Question

Joel Foster is the portfolio manager of the SF Fund, a $3 million hedge fund that contains the following stocks. The required rate of return on the market is 11.00% and the risk-free rate is 5.00%. What rate of return should investors expect (and require) on this fund? Stock Amount Beta A $1,075,000 1.20 B 675,000 0.50 C 750,000 1.40 D 500,000 0.75 Total $3,000,000

Answer 1

To calculate the rate of return investors should expect on the SF Fund, we need to use the Capital Asset Pricing Model (CAPM), which considers the risk and return of an investment.

Step-by-step explanation:

To calculate the rate of return investors should expect on the SF Fund, we need to use the Capital Asset Pricing Model (CAPM), which considers the risk and return of an investment. The formula for the required rate of return is:

R = Rf + β(Rm - Rf)

Where:
- Rf is the risk-free rate (5.00%)
- β is the beta coefficient for each stock
- Rm is the required rate of return on the market (11.00%)

Using this formula, we can calculate the rate of return for each stock by multiplying the amount invested in each stock by its beta, summing the results, and dividing by the total amount invested in the SF Fund. The rate of return investors should expect is:

Answer 2

Investors should expect and require a rate of return of 7.35% on the SF Fund, based on the CAPM formula.

Step-by-step explanation:

To calculate the rate of return on the SF Fund, we need to use the Capital Asset Pricing Model (CAPM) which takes into account the beta values of the stocks in the portfolio. The formula for the expected rate of return is:

Rf + BetaA × (Rm - Rf) × (AmountA / Total) + BetaB × (Rm - Rf) × (AmountB / Total) + BetaC × (Rm - Rf) × (AmountC / Total) + BetaD × (Rm - Rf) × (AmountD / Total)

Where:

Rf = Risk-free rate (5.00%)

Rm = Required rate of return on the market (11.00%)

BetaA, BetaB, BetaC, BetaD = Beta values of stocks A, B, C, D

AmountA, AmountB, AmountC, AmountD = Amount invested in stocks A, B, C, D

Total = Total amount in the portfolio ($3,000,000)

Plugging in the values, we get: 5.00% + 1.20 × (11.00% - 5.00%) × (1,075,000 / 3,000,000) + 0.50×(11.00% - 5.00%) ×(675,000 / 3,000,000) + 1.40 × (11.00% - 5.00%) × (750,000 / 3,000,000) + 0.75 × (11.00% - 5.00%) v (500,000 / 3,000,000) = 7.35%

Therefore, investors should expect and require a rate of return of 7.35% on the SF Fund.