Question

You have been managing a $5 million portfolio that has a beta of 1.45 and a required rate of return of 9.975%. The current risk-free rate is 2%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.25, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

To determine the required return on the expanded portfolio, the weighted average beta is calculated, and then the CAPM formula is used with the risk-free rate and the market return.

Step-by-step explanation:

The question involves calculating the required return on an expanded portfolio using portfolio theory and the Capital Asset Pricing Model (CAPM). To calculate the new required return after adding the $500,000 investment with a beta of 1.25 to the existing $5 million portfolio with a beta of 1.45, you first need to compute the weighted average beta of the new combined portfolio. Next, you apply the CAPM formula using the risk-free rate and the computed portfolio beta.

The steps are as follows:

1. Calculate the total value of the portfolio: $5,000,000 + $500,000 = $5,500,000.
2. Calculate the weighted average beta (portfolio beta): (1.45 × $5,000,000 + 1.25 ×$500,000) / $5,500,000.
3. Use CAPM to find the required return: risk-free rate + portfolio beta ×(market return - risk-free rate). Assuming the market return is the same as the original required rate of return of the $5 million portfolio.
4. Compute the required return and round to two decimal places.

Answer 2

8.934%

Step-by-step explanation:

r(m) = r(f) + [b × r(p)]

r(m) = expected return = 9.975%

r(f) = risk free rate = 2%

b = beta = 1.45

r(p) = risk premium

so,r(p) = (9.975 - 2) ÷ 1.45

= 5.5%

for portfolio,

r(m) = r(f) + (b1 × w1 + b2 × w2) × r(p)

b1 = 1.45, w1 = (5 ÷ 5.5), b2 = 1.25, w2 = (0.5 ÷ 5.5)

r(m) = 2 + [1.45 × (5/5.5) + 1.25 × (0.5/5.5)] + 5.5

= 2 + 1.32 + 0.114 + 5.5

= 8.934%