# Portfolio Management: Risk Reduction

Given 3 assets all with the same likelihood of occurrence:

Asset Outcome 1 Outcome 2 Outcome 3 Expected Return

1 12 0 6 6

2 12 6 0 6

3 0 6 12 6

If the analyst constructs two-asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction?

A) Asset 1 and Asset 2. B) Asset 1 and Asset 3. C) Asset 2 and Asset 3. Answer: A is correct. An equally weighted portfolio of Asset 1 and Asset 2 has the highest level of volatility of the three pairs. All three pairs have the same expected return; however, the portfolio of Asset 1 and Asset 2 provides the least amount of risk reduction. Could someone please explain how a portfolio with Asset 1 and Asset two would have the least amount of risk reduction? Thank you!

Compute the correlations of returns for 50/50 portfolios.

Thank you! Do you know if the calculation for correlation for this particular type of question is required for students to do during the actual exam? It is a little lengthy …

My pleasure.

It’s not likely that you’ll do that during the real exam, but it’s good practice now.

They not going to test you how to calculate correlation, but they will ask you something related to it.

How can one calculate the correlation of returns? I know the calculation which uses weights and standard deviation, but the standard deviation is the same (calculated std. dev. for all three output for all 3 assets) for all 3 assets and the weights are 50-50. Is there a way to guess Asset 1 and 2 provide the least amount of risk reduction?