Hedging Strategies Using Futures 111
F
2
= futures price at time t
2
;
b
1
= basis at time t
1
; and
b
2
= basis at time t
2
.
Assume that the hedge is placed at time t
1
and closed out at time t
2
. en,
b
1
= S
1
– F
1
and
b
2
= S
2
– F
2
Suppose the hedger enters into a short position at time t
1
at F
1
, closes out the position by taking a long po-
sition in the futures contract at time t
2
at F
2
, and sells the asset in the spot market at S
2
. en the prot or
loss from the futures position is F
1
– F
2
. us, the eective price for the hedger is S
2
+ (F
1
– F
2
) = F
1
+ b
2
.
If the basis at time t
2
is known with certainty at time t
1
, then the hedger will face no risk, because
they will know for certain what price they will receive for their commodity. However, b
2