Historical Returns: Expected and Required Rates of Return You have observed the
ID: 2814599 • Letter: H
Question
Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:
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.
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 12Explanation / Answer
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%
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
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