How does the block maxima approach work in practice?

Question

AcadiFi · Accepted Answer

The block maxima approach divides the sample into non-overlapping blocks and extracts the maximum (or minimum for losses) from each. For 20 years of daily returns, annual blocks yield 20 maxima; monthly blocks yield 240 maxima. The Fisher-Tippett theorem guarantees that normalized block maxima converge to GEV as block size grows.

Workflow for Garnetwood Fund: (1) define block length trade-off - longer blocks reduce dependence bias but shrink sample; (2) extract max loss in each block; (3) fit GEV via MLE yielding shape xi, scale sigma, location mu; (4) test if xi is significantly different from zero to choose among Gumbel/Frechet/Weibull types; (5) compute return levels. The T-year return level is x_T = mu - (sigma/xi)*(1 - (-ln(1-1/T))^(-xi)).

At Garnetwood, monthly block maxima of 2% typical losses fit GEV with mu=1.8%, sigma=0.9%, xi=0.24. The 10-year monthly maximum return level is 5.7%. Advantage: automatic handling of within-block dependence. Disadvantage: wastes data (only one observation per block). For thin datasets, POT is more efficient; for highly autocorrelated series (GARCH effects), block maxima is cleaner. Always check residuals against GEV quantiles; systematic deviation indicates non-stationarity or wrong block size.

How does the block maxima approach work in practice?

Master Level II with our CFA Course

Related Questions

Practice Questions