c.If you do not receive interest on the proceeds of the short sales, then the $1200 you
receive will not be invested but will simply be returned to you.
The proceeds
from the strategy in part (b) are now negative: an arbitrage opportunity no
longer exists.
CF Now
CF in 6 months
Buy futures
0
S
T

1,218
Sell shares
1,200

S
T

15
Place $1,200 in margin account

1,200
1,200
Total
0
33
−
d.
If we call the original futures price F
0
, then the proceeds from the long
futures, shortstock strategy are:
CF Now
CF in 6 months
Buy futures
0
S
T

F
0
Sell shares
1,200

S
T

15
Place $1,200 in margin account

1,200
1,200
Total
0
1,185
F
−
0
Therefore, F
0
can be as low as 1,185 without giving rise to an arbitrage
opportunity.
On the other hand, if F
0
is higher than the parity value (1,221),
then an arbitrage opportunity (buy stocks, sell futures) will exist.
There is no
shortselling cost in this case.
Therefore, the noarbitrage range is:
1,185
F
≤
0
1,221
≤
4.
a.Call p the fraction of proceeds from the short sale to which we have access.
Ignoring transaction costs, the lower bound on the futures price that precludes
arbitrage is the following usual parity value (except for the factor p):
S
0
(l + r
f
p) – D
The dividend (D) equals: 0.012
×
1,350 = $16.20
The factor p arises because only this fraction of the proceeds from the short sale
can be invested in the riskfree asset.
We can solve for p as follows:
1,350
×
(1 + 0.022p) – 16.20 = 1,351
⇒
p = 0.579
232