# 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.

• Can you assume independence? If yes then this would answer your question:math.stackexchange.com/questions/2701928/…. Otherwise you will need to make assumptions around the correlation. – Magic is in the chain Jul 5 '19 at 22:00
• The Sharpe Ratio of the combined stream cannot be computed unless you know the exact dates of the trades and thus how much the different strategies overlap in time. (For ex if Srat2 is long when Strat1 is also long it adds no value, if Strat2 is often long when Strat1 is flat it adds value). – Alex C Jul 6 '19 at 15:24
• Put differently: if the strategies trade the same underlying, independence should not be assumed and it becomes essential to measure the degree of overlap accurately. Originality of thought is essential when adding strategies to a successful fund, copycat strategies are no good even if they have good stand-alone Sharpe ratio. – Alex C Jul 6 '19 at 15:55
• @Eric, your issue with combining Sharpe ratios isn't with the number of trades each strategy trades, but with correlation of the underlying return streams. you could assume correlation of zero and then combined Sharpe would be combined portfolio return (ie, weighted average of excess returns) divided by the portfolio SD (ie, sqrt of square-weighted variances). Making this assumption likely defeats the purpose of combining the strategies in the first place though, as you lose the benefit of diversification. No way to get around this aside from getting the underlying PnL or returns. – Chris Jul 10 '19 at 22:46