Question

Assume the risk-free rate is 4%. For a fund XYZ with a beta of 1.2, its expected return according to CAPM is 16%. The market portfolio has a volatility of 20%. Calculate the following:

1. The expected return on the market portfolio is _____

2. The slope of SML is______

3. If the historical average of fund XYZ return is 14.5%. Fund XYZ has an alpha of ______

4. Fund XYZ is  ._______(Input U for underpriced, O for overpriced.

5.. For a zero-beta stock, the expected return should be _______

6. The covariance between the zero-beta stock and the market should be ________.

7. The covariance between portfolio XYZ and the market is _______

Answer 1

1. As per CAPM,

Rf = Risk free Return = 4%

Rm = Market return

Beta = 1.2

Expected return of Stock = 16%

16% = 4% + 1.2(Rm - 4%)

12% = 1.2Rm - 4.8%

Rm = 14%

So, the expected return on the market portfolio is 14%

2. Slope of SML = Rm - Rf

= 14% - 4%

= 10%

So, Slope of SML is 10%

3.  Historical average of fund XYZ return = 14.5%

Expected return according to CAPM = 16%

Alpha = Actual Return - Expected return as per CAPM

= 14.5% - 16%

= -1.5%

So, Alpha of XYZ fund is -1.5%

4. As Actual Return is lower than Expected return as per CAPM. So, XYZ Fund is O (Overpriced).

5. Zero Beta Stock's are those stocks which do not get effected with the change in the market, i.e., Zero Beta stocks are Risk-Free Stocks.

The Expected Return of Zero Beta Stock is 4%

6. Covariance of Zero beta Stock and market is 0(Zero).

7. Covariance between portfolio XYZ and the market = [(Standard Deviation of Market)^2]*Beta of XYZ

= [(20)^2]*1.2

= 480

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