bleach

I find it to be a useful rule of thumb: if you want to increase the Sharpe of your portfolio, a small allocation to a new asset would increase the portfolio Sharpe as long as Sharpe of the new asset is greaterer than the product of the portfolio Sharpe and the correlation. Some of the questions you need to answer are:

1) What is your investment objective? (For example, if it's information ratio, you can derive a similar rule that includes information ratio instead of Sharpe. Or maybe due to some constraints you can't leverage up your portfolio and you really care about expected return rather than Sharpe, etc).

2) How to estimate the Sharpe ratios and correlations?
You can look at historical results and particularly look at observed ranges of values. Be cautious of unsustainable performance.

3) What are the expected ranges of the parameters and how sensitive is your decision to include a new security (asset, etc) on the parameters? For example, if you expect that your portfolio Sharpe is between 0.5 and 1, a low correlated asset (correlation below 0.3) would add value under all scenarios as long as its Sharpe is above 0.3 whereas a highly correlated asset would have to have a much higher Sharpe.

Is that helpful?