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Econ 434
Professor Ickes
Fall 2009
Homework Assignment #1: Answer Sheet
This assignment is due on Tuesday, September 15, at the beginning of class (or sooner).
1.
Consider the following returns data for two economies, Macrodonia and Microdonia:
Panel A
−−−−−−−−−−−−−−−−−−−−−−−
Panel B
−−−−−−−−−−−−−−−−−−−−−−−−−
Year
Macrodonia
%
Microdonia
%
x
%
y
%
Return
%
Risk
%
1994
−
9
.
52
8
.
11
0
0
0
1
3
.
38
23
.
15
1995
56
.
76
9
.
4
9
01
3
.
85
21
.
53
1996
6
.
22
1
.
1
8
02
4
.
31
20
.
52
1997
36
.
62
5
.
3
7
03
4
.
77
20
.
2
1998
14
.
31
0
.
7
6
04
5
.
24
20
.
61
1999
−
12
.
56
7
.
7
5
05
5
.
72
1
.
71
2000
42
.
6
−
28
.
6
4
06
6
.
17
23
.
4
2001
−
0
.
5
−
34
.
0
3
07
6
.
64
25
.
56
2002
−
12
.
1
−
13
.
9
2
08
7
.
12
8
.
09
2003
12
.
4
.
5
1
09
7
.
57
30
.
89
average
13
.
38
18
.
03
0
100
18
.
03
33
.
90
standard deviation
23
.
15
33
.
90
correlation
0
.
127
(a)
Calculate the average return and the standard deviation of returns for each country over
this period (use a calculator or an excel spreadsheet,whichhasabui
ltinformu
laforthis,
or the excel program I provided for the class in my lecture). Also calculate the correlation
of returns across the countries. The latter is denoted by
ρ
ij
.
brief answer
see table.
(b)
The expected return for a portfolio with two assets is given by
R
p
=
xR
i
+
yR
j
.L
e
t
i
be Macrodonia and
j
be Microdonia, and let
x
be the share of the portfolio invested in
Macrodonia assets, and
y
the share in Microdonia assets. Calculate the expected returns
for each of the ten portfolios given by the weights in panel B of the table.
brief answer
see table.
(c)
Ther
isko
faport
fo
l
ioisg
ivenbyitss
tandarddev
iat
ion
,
σ
. For a portfolio of two assets
this is given by the formula:
σ
P
=
³
x
2
σ
2
i
+
y
2
σ
2
j
+2
xy
σ
i
σ
j
ρ
ij
´
1
2
Use this formula to calculate the riskiness of each of the ten portfolios in panel B of the
table(remember the excel program).
brief answer
see table.
1
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14
15
16
17
18
19
15
17
19
21
23
25
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29
31
33
35
R
e
t
u
r
n
Standard Deviation
Set of Feasible Portfolios
MinimumVariancePortfolio
70% Macrodonia
30% Microdonia
Setof EfficientPortfolios
Figure 1:
(d)
Using your calculations of the risk and return of the ten portfolios make a graph of the
feasible set of portfolios. Which portfolio has the minimum risk?
(e)
Label the e
ﬃ
cient set of portfolios in your graph. Explain why a portfolio that is comprised
only of home assets would be a poor choice for residents of either country.
brief answer
A portfolio comprised of %100 Macrodonia assets has
R
p
=13
.
38 and
σ
p
=23
.
15
. Th
i
si
sno
te
ﬃ
cient — you could get a higher return with the same
amount of risk. For example, 40% Microdonia 60% Microdonia yields
R
p
=16
.
17
and has the same level of risk. A portfolio comprised of all Microdonia assets would
be optimal only for investors who did not care about risk, only return. If an investor
was risk neutral her indi
f
erence curves would be horizontal (can you explain why)
and thus would hold only Microdonia assets. An investor that was risk averse would
choose a portfolio somewhere on the e
ﬃ
cient frontier, but most likely a diversi
f
ed
portfolio.
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This note was uploaded on 01/11/2012 for the course ECONOMICS 434 taught by Professor Staff during the Fall '11 term at Pennsylvania State University, University Park.
 Fall '11
 staff

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