THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2309
The Statistics of Investment Risk
First Semester, 20092010
Problem Sheet 4
Assignment 2: Answer Problem Sheet 3: Q2, Q4, Q5 and Problem Sheet 4: Q2, Q6, Q7.
Time due: Friday 5:00pm of October 23, 2009
1.
(a) Given the following information on 7 assets.
Expected
Standard
Asset
return (in %)
deviation (in %)
μ
i
σ
i
A
15
10
B
20
15
C
18
20
D
12
10
E
10
5
F
14
10
G
16
20
Suppose that the returns on the 7 assets have common pairwise correlation of 0.5 and
the riskfree interest rate is 5%.
What are the optimal weightings of the tangency
portfolio if short selling is not allowed?
(b) Suppose you hold a portfolio
P
with expected return
E
(
R
P
)
and risk
σ
P
. You are now
offered the opportunity to add a new asset
Q
with expected return
E
(
R
Q
)
and risk
σ
Q
to your portfolio. Your investment objective is to maximize the expected return of your
portfolio, for a given level of portfolio risk but you are not willing to sell short. Show
that you will add the new asset
Q
to your current portfolio if the following condition
met:
SR
Q
> SR
P
Corr
(
R
Q
, R
P
)
,
where
SR
P
and
SR
Q
are the Sharpe ratios
1
of portfolio
P
and asset
Q
respectively.
(c) You are a chief investment officer of a Hong Kong pension fund invested in Hong Kong
equities and Hong Kong bonds. Your analyst supplies you with the following data on
the fund portfolio and an index representing US equities.
Current pension
US equity
fund portfolio
market index
Expected return
8%
9%
Standard deviation
20%
30%
Given that the riskfree interest rate is 3% and correlation between the current pension
fund portfolio and the US equity market index is 0.5, explain whether you should add
US equities to the fund portfolio.
1
The Sharpe ratio of a portfolio
P
is defined as
(
E
(
R
p
)

R
f
)
/σ
p
.
1
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2. A financial analyst provides the following types of information based on the single index
market model (SIMM).
Expected
Beta
Residual variance
Stock
return (in %)
coefficient
in SIMM
μ
i
β
i
τ
2
i
A
15
1.5
500
B
11
1.1
625
C
9
1.0
600
D
8
0.9
800
E
7
0.7
600
Suppose that the market index has a standard deviation of 20% and the riskfree interest
rate is 4%. Assume that short selling is not allowed. Without using PORTimizer, answer
the following questions:
(a) Find the tangency portfolio.
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 Spring '11
 S.Chiu
 Modern portfolio theory, Stock market index

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