Question

An active portfolio has an average active return of 0.5%, a tracking error of 4%, and a beta of 0.90 relative to its benchmark. If we accept CAPM as the correct model for risk and returns, which of the following statements must be TRUE?

Group of answer choices The market risk premium is 10%. The portfolio's information ratio is greater than 1. The portfolio's alpha is negative. The Sharpe ratio of the benchmark is negative. The portfolio's alpha is larger than 0.5%.

Answer 1

Correct answer: The Portfolio's alpha is larger than 0.5%

Active return = Actual return of Portfolio - Benchmark return

0.5% = Actual return of Portfolio - Benchmark return

Actual return of Portfolio = 0.5% + Benchmark return

Now,

Alpha = Actual return of portfolio - Expected return of portfolio (under CAPM)

Alpha = (0.5% + Benchmark return) - Expected return of portfolio (under CAPM)

We know that when portfolio beta is less than 1 then portfolio expected return always less than benchmark (market) return.

In given case, Beta of portfolio is 0.9

which means, Expected return of portfolio would be less than benchmark return

For example: Assume benchmark return is 10% and risk free rate is 0%. Thus, expected return of portfolio under CAPM would be:

Expected return of portfolio = 0%+0.9*(10%-0%) = 9%

Putting the values in above alpha equation:

Alpha = (0.5% + 10%) - 9%

Alpha = 1.50%

The portfolio's Alpha is larger than 0.5%.

For given case, Portfolio's alpha is always larger than 0.5%