International Finance: Putting Theory Into Practice

166 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY

Figure 4.8:Extracting spot and forward rates from theJPYswap rates

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1 3 5 7 9

swap r

spot r

forw r

swap,

% p.a.

spot,

% p.a.

forwd,

% p.a.

1 0.610 0.610 0.610

2 0.935 0.937 1.264

3 1.195 1.199 1.727

4 1.405 1.413 2.058

5 1.580 1.593 2.316

6 1.725 1.744 2.499

7 1.855 1.880 2.701

8 1.965 1.996 2.814

9 2.050 2.086 2.812

10 2.125 2.167 2.894

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1 3 5 7 9

swap r

spot r

forw r

swap,

% p.a.

spot,

% p.a.

forwd,

% p.a.

1 0.610 0.610 0.610

2 0.935 0.937 1.264

3 1.195 1.199 1.727

4 1.405 1.413 2.058

5 1.580 1.593 2.316

6 1.725 1.744 2.499

7 1.855 1.880 2.701

8 1.965 1.996 2.814

9 2.050 2.086 2.812

10 2.125 2.167 2.894

Key Swap and spot are so close, in these figures, that on the graph you no longer spot the
difference; you need to look at the numbers.

coupon loan—especially in an example where, like in ours, interest rates are generally
low. In Figure 4.7, which shows the four term structures graphically, those for swap
and spot rates overlap almost perfectly.

This illustrates how theTSof forward rates contains all information for pricing,
so thatTStheories are basically theories about forward rates. It also gives you a
feeling how swap dealers set their long-term interest rates, yields-at-par for bullet
bonds. Like us here, they construct them from spot rates. These spot rates, in
turn, are obtained fromPVfactors extracted, via regression analysis, from bond
prices in the secondary market. You can, of course, reverse-engineer all this and
extractPVfactors from swap rates, and thence forward rates. Then you may ask
the question whether there seem to be good reasons for the forward rate to behave
as it appears to do, and perhaps invest or disinvest accordingly. For instance, in
Figure 4.8 we have taken thejpyswap rates from Chapter 7 and extracted spot and
forward rates. Spot rates are familiarly close to swap rates (yields at par for bullet
bonds) but the forward rate, equally familiar, moves much faster than the spot rate
(a rolling average). So one can ask the question how these forward rates compare
to your expectations about future spot rates.

A second insight you should remember is that there is no such thing as “the”
TS. Academics would first think of theTSof spot rates or forward rates (and be
precise about that). But practitioners first think about theTSof yields at par for
bullet bonds, the numbers one sees in the newspaper or that are quoted by swap
dealers (who call them swap rates). Many traditional practitioners would apply the
yield-at-par rates for any instrument, whether it is a bullet loan or not. That can
imply serious errors and inconsistencies.

Yields are funny. Even if we just consider bullet bonds, there still is a yield for