Question

Two investment advisers are comparing performance. One averaged a 16.42% rate of return and the other a 20.59% rate of return. However, the β of the first investor was 1.5, whereas that of the second investor was 1.

Required: Suppose that the T-bill rate was 3% and the market return during the period was 15%. Aside from the issue of general movements in the market, outline the difference between the superior and inferior portfolios.

_____% Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).

Answer 1

Capital Asset Pricing Model(CAPM) is a model used to determine the required rate of return on an asset or a portfolio. It describes the relationship between systematic risk and expected return for the assets.

The formula of CAPM,

where,

E(R) = Required return

rf = Risk-free rate

B = Beta

rm = Return on market

We can calculate the required return of both the investment advisors using CAPM,

Advisor A

Beta = 1.5

rf = 3%

rm = 15%

E(R) = 3% + 1.5(15% - 3%) = 21%

Advisor B

Beta = 1

E(R) = 3% + 1(15% - 3%) = 15%

The abnormal return can be calculated as

Abnormal return(AR) = Actual return - required return E(R)

Advisor A

AR = 16.42% - 21% = -4.58%

Advisor B

AR = 20.59% - 15% = 5.59%

Advisor B has superior abnormal returns of 5.59%. He got 5.59% more return than the required return. Whereas Advisor A's actual return fell short to its required return by 4.58%.

The difference between superior and inferior portfolios is 5.59% - (-4.58%) = 10.17%.

Hence the difference between the superior and inferior portfolios is 10.17%.

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