# How to prove that the return criteria for adding an investment A to an existing portfolio can be represented using Sharpe Ratio Approach

How can I prove that the return criteria for adding an investment A to an existing portfolio can be represented as the below inequality using the Sharpe Ratio Approach for risk adjusted returns as applied to portfolio decision making?

• The Sharpe Ratio condition for the new portfolio (with A) to be better than the old (without A) is $SR_p^{new} \ge SR_p^{old}$. From this we should be able to derive the above. The only probem is that I don't know what $\alpha$ is, how is it defined ? – noob2 Apr 5 at 3:40