using the CAPM, compute the expected rate of return for a portfolio with 25% stake in company A and 75% stake in company B. Assume a market risj premium of 3% and a risk free rate of 4%.
To calculate the expected rate of return for a portfolio using the Capital Asset Pricing Model (CAPM), you will need the following information:
1. The weight or proportion of each company in the portfolio.
2. The beta (β) for each company, which measures its sensitivity to market movements.
3. The market risk premium, which represents the excess return expected for taking on additional risk compared to the risk-free rate.
4. The risk-free rate, which is the return on a risk-free investment such as Treasury bonds.
Let's start by calculating the weighted average beta (β) for the portfolio:
1. Company A has a 25% stake, and Company B has a 75% stake in the portfolio.
Next, you need to know the beta (β) for each company:
2. Let's assume Company A has a beta of 1.2, and Company B has a beta of 0.8.
Next, calculate the expected rate of return for each company using the CAPM formula:
Expected Return = Risk-free Rate + β × Market Risk Premium
3. The risk-free rate is given as 4% (0.04).
4. The market risk premium is given as 3% (0.03).
Now we can calculate the expected rate of return for each company:
For Company A:
Expected Return_A = 0.04 + 1.2 × 0.03 = 0.04 + 0.036 = 0.076 (or 7.6%)
For Company B:
Expected Return_B = 0.04 + 0.8 × 0.03 = 0.04 + 0.024 = 0.064 (or 6.4%)
Finally, calculate the weighted average expected rate of return for the portfolio by multiplying each company's expected return by its weight, and then summing them:
Weighted Average Expected Return = (Weight_A × Expected Return_A) + (Weight_B × Expected Return_B)
Weight_A = 0.25 and Weight_B = 0.75
Weighted Average Expected Return = (0.25 × 0.076) + (0.75 × 0.064) = 0.019 + 0.048 = 0.067 (or 6.7%)
Therefore, the expected rate of return for the portfolio with a 25% stake in Company A and a 75% stake in Company B, assuming a market risk premium of 3% and a risk-free rate of 4%, is 6.7%.