Historical Returns: Expected and Required Rates of Return You have observed the
ID: 2764539 • Letter: H
Question
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:
Year Stock X Stock Y Market
2011 12% 11% 13%
2012 18% 6% 12%
2013 -15% -7% -12%
2014 2% 2% 1%
2015 21% 13% 14%
risk-free rate is 4% and the market risk premium is 6%. Do not round intermediate calculations.
A. 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.
B. 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.
Explanation / Answer
Stock X :
year 2011 :
0.12 = 0.04 + beta (0.06)
0.12 = 0.04 + beta (0.06)
0.12 - 0.04 = beta 0.06
0.08 / 0.06 = beta
beta = 1.33
year 2012:
0.18 = 0.04 + beta(0.06)
0.18 - 0.04 = beta (0.06)
0.14 = beta(0.06)
beta = 2.33
year 2013:
-0.15 = 0.04 + beta (0.06)
- 0.15 - 0.04 = beta (0.06)
-0.19 / 0.06 = beta
beta = - 3.17
year 2014:
0.02 = 0.04 + beta(0.06)
0.02 - 0.04 = beta (0.06)
-0.02 / 0.06 = beta
beta = - 0.33
year 2015:
0.21 = 0.04 + beta ( 0.06)
0.21 - 0.04 = beta (0.06)
0.17 / 0.06 = beta
beta = 2.83
Stock Y:
year 2011:
0.11 = 0.04 + beta(0.06)
0.07 / 0.06 = beta
beta = 1.17
year 2012:
0.06 = 0.04 + beta (0.06)
beta = 0.33
year 2013:
-0.07 = 0.04 + beta (0.06)
beta = -1.83
year 2014:
0.02 = 0.04 + beta(0.06)
beta = -0.33
year 2015:
0.13 = 0.04 + beta (0.06)
beta = 1.5
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