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Financial Economics
V 3025
Fall 2009
Rajiv Sethi
5B Lehman
Phone: 854 5140
rs328@columbia.edu
Midterm Exam: Solutions
1. An investor with $7000 in her account decides to sell short 200 shares of an asset that
is currently priced at $40 per share. What does her balance sheet look like immediately
after the trade?
Assets
Liabilities and NW
Cash
15000
8000
Shares owed
7000
Net Worth
If the maintenance margin is 50%, how high can the share price rise before she receives
a margin call?
Solve
15000
200
P
200
P
= 0
:
5
to get
P
= $50
.
2. An investor has access to two risky assets
P
and
Q
with the following statistical
properties:
E
(
r
p
) = 10%
p
= 5%
; E
(
r
q
) = 20%
q
= 20%
:
She can combine either
of these assets with bills that pay a riskfree rate of 5%. State whether the following
statements are true or false, and give reasons.
(a) \If the investor prefers
P
to all combinations of bills and
Q
, then she must be
riskaverse."
This is true. There are combinations of bills and
Q
that have a
higher expected return than
P
. If the investor were risk neutral or risk seeking
she would prefer any of these combinations to
P:
Since she prefers
P
to all these
combinations, she must be riskaverse.
(b) \If the investor prefers
Q
to all combinations of bills and
P
, then she cannot be
riskaverse."
This is false. Since
Q
has a higher expected return than
P
, some
Q
to all combinations of bills and
P:
(c) \The investor’s optimal choice cannot be a portfolio that has weight
4
5
in bills
and
1
5
in
Q
."
This is true. The portfolio has expected return
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 Winter '09
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