Assume you have created a 2-stock portfolio by investing $30,000 in stock X with a beta of 0.8,
and $70,000 in stock Y with a beta of 1.2. Market risk premium is 8% and risk-free rate is 6%.
The followings are the probability distributions of Stocks X and Y’s future returns:
State of Economy
Recession
Below average
Average
Above average
Boom
Probability
0.1
0.2
0.4
0.2
0.1
rx
-10%
2%
12%
20%
38%
State of Economy
Recession
Below average
Average
Above average
Boom
Probability
0.1
0.2
0.4
0.2
0.1
return %
-35%
0%
20%
25%
45%
rY(return %)
-35%.
0%
20%
25%
45%.
prob return stock X
-1
0.4
4.8
4.0
3.8
prob return stock Y
-3.5
0
8
5
4.5
1. Calculate the portfolio’s expected rate of return and the standard deviation of its future
returns
Required Return of stock X = 6 + 0.8*(8) = 12.4%
Required Return of stock Y = 6 + 1.2*(8) = 15.6%
ERoR stock X = -1+0.4+4.8+4+3.8 = 12%
ERoR stock Y = -3.5+0+8+5+4.5 = 14%
STD dev of Stock X = √(0.1(-.1-.12)^2 +0.2(.02-.12)^2 + .4(.12-.12)^2 +.2(.20-.12)^2)
 0.1(0.38-0.12)^2)^0.5  = 12.19%
STD dev of Stock Y = √(0.1(-.35-.12)^2 +0.2(0-.12)^2 + .4(.2-.12)^2 +.2(.25-.12)^2)
 (0.1(0.45-0.12)^2)^.5 = 20.44%
2. Calculate the required rate of return of your portfolio.
RRx = Required Return of Stock X
RRy = Required Return of Stock Y
Required Portfolio Return = % invested in stock X * RRx + % invested in Stock Y * RRy
0.3 * 12.4% + .7 * 15.6%  14.64%
3. Which stock in your portfolio is currently under-valued? Explain.
Both stock X and Y are undervalued because the required rate of return is higher than the
expected rate of return(s)