(b)
What is BRK's covariance and correlation with the market portfolio's return?
(c)
Estimate the following covariances:
Cov
(
BRK, APPL
)
,
Cov
(
BRK, MSFT
)
, and
Cov
(
APPL, MSFT
)
.
Assume all unsystematic return components are uncorrelated across stocks.
(d)
Consider an equally weighted portfolio of BRK and APPL. Calculate the portfolio's total risk (i.e. variance),
systematic risk and unsystematic risk? Verify that
σ
2
P
=
1
N
2
N
i
=1
σ
2
i
.
(e)
Consider an equally weighted portfolio of all three stocks. Calculate the portfolio's total risk (i.e. variance),
systematic risk and unsystematic risk? Verify that
σ
2
P
=
1
N
2
N
i
=1
σ
2
i
. What happens to unsystematic risk as
the number of assets becomes large?
Q3
Consider a market that consists of only two assets, A and B. Asset A has a weight of 0.4 (40%) in the
market portfolio and a standard deviation of 0.2 (20%). Asset B has a standard deviation of 0.5 (50%). The
correlation between the two assets is 0.3. The expected return on the market is 13%,
E
[
r
M
] = 0
.
13
and the
risk free rate is 3%,
r
f
= 0
.
03
.
(a)
What is the variance of the market portfolio?
(b)
What are the covariances with the market portfolio of the two assets?
(c)
What are the CAPM
β
s of the two assets and the market portfolio?
(d)
What are the rewardtorisk (use variance as risk) ratios of the two assets and the market portfolio?
(e)
What are the contributions of each asset to the market excess return,
E
[
r
M
]

r
f
?
(f)
What are the contributions of each asset to the market variance,
σ
2
M
?
(g)
What are the contributions of each asset to the rewardtorisk ratio of the market?
(h)
Suppose you had found that the contribution of asset A to rewardto risk ratio of the market was 1 and
that the contribution of asset of B to the same ratio was 0.8. How could you construct a portfolio that beats
the market? Could this be an equilibrium?
Selected endofchapter questions (optional)
•
BKM Chapter 8: Q8,9,10,11,12
•
BKM Chapter 9: Q14, 9, 1721
•
BKM Chapter 10: Q1,4,5,11
Marking:
To obtain the full credit, you need to attempt parts of questions 1, 2, and 3. To obtain half
credit, you need to attempt two questions from 1, 2, and 3.