2-7: The Relationship between Risk and Return in the Capital Asset Pricing Model

ID: 2711999 • Letter: 2

Question

2-7: The Relationship between Risk and Return in the Capital Asset Pricing Model Problem

2-14 Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time: Year; Stock X; Stock Y; Market;

2011 12% 12% 13%

2012 19 7 12

2013 -17 -8 -10

2014 3 2 1

2015 19 12 13

Assume that the risk-free rate is 4% and the market risk premium is 7%. Do not round intermediate calculations.

What is the beta of Stock X? Round your answer to two decimal places.

What is the beta of Stock Y? Round your answer to two decimal places.

What is the required rate of return on Stock X? Round your answer to one decimal place. %

What is the required rate of return on Stock Y? Round your answer to one decimal place. %

What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Round your answer to one decimal place. %

Beta = Covaraince (stock,market)/Variance(market)

Covariance can be calculated using the covar function of excel and variance can be caclulated using the var function of excel.

Covariance(X,Market) = covar(X,Market) = 0.011904

Covariance(Y,Market) = covar(Y,Market) = 0.00666

Variance(Market) = 0.010370

Beta of stock X = 0.011904/0.010370 = 1.15

Beta of stock Y = 0.00666/0.010370 = 0.64

Using CAPM model,

Required return = risk free rate + beta * market risk premium

Required return on X = 4% + 1.15 * 7% = 12.0%

Required return on Y = 4% + 0.64* 7% = 8.5%

Required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y

= 80% * 12 + 20% * 8.5 = 11.3%

X Y Market 2011 12% 12% 13% 2012 19% 7% 12% 2013 -17% -8% -10% 2014 3% 2% 1% 2015 19% 12% 13%

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