5.4. USING FORWARD CONTRACTS (3): SPECULATION 191
Figure 5.6:Speculating on a rise in the swap rateS = 100.00t = Jan 1 T = Apr 1 T = June 1F = 100.30 F = 100.70w = 0.30
w = 0.70time
rates
t t,T 1 t,T 2t,T 1
t,T 2
T ,T 1 2implied w = 0.40T ,T1 2you are placing a bet on future revisions of the expectation. Consider the example
in Figure 5.6. On January 1, the swap rate for delivery on April 1 is 0.30, implying
that the risk-adjusted expected rise is 0.30 over that horizon. On the same date, the
6-month swap rate is 0.70, implying a risk-adjusted expected rise by 0.70 over six
months. Implicit in these numbers is a risk-adjusted expected rise of 0.70–0.30=0.40
between April 1 and June 31. Suppose that you feel pretty certain that, by April 1,
the market will revise its expected three-month rise upward. Your bet is that, on
April 1, the three-month swap rate will exceed 0.40.
How would you do it? The answer, as we verify in the next Example, is as follows:- you speculate on a rise of the entire forward rate (spot plus swap), as before;
- but you immediately also hedge away the spot-rate risk component, by a
forward sale for delivery in April, leaving you with exposure to just the swap
rate; - you gain if, and to the extent that, the future swap rate exceeds the difference
between the current swap rates (june minus April).
To explain this via an example, let us again consider a bet that the swap rate
will rise:
Example 5.17
Current data:
Spot DateTi Forward swap rate
100 Apr 1 100.3 0.3
id Jun 31 100.7 0.7
Spread JunvApr 0.4 0.4The little table below lists the two ingredients in the combined strategy (the spec-
ulative bet on a fire in the forward rate, and the spot hedge) and, for each of these,
the actions undertaken now and in April, plus the payoffs. The payoff of the first
component is the difference between the April forward (for delivery in June) and
the initial one, 100.07; the April rate is immediately written asS ̃Apr+ ̃wApr-Jun,
where ̃wis the swap rate: