to introduce a new method of estimating risk as an alternative to value at risk (VaR), drawing on the risk assessment literature in environmental science.

A commonly used and accepted measure of market risk is VaR, defined as the difference between initial portfolio value and a probabilistic lower bound B on the portfolio value at time T. To take account of situations where the portfolio value may fall below B prior to time T, an an alternative to VaR is proposed based on first passage time distributions.

It is argued that the resulting expected minimum portfolio value over the time frame T provides a clear alternative measure of market risk. Analytical expressions are obtained and numerical comparisons given when the distribution of portfolio returns is lognormal.

Analytical results are presented for lognormal distributions for returns. Results for other models can be easily obtained from simulation.

The new measure of risk recognizes that investors might be sensitive to risks of decline in the value of a portfolio at any time within a given time horizon, not just at the end of the anticipated period of investment. The expected minimum portfolio value measures the largest loss that is expected at some stage over that period.

A new measure of risk is presented that arises from literature on risk assessment in environmental science. It is complementary to VaR for assessing risk.