You have observed the following returns over time: Year Stock X Stock Y Market 2
ID: 2710770 • Letter: Y
Question
You have observed the following returns over time:
Year Stock X Stock Y Market
2009 14% 13% 12%
2010 19 7 10
2011 -16 -5 -12
2012 3 1 1
2013 20 11 15
Assume that the risk free rate is 6% and the market premium is 5%
A. What are the betas of stocks X and Y?--Answer is bx = 1.3471; by = 0.6508
B What are the required rates of return on stocks X and Y?--Answer is rx = 12.7355%; ry = 9.254%
C. What is the required rate of return on a portfolio consisting of 8% of Stock X and 20% of stock Y? Answer is rp = 12.04%
YOU MUST SHOW DETAILED WORK AND FORMULAS TO SUPPORT the ANSWERS PROVIDED
Explanation / Answer
Year
Market (X)
Stock X (Y)
(x-x)
(y-y)
(x-x)(y-y)
(x-x)2
2007
12
14
2
0.75
1.5
4
2008
12
16
2
2.75
5.5
4
2009
1
3
-9
-10.25
92.25
81
2010
15
20
5
6.75
33.75
25
40
53
133
114
X
10
Y
13.25
=
Cov(x,y)/?x
1.08
?x
6.16
Rf
6%
Rm-Rf
5%
Cov(x,y)
44.33
6.66
ReX
11.40%
Year
Market(X)
Stock Y (Y)
(x-x)
(y-y)
(x-x)(y-y)
(x-x)2
2007
12
13
2
5.5
11
4
2008
12
5
2
-2.5
-5
4
2009
1
1
-9
-6.5
58.5
81
2010
15
11
5
3.5
17.5
25
40
30
0
82
114
X
10
Y
7.5
=
Cov(x,y)/?x
0.85
?x
6.16
Rf
6
Rm-Rf
5
Cov(x,y)
27.33
5.23
ReY
10.24
Return on x = 13.25 %
Return on Y = 7.5 %
Return on Portfolio combining X & Y = 13.25*.80 +7.50*.20
= 12.10 %
If Expected return is 22 % , Actual return 12.10%
Stock is Overvalued,Hence investor should go short.
Year
Market (X)
Stock X (Y)
(x-x)
(y-y)
(x-x)(y-y)
(x-x)2
2007
12
14
2
0.75
1.5
4
2008
12
16
2
2.75
5.5
4
2009
1
3
-9
-10.25
92.25
81
2010
15
20
5
6.75
33.75
25
40
53
133
114
X
10
Y
13.25
=
Cov(x,y)/?x
1.08
?x
6.16
Rf
6%
Rm-Rf
5%
Cov(x,y)
44.33
6.66
ReX
11.40%
Year
Market(X)
Stock Y (Y)
(x-x)
(y-y)
(x-x)(y-y)
(x-x)2
2007
12
13
2
5.5
11
4
2008
12
5
2
-2.5
-5
4
2009
1
1
-9
-6.5
58.5
81
2010
15
11
5
3.5
17.5
25
40
30
0
82
114
X
10
Y
7.5
=
Cov(x,y)/?x
0.85
?x
6.16
Rf
6
Rm-Rf
5
Cov(x,y)
27.33
5.23
ReY
10.24
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