When to Add An Investment to a Portfolio
When you're given an investment's return, risk, and correlation with your portfolio, how do you tell if you should add it to your portfolio?
All things considered, you want to add it when doing so makes the Sharpe ratio of your portfolio increase.
This section on whether to add an investment or asset class to a Portfolio is often tested, but under emphasized in the curriculum.
Here's our official explanation for what you need to do to solve this type of equation:
When deciding whether to add an investment to a portfolio we look at the Sharpe Ratio of the proposed investment and compare it to the Sharpe ratio of the current portfolio while also taking into account the correlation of the new investment with the portfolio. Basically, if the Sharpe ratio of the new investment is greater than the Sharpe ratio of the existing portfolio multiplied by the correlation of portfolio returns and the new investment then we would want to add the investment. If it is lower we would not."
If the above relationship is true, we would add the new investment. If it is not, we would not.
 Remember, the Sharpe ratio is a measure of risk-adjusted return which equals: Sharpe = E(r)-Rf/standard deviation
 As we know, if the investment is less correlated with the portfolio it is more desirable from a diversification standpoint all else equal.
Now Go Study!