Calculating Combined Sharpe Ratios from Strategy Returns and Covariances

Summary

The document poses a portfolio-combination question: how to estimate the Sharpe ratio of several strategies when only each strategy's expected return, standard deviation, Sharpe ratio, and trade count are available. It highlights that averaging standard deviations directly is not a suitable way to combine strategies, especially when their trade counts differ.

No answer or calculation method is provided. In particular, the document supplies no strategy return series, cross-strategy covariances, weighting scheme, or assumptions about how trade counts relate to return frequency. Those missing inputs prevent a combined Sharpe ratio from being calculated from the information shown; the document is therefore a useful statement of the problem, but not a worked solution.

Key ideas

• The question concerns the Sharpe ratio of a portfolio formed from multiple strategies.
• A strategy table may include expected return, volatility, Sharpe ratio, and number of trades.
• The document questions whether volatility can be combined by averaging standard deviations.
• It gives no solution and provides no return covariance or portfolio weights.

Tags

# Given multiple strategies with their ER, volatility, how would I calculate the combined Sharpe?


# Given multiple strategies with their ER, volatility, how would I calculate the combined Sharpe?












Without knowing the actual daily returns, I have a table something like this:

```
        ER   Stdev  Sharpe   number of trades
strat1  0.1  10     0.01     100
strat2  0.02 4      0.005    10
.
.
stratM  ....
```

How would I know the expected value of the Sharpe ratio? The problem is I can't just average the standard deviations since the number of trades are different.

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