You have observed two stocks, Stock X and Stock Y, as well as the overall stock
ID: 2737492 • Letter: Y
Question
You have observed two stocks, Stock X and Stock Y, as well as the overall stock market, over a number of years and have calculated the following information from the raw observations (data) you collected:
Stock X: Stock Y: Market (M):
Expected return 8.0% 5.4% 5.2%
Variance 225.5 54.8 119.7
Covariance with Market 161.25 77.9 119.7
1) Calculate the 3 Betas for X, Y and M.
2) What is the required rate of return for the 2 stocks, and for the market, if 10-year U.S.
Treasuries are priced to yield 6% and the market risk premium is 5%?
3) If you combined the two stocks into a portfolio consisting of 80% Stock X and
20% Stock Y, would you be able to determine the portfolio's beta without the raw
data being available for X, Y and M? If no, so state. If yes, calculate the portfolio's
beta.
First row is stock X, then Y then the Market.
Explanation / Answer
1) calculations of betas=covariance with market return/variance of the market return
x beta=161.25/225.5=0.7151
y beta= 77.9/54.8=1.4215
m beta= 119.7/119.7=1
2)required rate of returns= risk free rate+beta(risk premium)
x stock required return = 6%+0.7151*5%
= 6%+3.5755%
=9.5755%
y stock required return = 6%+1.4215*5%
= 6%+7.1075%
= 13.1075%
3)Each beta is then multiplied by the percentage of your total portfolio that stock represents
beta of portfolio= 80% stock*x beta+20% stock*y beta
=0.8*0.7151+0.2*1.4215
=0.57208+0.2843
=0.85638 this is the portfolio beta ( in this calculation not used the raw data)
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