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Interview prep / Probability

Expected return of a three-asset equal-weight mix

Question

You hold equal weights in three assets whose annual returns are random:

Asset A: $10\%$ with probability $0.3$ , $5\%$ with probability $0.5$ , $-2\%$ with probability $0.2$ .
Asset B: $12\%$ with probability $0.4$ , $7\%$ with probability $0.3$ , $-4\%$ with probability $0.3$ .
Asset C: $18\%$ with probability $0.2$ , $3\%$ with probability $0.5$ , $-1\%$ with probability $0.3$ .

Give the portfolio's expected annual return as a decimal.

Short answer

$0.052$ . By linearity, the portfolio's mean is the average of the three means: $5.1\%$ , $5.7\%$ and $4.8\%$ average to $5.2\%$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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