Question

QUESTION 17 You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 126 and the total portfolio is equally as risky as the market. Required: What must the beta be for the other stock in your portfolio? (Round your answer to 2 decimal places leg.32.16).) Beta: QUESTION 18 A stock has a beta of o92, the expected return on the market is 103 percent, and the risk-free rate is 4.80 percent Required: What must the expected return on this stock be? (Do not include the percent sign (%). Round your answer to 2 decimal places leg.32.16).)

Answer 1

17. Beta of portfolio can be calculated in following manner

Beta of portfolio = Beta of Stock 1 * weight of stock 1 in portfolio + Beta of Stock 2 * weight of stock 2 in portfolio + Beta of risk free asset * weight of risk free asset in portfolio

We know that all the above three securities are equally weighted in this portfolio, therefore

Weight of stock 1 in portfolio = Weight of stock 2 in portfolio = weight of risk free asset =1/3

Beta of portfolio = 1 (the portfolio as risky as market)

Beta of Stock 1 = 1.26

Beta of Stock 2 =?

Beta of risk free asset = 0

Now put the values into above equation

1 = 1.26 * (1/3) + Beta of Stock 2 * (1/3) + 0 * (1/3)

Beta of Stock 2 = 1 - 1.26 * (1/3) = 0.42

Therefore beta of other stock must be 0.42

18. Expected rate of return of stock = risk free rate + beta of stock * (The rate of market return- risk free rate)

Where,

Expected rate of return of stock =?

Risk free rate = 4.80%

Beta of stock = 0.92

The rate of market return = 10.3%

Therefore,

Expected rate of return of stock = 4.80% + 0.92 * (10.3% - 4.80%)

= 4.80% + 0.92 * 5.50%

= 4.80% + 5.06% = 9.86%

Expected rate of return of this stock must be 9.86%