Chapter 2 has much detail about the intricacies of futures markets. Read it closely. The most
relevant to this class are:
Positions
Closed Out
not usually delivered
As delivery date nears, futures price should
converge
to spot price
Futures contracts have
daily settlement
(so cash flows)
Recall the basic types of investors: hedgers, speculators, and arbitrageurs. Chapter 3
concentrates on hedgers.
A hedge is basically locking in cash flows at an early date before the asset changes hands.
Consider a position, S
t
, that will have value S
T
at some future date, T. If that asset is hedged then
a forward is sold at time T and bought at time t, so that the net asset position is S
T
F
T
+ F
t
. We
expect that, by the time of expiration, the spot and futures price will be equal (or else there would
be arbitrage opportunities) so we expect that, by date T, S
T
F
T
= 0. So the hedge is
exchanging a volatile price (S
t
becoming S
T
) for a known price, F
t
.
Short Hedge
: own an asset and short a forward to sell at a pre-specified price.
examples: gold mines might sell the gold, that's still in the ground, at pre-determined
prices at some date in the future to "lock in" a profit; farmer can sell the crop forward; exporter
with short-term receivables might pre-sell (sell forward) to lock in a profit rate. Consider an
insurer selling annuities in Japan that doesn't want the business affected by FX fluctuations so it
could sell forward contracts for 3, 6, 9, 12 months (based on expected sales over the year). If
these revenues are to be invested in, say, US Treasury securities, then these securities can be
bought forward as well.
Hedge can be considered by comparing the money lost on the asset position with the money
gained from the offsetting hedge. For instance, if the insurer above is getting ¥100,000,000 in 3
months. Right now the rate is 112¥/$ so this is worth $892,857.14. If the rate increases to 122¥/
$ then this is worth only $819,672.13. The movement of ¥10 in the FX rate meant a loss of
$73,185.01 on the asset position. If the forward price is also 112¥/$ then selling ¥112 forward
(getting one dollar delivered in 3 months) would mean that, if the yen increased to 122 per dollar
then the short forward position would mean that the company could sell ¥112 for $1 and still
have ¥10 left over to buy dollars (0.0819 worth). This 8-penny gain is small compared to the
$73,185.01 loss
but the company could sell more than ¥112. How many 112¥/$ contracts?
73,185.01/0.0819 = 892,857.14 worth (which is exactly the number we discovered earlier). This
might seem like the long way to go about it but it is worth showing the basic method: one
position loses a certain amount; it can be hedged if I can find some other position that would gain
that same amount. Most companies use hedges with much more complicated structures, but the
basic idea remains: construct two offsetting positions so that, as one loses the other gains (and
vice versa).
Long Hedge