Regression to the mean, the top fund's next year

Question

A fund's performance last year was 2 standard deviations above the peer average. Assume year-over-year performance (in standardized units) is bivariate normal with correlation $\rho = 0.3$ .

What is the fund's expected performance this year? Explain the mechanism, and why regression to the mean is not a causal force.

Accepted Answer

The computation. For a standardized bivariate normal pair, the conditional expectation is linear: \mathbb{E}[Y \mid X = x] = ho x. With x = 2 and ho = 0.3: expected performance this year is 0.3 	imes 2 = 0.6 standard deviations above average. Still good, but the expectation gives back 70% of the outperformance. (The conditional distribution is \mathcal{N}(ho x,\, 1 - ho^2), so there's plenty of spread around that 0.6, too.) The mechanism: selection on signal-plus-noise. Decompose an extreme observation as X = 	ext{skill} + 	ext{luck}. Conditioning on X being extreme selects jointly…

Regression to the mean, the top fund's next year

Your answer

More Statistics questions