The riskfree rate is 27 percent The Cumnock Development fund

The risk-free rate is 2.7 percent. The Cumnock Development fund has a rate of return of 11 percent with all money invested in 4 stocks as follows:  

1. What is the beta of the portfolio?

2. What is the market risk premium?

3. If the fund manager sells all of stock A and stock B and invests half of the proceeds in stock E with a beta of 1.6 and half of the proceeds in Stock F with a beta of 1.5, what will be the percent change in the beta of the portfolio?

Solution

Answer 1.

Total Value of Portfolio = $200,000 + $175,000 + $375,000 + $225,000
Total Value of Portfolio = $975,000

Weight of Stock A = $200,000/$975,000
Weight of Stock A = 0.2051

Weight of Stock B = $175,000/$975,000
Weight of Stock B = 0.1795

Weight of Stock C = $375,000/$975,000
Weight of Stock C = 0.3846

Weight of Stock D = $225,000/$975,000
Weight of Stock D = 0.2308

Portfolio Beta = 0.2051 * 1.4 + 0.1795 * 1.3 + 0.3846 * 1.2 + 0.2308 * 0.9
Portfolio Beta = 1.19

Answer 2.

Portfolio Return = Risk-free Rate + Portfolio Beta * Market Risk Premium
11% = 2.7% + 1.19 * Market Risk Premium
8.3% = 1.19 * Market Risk Premium
Market Risk Premium = 6.97%

Answer 3.

Amount received from Sale of Stock A and Stock B = $200,000 + $175,000
Amount received from Sale of Stock A and Stock B = $375,000

Amount invested in Stock E = $375,000 * 1/2
Amount invested in Stock E = $187,500

Amount invested in Stock F = $375,000 * 1/2
Amount invested in Stock F = $187,500

Weight of Stock E = $187,500/$975,000
Weight of Stock E = 0.1923

Weight of Stock F = $187,500/$975,000
Weight of Stock F = 0.1923

New Portfolio Beta = 0.1923 * 1.6 + 0.1923 * 1.5 + 0.3846 * 1.2 + 0.2308 * 0.9
New Portfolio Beta = 1.27

% Change in Portfolio Beta = (1.27 - 1.19) / 1.19
% Change in Portfolio Beta = 6.72%