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if I do a periodical rebalance of my portfolio based on sharpe ratio optimization, how many historical data should I take in account for optimizing with respect to the frequency of rebalancing?

For example, let's say I rebalance once every month. Do I have to perform sharpe ratio optimization based on data from the last 3 months? 6 months? 12 months?

Thanks

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    $\begingroup$ It makes no difference if you can't accurately predict future returns $\endgroup$ – amdopt Jul 17 '20 at 13:05
  • $\begingroup$ An alternative therefore might be to use a method such as Risk Parity (Naive RP or ERC) which only uses volatilities and not expected returns $\endgroup$ – noob2 Jul 17 '20 at 13:13
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It is hard to tell, because means and standard deviations are hard to estimate.

Take a look at the example below from De Miguel et al:

enter image description here

The row you are interested in is the third row ($mv$). They simulate normally distributed data, and realise that only when you have 6000 months of data (i.e. 500 years), mean variance starts to be close to the true sharpe ratio (0.15 in their economy).

Which means, that most likely it does not matter whether you use 3 months, 6 months or 12 months of data, the results you will get will be a matter of luck.

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  • $\begingroup$ According to this article, you can't get a better Sharpe Ratio than a simple 1/N allocation. So basically any effort for optimization would be useless. $\endgroup$ – Daniele Chirivì Jul 17 '20 at 11:48
  • $\begingroup$ No any effort. Any of the optimising strategies analyzed in that paper yes. Which does not mean there may be some strategy out there that is better than 1/N. $\endgroup$ – phdstudent Jul 17 '20 at 11:58
  • $\begingroup$ a follow-up paper by Kirby and Ostdiek (2012) discredited the de Miguel et al paper for magnifying estimation risk and turnover rates. They instead make the mean-variance model target the conditional expected return of the 1/N portfolio and no higher to show that it actually does outperform the 1/N without transaction costs $\endgroup$ – develarist Jul 17 '20 at 12:52
  • $\begingroup$ Thanks for the reference. Wasn't aware of that. But still ignoring transaction costs does not seem right as in the end what you care as an investor is return after costs. $\endgroup$ – phdstudent Jul 17 '20 at 12:54
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First of all, welcome.

I don't think there's a golden rule for that. Trial and Error and see what works best for your use-case.

Personally, I think there might be an argument for a 12 month window, since it follows the momentum logic in it's orginal formulation. And a longer horizon might be more stable.

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