Financial Economics
V 3025
Fall 2009
Rajiv Sethi
5B Lehman
Phone: 854 5140
[email protected]
Problem Set 2: Solutions
Due Date: Monday, October 19
1. An investor has access to two risky assets
P
and
Q
with the following statistical
properties:
E
(
r
p
) = 7%
; °
p
= 6%
; E
(
r
q
) = 8%
; °
q
= 8%
:
The correlation coe°cient
between the two asset returns is zero and the riskfree rate of interest is 5%
:
(a) The rewardtovariability ratios are
1
3
for asset
P
and
3
8
for asset
Q;
so
Q
has the
higher ratio.
(b) The expected return of a portfolio consisting of equal weights in the two risky
assets is
E
(
r
) =
1
2
(0
:
07) +
1
2
(0
:
08) = 0
:
075 = 7
:
5%
and the standard deviation is
°
=
s
1
4
(0
:
0036) +
1
4
(0
:
0064) = 0
:
05 = 5%
(c) No, this is not possible.
For every combination of bills and
P;
there exists a
combination of bills and
Q
that has a higher expected return for the same risk.
2. See spreadsheet
3. If the riskfree rate falls then (i) the expected return and standard deviation of the
optimal risky portfolio both fall, (ii) the share of bonds in the optimal risky portfolio
rises while the share of equities falls, and (iii) the slope of the optimal CAL increases.
An investor whose preferences are such that she would have borrowed (to buy risky
assets on margin) at the original riskfree rate is clearly better o±: for any point beyond
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 Winter '09
 chudnovsky
 Standard Deviation, Variance, Probability theory, Optimal risky portfolio

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