Choosing a Lookback Window for Sharpe-Ratio Portfolio Rebalancing

Summary

The document considers how much historical data to use when monthly portfolio rebalancing is based on Sharpe-ratio or mean-variance optimization. It does not identify a universally suitable window. One response emphasizes that expected returns and volatility are difficult to estimate and cites a simulated example in which a very long history was needed for mean-variance estimates to approach the true Sharpe ratio. This cautions that short windows can produce unstable, noisy allocations.

Another response suggests that a year may be a reasonable starting point because it may yield more stable estimates and aligns with a momentum horizon, while also recommending trial and error for the particular use case. The discussion does not establish that a year is optimal or compare windows through a supplied backtest. Window choice should therefore be treated as an empirical design decision, with substantial estimation uncertainty and sensitivity to the portfolio, assets, and market conditions.

Key ideas

• There is no universal historical window for Sharpe-based portfolio rebalancing.
• Expected returns and standard deviations are difficult to estimate reliably.
• A cited simulation suggests mean-variance estimates can require extensive data to approach true values.
• A one-year window is offered as a possible stability-oriented starting point, not a proven optimum.
• Window selection requires evaluating sensitivity in the intended portfolio and setting.

Tags

# Portfolio rebalance - How many data back do I need to perform sharpe ratio optimization


# Portfolio rebalance - How many data back do I need to perform sharpe ratio optimization












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

## Answer by phdstudent (score 3)

https://quant.stackexchange.com/a/55742

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:

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.

## Answer by Richard (score 0)

https://quant.stackexchange.com/a/55739

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