Gretta\'s portfolio consists of $700,000 invested in a stock that has a beta of

Question

Gretta's portfolio consists of $700,000 invested in a stock that has a beta of 1.2 and $300,000 invested in a stock that has a beta of 0.8. The risk-free rate is 6% and the market risk premium is 5%. Which of the following statements is CORRECT?

The required return on the market is 10%.

The portfolio's required return is less than 11%.

If the risk-free rate remains unchanged but the market risk premium increases by 2%, Gretta's portfolio's required return will increase by more than 2%.

If the market risk premium remains unchanged but expected inflation increases by 2%, Gretta's portfolio's required return will increase by more than 2%.

If the stock market is efficient, Gretta's portfolio's expected return should equal the expected return on the market, which is 11%.

The required return on the market is 10%.

The portfolio's required return is less than 11%.

If the risk-free rate remains unchanged but the market risk premium increases by 2%, Gretta's portfolio's required return will increase by more than 2%.

If the market risk premium remains unchanged but expected inflation increases by 2%, Gretta's portfolio's required return will increase by more than 2%.

If the stock market is efficient, Gretta's portfolio's expected return should equal the expected return on the market, which is 11%.

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Step 1: Calculate Portfolio Beta:

Portfolio Beta = 1.2*700000/(700000 + 300000) + .8*300000/(700000 + 300000) = 1.08

Step 2: Calculate Required Rate of Return:

Required Rate of Return = Risk Free Rate + Beta*Market Risk Premium = 6 + 1.08*5 = 11.40%

Answer:

Option B (If the risk-free rate remains unchanged but the market risk premium increases by 2%, Gretta's portfolio's required return will increase by more than 2%) is the correct answer

Verification = 6 + 1.08*(5+2) = 13.56%

% Increase = (13.56 - 11.40)/11.40*100 = 18.94% which is more than 2%.

Thanks

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