Question

Dr. Francesco Totti's portfolio consists of $100,000 invested in a stock which has a beta = 0.8, $150,000 invested in a stock which has a beta = 1.2, and $50,000 invested in a stock which has a beta = 1.8. The risk-free rate is 7 percent. Last year nothing changed except for the fact that the market risk premium has increased in the amount of 2 percent (two percentage points, for instance, from 9% to 11%) on top of last year's market risk premium. What is the portfolio's current required rate of return?

Answer 1

Calculation of required return using CAPM model:

Expected return ​= Rrf ​+ βa​∗(Rm​ − Rrf​)

= 7% + 1.17*11% = 19.87%

Hence the current required return using CAPM model is 19.87%

where:

Rrf​=Risk-free rate

Rm​=Expected return of the market

βa​=The beta of the security

(Rm​−Rrf​)=Equity market premium

Calculation of Beta of the portfolio:

• Beta of a portfolio is the weighted average betas of the individual assets.

Total value of portfolio = 100000 + 150,000 + 50000 = $300,000

Beta of portfolio = weights of stock in portfolio* stock beta

first stock = 0.333 * 0.8 = 0.266

second stock = 0.50 * 1.20 = 0.60

third stock = 0.1667 * 1.80 = 0.30

therefore portfolio beta = 1.17