Consider the following two securities X and Y
X y
Return- 20.0% Return- 10.0%
Standard Deviation- 20.0% Standard Dev 30%
Beta- 1.50 Beta- 1.0
Risk-free asset
Return- 5.0%
Using the data from the table, what is the portfolio expected return and the portfolio beta if you invest 35 percent in X, 45 percent in Y, and 20 percent in the risk-free asset?
To calculate the portfolio expected return and portfolio beta, we need to combine the returns and betas of the securities in the portfolio. Here's how you can calculate them:
Step 1: Calculate the weighted average return of the portfolio:
Portfolio Expected Return = (Weight of X * Return of X) + (Weight of Y * Return of Y) + (Weight of Risk-Free Asset * Return of Risk-Free Asset)
= (0.35 * 20.0%) + (0.45 * 10.0%) + (0.20 * 5.0%)
= 7.0% + 4.5% + 1.0%
= 12.5%
So, the portfolio expected return is 12.5%.
Step 2: Calculate the weighted average beta of the portfolio:
Portfolio Beta = (Weight of X * Beta of X) + (Weight of Y * Beta of Y) + (Weight of Risk-Free Asset * Beta of Risk-Free Asset)
= (0.35 * 1.50) + (0.45 * 1.0) + (0.20 * 0)
= 0.525 + 0.45 + 0
= 0.975
So, the portfolio beta is 0.975.
Therefore, if you invest 35% in X, 45% in Y, and 20% in the risk-free asset, the portfolio expected return will be 12.5% and the portfolio beta will be 0.975.