Question

John Smith has the following portfolio:

Stock Investment Beta
A.$50,000 1.40
B.$150,000 0.80
C.$125,000 1.00
D.$50,000 1.20
He plans to sell Stock A and replace it with Stock E which has a beta of 0.80. If the government bond rate is 4% and the market return is 10%, what is the expected return on John's revised portfolio?

Answer 1

The expected return on John Smith's revised portfolio after replacing Stock A with Stock E, given the government bond rate of 4% and market return of 10%, is 9.52%.

Step-by-step explanation:

Calculating Expected Return on Revised Portfolio

To calculate the expected return on John's revised portfolio after selling Stock A and buying Stock E, we first need to determine the weighted average beta of the revised portfolio. Once we have the beta, we can use the Capital Asset Pricing Model (CAPM) to find the expected return. CAPM states that the expected return on an investment is equal to the risk-free rate plus the investment's beta times the market risk premium (the difference between the market return and the risk-free rate).

Original Portfolio Beta: ($50,000 × 1.40) + ($150,000 × 0.80) + ($125,000 × 1.00) + ($50,000 × 1.20) = $70,000 + $120,000 + $125,000 + $60,000 = $375,000
Total Portfolio Value: $50,000 + $150,000 + $125,000 + $50,000 = $375,000
Weighted Average Beta: $375,000 ÷ $375,000 = 1.0

After selling Stock A and buying Stock E, the new beta is as follows:

Revised Portfolio Beta: ($150,000 × 0.80) + ($125,000 × 1.00) + ($50,000 × 1.20) + ($50,000 × 0.80) = $120,000 + $125,000 + $60,000 + $40,000 = $345,000
Total Portfolio Value (unchanged): $375,000
Weighted Average Beta: $345,000 ÷ $375,000 = 0.92

Using CAPM, the expected return on the revised portfolio is calculated using the given government bond rate and market return:

Expected Return = Risk-Free Rate + (Beta × Market Risk Premium)
Expected Return = 4% + (0.92 × (10% - 4%))
Expected Return = 4% + (0.92 × 6%)
Expected Return = 4% + 5.52%
Expected Return = 9.52%

Therefore, the expected return on John's revised portfolio is 9.52%.

Answer 2

The expected return on John's revised portfolio is 11.568%.

Step-by-step explanation:

To calculate the expected return on John's revised portfolio, we need to calculate the weighted average of the expected returns of his current stocks and the expected return of the new stock he plans to buy. The formula for weighted average return is:

Weighted Average Return = (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) + (Weight of Stock D * Expected Return of Stock D) + (Weight of Stock E * Expected Return of Stock E)

Given that the weights are: Weight of A = 50000/325000, Weight of B = 150000/325000, Weight of C = 125000/325000, Weight of D = 50000/325000, and Weight of E = 1/325000 and the expected returns are: Expected Return of A = 10%, Expected Return of B = 10%, Expected Return of C = 10%, Expected Return of D = 10%, and Expected Return of E = 10%, we can plug these values into the formula and calculate the weighted average return.

Weighted Average Return = (50000/325000 * 10%) + (150000/325000 * 10%) + (125000/325000 * 10%) + (50000/325000 * 10%) + (1/325000 * 10%)

Weighted Average Return = 0.1538 * 10% + 0.4615 * 10% + 0.3846 * 10% + 0.1538 * 10% + 0.0031 * 10%

Weighted Average Return = 1.538% + 4.615% + 3.846% + 1.538% + 0.031% = 11.568%

Therefore, the expected return on John's revised portfolio is 11.568%.