Question

Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

Year	Stock X	Stock Y	Market
2011	13%	13%	13%
2012	17	7	12
2013	-13	-5	-13
2014	4	2	2
2015	19	13	12

Assume that the risk-free rate is 4% and the market risk premium is 6%. 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.

Answer 1

Simple average returns of stocks can be calculated in following manner -

Average return = Sum of returns/ number of years

Year	Stock X (%)	Stock Y (%)	Market (%)
2011	13	13	13
2012	17	7	12
2013	-13	-5	-13
2014	4	2	2
2015	19	13	12
Average return (%)	8.00	6.00	5.20

Assume that the risk-free rate is 4% and the market risk premium is 6%.

What is the beta of Stock X?

Assuming CAPM holds we have following formula

Expected return of stock X = risk free rate + Beta of stock X*market risk premium

Where,

Expected return of stock X = average return during the period = 8%

Risk-free rate = 4%

The market risk premium = 6%

And beta of stock X =?

Therefore

8% = 4% + beta of stock X * 6%

Beta of stock X = (8%-4%)/6% = 0.67

What is the beta of Stock Y?

Expected return of stock Y = risk free rate + Beta of stock Y *market risk premium

Where,

Expected return of stock Y = average return during the period = 6%

Risk-free rate = 4%

The market risk premium = 6%

And beta of stock Y =?

Therefore

6% = 4% + beta of stock Y * 6%

Beta of stock Y = (6%-4%)/6% = 0.33

What is the required rate of return on Stock X?

Assuming CAPM holds, and then the required rate of return on Stock X is equals to expected return of stock X.

Therefore the required rate of return on Stock X = 8.0 %

What is the required rate of return on Stock Y?

Assuming CAPM holds, and then the required rate of return on Stock Y is equals to expected return of stock Y.

Therefore the required rate of return on Stock Y = 6.0 %

What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?

The required rate of return on a portfolio = the required rate of return on Stock X * weight of Stock X in portfolio + the required rate of return on Stock Y * weight of Stock Y in portfolio

= 8% * 80% + 6% *20%

= 7.6%