The Economic Value of Forecasts in Reducing Extreme Total Losses

A major aim of weather and other types of environmental forecasting is to provide early warning of extreme hazards that can then be used to take preventative actions to reduce loss. This study investigates what determines the loss distribution in the simplest context of repeatedly predicting/diagnosing the occurrence or not of a severe event/condition. Mathematical expressions for the expected total loss and variance of the total loss are derived in terms of the probability of event occurrence (the base rate), the cost‐loss ratio and the hit rate (H) and false alarm rate (F) of the forecasting system. Expected loss and variance behave very differently as functions of hit and false alarm rate: expected loss is a linear function of and with a minimum at whereas variance is a non‐linear function with a minimum at . For vanishingly rare events, expected loss can be less than that of taking no action only if and the forecasting system issues warnings at a rate that is much less than the rate at which events occur. Rather than minimise expected losses, one might expect the value of a forecasting system to be its ability to reduce the risk of large losses. Large losses, quantified using the Value‐at‐Risk (VaR) measure, depend upon both the expected loss and the variance of the loss but become more determined by the variance as the base rate decreases. Minimum VaR occurs at a larger false alarm rate than does minimum expected value and so can be achieved with a forecasting system that issues warnings at a higher rate that is more comparable to the rate at which observed events occur.