Question

Assume CAPM is correct (the market is the tangency portfolio), and all securities are priced correctly. a), b) Fill in the blanks.

Security          Expected        Variance        Standard        Correlation BETA

                        Returns                                  Deviation        (with Market)

Market           0.08                 ________        0.40                 ________        ________

Risk-free        0.02                 ________        _______          0.0                   ________

Stock D           ________        ________        0.50                 ________        0.8

Stock E           ________        ________        1.60                 0.40                 ________

c) Suppose a well known fund manager invites you to invest in a special fund that promises expected returns of 0.06, with a BETA of 0.2. How would you approach the idea?

Answer 1

Variance = (Standard Deviation)^2

Variance of Market = (0.40)^2 = 0.16

Variance of Risk Free = (0)^2 = 0 _ _ _ (Standard Deviation of Risk Free Security is always 0)

Variance of Stock E = (0.50)^2 = 0.25

Variance of Stock D = (1.6)^2 = 2.56

Standard Deviation of Risk Free is always 0.

Correlation with Market = Cov(market,security) / Standard Deviation of Market * Standard Deviation of Security

OR

= (Beta of Market * Beta of Security * Variance of Market) / (Standard Deviation of Market * Standard Deviation of Security)

Correlation of Market with Market = 1 _ _ _ (Correlation of market with market)

Correlation of stock D =(Beta of Market * Beta of Security D * Variance of Market) / (Standard Deviation of Market * Standard Deviation of Security)

= (1 * 0.8 * 0.16) / (0.4 * 0.5)

= 0.64

Beta can be calculated by using the above formula only.

Correlation of stock E = (Beta of Market * Beta of Security E* Variance of Market) / (Standard Deviation of Market * Standard Deviation of Security)

0.40 (Given) = (1 * Beta of Security E* 0.16) / (0.4 * 1.6)

0.40 (Given) = Beta of Security * 0.25

Beta of Security E = 0.40 / 0.25

Beta of Security E = 1.6

Beta of Market is always 1

Beta of Risk Free is always 0.     

Expected Return = Rf + Beta (Rm - Rf)

Expected Return of Stock D = 2% + 0.8 (8% - 2%)

= 6.8%

Expected Return of Stock E = 2% + 1.60 (8% - 2%)

= 11.6%

Answer c)

Expected Return from portfolio = Rf + Beta (Rm - Rf)

= 2% + 0.2(8% -2%)

= 3.2%

With beta of 0.2 the expected Return turns out to be 3.2% while the return promised by the manager is 6% Or 0.06. Here CAPM does not hold with manager.