Jun 10

Ambiguous Expected Return – 7 min screencast

by David Harper, CFA, FRM, CIPM

FRM |

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This hopes to clarify a common confusion: that expected return has (at least) two different meanings. Specifically,

  • The arithmetic return gives the future average (mean) stock price
  • The geometric return gives the future median price

This is because: when we assume periodic returns are normally distributed, then future price levels are lognormal. The lognormal is skewed, non-negative (i.e., your losses are limited such that zero is the worst future price level, but your upside has positive skew due to compounding). Because the lognormal is skewed, its mean does not equal its median. So, we can refer to either the future average price (higher) or the future median price (which will always be lower, specifically by one-half the variance; volatility erodes returns)

Screencast:

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