Investment Science
Chapter 10
Solutions to Suggested Problems
Dr. James A. Tzitzouris
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10.1
We are given that
S = $412
,
M = 3
(quarters), and
r = 9%
(compounded quarterly).
The
storage cost is
$2
per ounce per year, so
c
k
= $0.50
for each quarter
k = 0
,
1
, and
2
(at the
beginning of the quarter).
We use the formula:
along with the following intermediate results:
to arrive at
10.2
There is a typo in the text.
The exponent “M” should be “M” in the formula.
Suppose at time zero you:
1. borrow
S(0)
2. buy
1
unit of the asset for
S(0)
3. take a short position of
(1q)
M
units at a forward price of
F
per unit
4. at the beginning of each period, sell
q
units of the asset to pay the cost of carry
Note that the total cash outlay for these actions is zero.
F
=
S
d
0,3
∑
k
=
0
M
−
1
c
k
d
k , M
d
0,3
=
1
1
0.09
4
3
=
0.9354
d
1,3
=
1
1
0.09
4
2
=
0.9565
d
2,3
=
1
1
0.09
4
1
=
0.9780
F
=
$
440.45
$
0.5345
$
0.5227
$
0.5112
=
$
442.02
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(continued)
At the time of delivery, you have
(1q)M
units of the asset remaining.
Then you do the
following:
1. make delivery and receive
F(1q)M
as payment
2. repay your loan with
S(0)/d(0,M)
Your total profit is
F(1q)M – S(0)/d(0,M)
.
If this amount is anything but zero (negative
or positive), then you have made a profit (or received a loss) without making any
investment (i.e., without taking any risk).
Thus, consistent with our assumption that
arbitrage opportunities do not exist, the profit must be zero.
Here, we have glossed over
the case where the profit is negative.
Technically speaking, a negative profit is possible
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 Electromagnet, Forward contract, Forward price, minimum variance hedge, total cash outlay, positive arbitrage return

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