The worst division rebounds too

Question

A company's worst-performing division came in $2.5$ standard deviations below the average across all divisions this year. Assume year-over-year division performance (in standardized units) is bivariate normal with correlation $\rho = 0.4$ .

What is that division's expected performance next year? What does this say about crediting a turnaround program installed after the bad year?

Accepted Answer

The computation. For a standardized bivariate normal pair, \mathbb{E}[Y \mid X = x] = ho x regardless of sign. With x = -2.5 and ho = 0.4: \mathbb{E}[Y \mid X = -2.5] = 0.4 	imes (-2.5) = -1.0 	ext{ standard deviations.} The division is still expected to be below average next year, but it recovers 60\% of the way back toward the mean, from -2.5 up to -1.0, entirely on its own. The mechanism. An extreme low is selection on low underlying quality and bad luck. The bad luck (a soured deal, a one-off write-down, a rough market for that unit) does not repeat in expectation; it resets to zero…

The worst division rebounds too

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