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?

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    $\begingroup$ Remember that stock returns are a random variable with an enormous standard deviation, on an annual basis it is actually larger than the mean. Example: mean return of 8% a year, standard deviation of 16% for S&P500. $\endgroup$ – noob2 Nov 20 '15 at 16:05
  • $\begingroup$ @noob2, it does not depend on the value of the standard deviation, even you have a 5% stdev you would (almost) never get exactly the expected return. $\endgroup$ – Louis. B Nov 21 '15 at 0:49
  • $\begingroup$ Thank you! I understand that the variability of returns causes actual returns to differ from their expected values but wouldn't rebalancing have helped preserve the risk-return profile of the portfolio? Sorry if this seems like a naive question. $\endgroup$ – user51462 Nov 21 '15 at 0:54
  • $\begingroup$ @user51462 you should have commented the answer. Anyway, even with rebalancing you're still exposed to some risk with the rebalancing period. Risk is precisely what will drive your realized return form the expected one. If you play a game with 50% chance to win $100 and 50% chance to loose $100, in expectation you have $0, but you will never get $0 at the end, you will always have either $100 or -$100. It's an extreme case of course, but the idea is the same. if you could come up with a portfolio or a strategy with a 20% return for sure, you should be able to get rich... quickly ;) $\endgroup$ – Louis. B Nov 21 '15 at 22:52
  • $\begingroup$ Rebalancing Is a complicated issue to analyze mathematically. For a skeptical view see some recent work by Campbell Harvey (marketwatch.com/story/…). Much depends on what you assume about markets (perfectly efficient? a little bit of mean reversion? a little bit of momentum?). I have read a lot of different opinions by serious scholars, andhaven't made my mind up yet. $\endgroup$ – Alex C Nov 21 '15 at 23:19

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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