Fin 3322: Cashman
CAPM In-class
1. You have a $25,000 portfolio comprised of three assets, Treasury Bills, Google, and
Ford. If you want a portfolio β of 1.3, the β’s of Google and Ford are 2.5 and 0.8,
respectively, and you have $12,000 invested in Google. How much do you have
invested in each asset? What are the portfolio weights?
1.3 = (12 / 25)*(2.5) + (Ford / 25) *(0.8) + (TB / 25)*(0)
1.3 = (12 / 25)*(2.5) + (Ford / 25) *(0.8) + 0
1.3 = (12 / 25)*(2.5) + (X) *(0.8) + 0
1.3 = 1.2 + 0.8X
0.1 = 0.8X
X = 1/8, so 1/8 of the portfolio is invested in Ford. The $ investment = 25,000/8 =
3,125
So we have 25,000 – 12,000 – 3,125 = $9,875 invested in TB
Google
Ford
TBs
$12,000
$3,125
$9,875
48%
12.5%
39.5%
2. Stock P and stock Q have had annual returns of -10%, 12%, 28% and 8%, 13%, 24%
respectively. Calculate the covariance, and correlation coefficient of returns between
the securities.
Expected Return P = 10%
Expected Return Q= 15%
Var
(P) = (1/3)*(-0.1-0.1)2+(1/3)*(0.12-0.1)2+(1/3)*(0.28-0.1)2 = 0.0242667
Std Dev (P) = 0.0242667^(0.5) = 0.156
Var
(Q) = (1/3)*(0.8 -0.15)2+(1/3)*(0.13-0.15)2+(1/3)*(0.24-0.15) 2 =
0.00446667
Std Dev (Q) = 0.009933^(0.5) = 0.067
Covar(P,Q) = (1/3)*(-0.1-0.1)* (0.8 -0.15)+(1/3)*(0.12-0.1)* (0.130.15)+(1/3)*(0.28-0.1)* (0.24-0.15) = 0.009933
Correlation Coefficient =
0.009933/(0.156*0.067) = 0.95
3. If the correlation coefficient between stock C and stock D is +1.0 and the standard
deviation of return for stock C is 15% and that for stock D is 30%, calculate the
covariance between stock C and stock D.
Correlation Coefficient = Covariance / (StdDevC * StdDevD)
1 = Covar / (0.15 * 0.3)
Covar = 0.15 * 0.3 = 0.045
4. An investor wants to evaluate the $2.5 million portfolio described below:
The market rate of return is 11.5 % and the risk free rate is 5.25%.
Stock's
Beta
1.3
0.7
1.25
1.1
0.9
Portfolio
Composition
$750,000
$250,000
$500,000
$500,000
$500,000
$2,500,000
a. Compute the expected return of the 5-asset portfolio.
Stock
I
II
III
IV
V
Stock's Expected
Return
15%
8%
16.25%
12.50%
9%
Proportions
0.30
0.10
0.20
0.20
0.20
Expected Return =0.3*0.15 + 0.1*0.08 + 0.2*0.1625 + 0.2*0.125 + 0.2*0.09
Expected Return: 0.1285
b. Compute the weighted-average beta and the expected return according to
CAPM for this 5-asset portfolio.
Portfolio Beta = 0.3*1.3 + 0.1*0.7 + 0.2*1.25 + 0.2*1.1 + 0.2*0.9
Portfolio Beta = 1.11
CAPM predicted return = 0.0525 + 1.11 (0.115 – 0.0525) = 0.121875
CAPM predicted return = 12.1875%
c. Based on the above calculations, would you recommend for or against
investing in this portfolio. Briefly explain your answer. Plot on the SML.
Expected Return
I would recommend that we invest in the portfolio, as the expected return is greater than
the return predicted by CAPM
Portfolio
SML
SL
LL
ML
LL
Rf
β
5. Suppose the current risk free rate is 7.6%. Potpourri Inc. stock has a beta of 1.7 and
an expected return of 16.7%. (Assume CAPM is true)
a.
What is the market return, and the market risk premium?
Return = 0.167 = 0.076 + 1.7 * (market return – 0.076)
Market return = 12.95%
Market Risk Premium = 5.35%
b.
Magnolia Industries stock has a beta of 0.8. What is Magnolia stock’s
expected return?
Expected Return = 0.076 + 0.8 * (0.0535) = 0.1188 = 11.88%
c.
Suppose you have invested a total of $10,000 in both Potpourri and
Magnolia, and the beta of the portfolio is 1.07. How much did you invest in each
stock? What is the portfolio’s expected return?
Port Beta =1.07=Weight (Potpourri)*1.7+(1-Weight (Potpourri))* 0.8
1.07 = 1.7*W + 0.8 - 0.8*W
1.07 = 0.9W + 0.8
0.9W = 0.27
W = 0.27 / 0.9 = 0.3 = 30%
$3,000 invested in Potpourri, the remaining $7,000 in Magnolia
Portfolio’s Expected Return = 0.3 * 0.167 +0.7 * .1188 = 0.1333
Portfolio’s Expected Return = 13.33%
OR
Port Beta = 0.3*1.7 + 0.7*0.8 = 1.07
Return = 0.076 + 1.07 * .0535 = 13.33%