A portfolio consists of three stocks. The weight, expected rate of return and systematic risk for each stock are provided in the following table.
Stock Investments Expected return
A $7,500 20%
B $10,000 15%
C $2,500 10%
Beta
1.5
1
0.9
a) Calculate the weights invested in stocks A, B and C, respectively.
b) Calculate expected return on the portfolio.
c) Calculate the systematic risk of the portfolio, i,e. the portfolio beta
To answer these questions, we need to calculate the weights invested in each stock, the expected return of the portfolio, and the systematic risk of the portfolio (portfolio beta). Let's go step by step.
a) Calculate the weights invested in stocks A, B, and C, respectively:
To calculate the weights, we divide the investment in each stock by the total investment in the portfolio.
Total investment in the portfolio = $7,500 + $10,000 + $2,500 = $20,000.
Weight of stock A = Investment in stock A / Total investment = $7,500 / $20,000 = 0.375 or 37.5%
Weight of stock B = Investment in stock B / Total investment = $10,000 / $20,000 = 0.5 or 50%
Weight of stock C = Investment in stock C / Total investment = $2,500 / $20,000 = 0.125 or 12.5%
Therefore, the weights invested in stocks A, B, and C are 37.5%, 50%, and 12.5% respectively.
b) Calculate the expected return on the portfolio:
The expected return on the portfolio can be calculated by taking the weighted average of the expected returns of each stock, using the weights calculated in part a.
Expected return on the portfolio = (Weight of stock A * Expected return of stock A) + (Weight of stock B * Expected return of stock B) + (Weight of stock C * Expected return of stock C)
Expected return on the portfolio = (0.375 * 20%) + (0.5 * 15%) + (0.125 * 10%)
Expected return on the portfolio = 7.5% + 7.5% + 1.25%
Expected return on the portfolio = 16.25%
Therefore, the expected return on the portfolio is 16.25%.
c) Calculate the systematic risk of the portfolio (portfolio beta):
The systematic risk of the portfolio, also known as the portfolio beta, can be calculated by taking the weighted average of the betas of each stock, using the weights calculated in part a.
Portfolio beta = (Weight of stock A * Beta of stock A) + (Weight of stock B * Beta of stock B) + (Weight of stock C * Beta of stock C)
Portfolio beta = (0.375 * 1.5) + (0.5 * 1) + (0.125 * 0.9)
Portfolio beta = 0.5625 + 0.5 + 0.1125
Portfolio beta = 1.175
Therefore, the systematic risk of the portfolio, or the portfolio beta, is 1.175.