How do I interpret and estimate T-year return levels from EVT?

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AcadiFi · Accepted Answer

The T-year return level is the loss level expected to be exceeded, on average, once every T periods. For annual maxima, a 100-year return level is the loss exceeded with probability 1/100 in any given year. It equals the (1 - 1/T) quantile of the block-maxima distribution.

For GEV with parameters mu, sigma, xi and T-year return level: x_T = mu - (sigma/xi)*(1 - (-ln(1-1/T))^(-xi)) for xi != 0; x_T = mu - sigma*ln(-ln(1 - 1/T)) for xi = 0. For POT with GPD(xi, beta) and threshold u: x_T = u + (beta/xi)*((lambda*T)^(xi) - 1), where lambda is expected number of exceedances per period.

Cypress Risk Lab estimates 100-year loss for an energy portfolio: POT with u=3%, xi=0.31, beta=1.1%, 5 exceedances per year. x_100 = 3 + (1.1/0.31)*((5*100)^(0.31) - 1) = 3 + 3.55*(7.05 - 1) = 24.5% return level.

Important caveats: (1) return levels are based on stationary assumption; climate or regime change invalidates this. (2) Confidence intervals from profile likelihood are wide for long return periods. (3) The 100-year loss does not mean 'will occur in next 100 years' - it means 1/100 probability per period. Communicate probabilities explicitly to avoid misinterpretation.

How do I interpret and estimate T-year return levels from EVT?

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