Why a Mean-Variance Target Return Can Differ from Realized Return

Summary

The document explains why a portfolio built through mean-variance optimization for a target expected return may finish a holding period with a different realized return. It addresses whether the gap between the target and the outcome is necessarily caused by rebalancing.

The answer clarifies that portfolio weights selected to achieve a target return in expectation do not guarantee that exact return over the next period. The realized outcome is one observation of a random return, and it can be above or below its expected value because the portfolio bears risk. Thus, a realized return differing from the target is not, by itself, evidence that rebalancing was responsible. The explanation is conceptual and does not specify an optimization procedure, return model, or rebalancing policy. It also does not discuss estimation error, transaction costs, or how changing weights might affect outcomes; it focuses on the distinction between expected and realized return.

Key ideas

• Mean-variance weights target an expected return rather than a guaranteed outcome.
• A realized return can be higher or lower than the portfolio’s expected return.
• The gap between target and realized return reflects the uncertainty of a risky investment.
• A deviation from the target alone does not establish that rebalancing caused it.

Tags

# Mean variance efficient portfolios and target returns


# Mean variance efficient portfolios and target returns












If I use mean variance optimisation to create an efficient portfolio with a target expected return of 20% in a year's time and find that the actual return at the end of the year was 24%, what explains the deviation from the target? Is it just a matter of rebalancing?

## Answer by Louis. B (score 0, accepted)

https://quant.stackexchange.com/a/21855

If you form a portfolio at time $t$, in which the weights are chosen to get an expected return of 20%, you will certainly not get exactly 20% at $t+1$. If that was the case, you would not bear any risk.

What you do is that you form a portfolio that will get a 20% return in expectation (on average if you want), you may end-up with more or less than that in the end.

This is just a matter of expected value and realized value of a random variable.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.