International Finance: Putting Theory Into Practice

13.3. MEASURING AND HEDGING OF OPERATING EXPOSURE 505

Table 13.2:Joint distribution ofS ̃TandCF ̃ Tfor the Freedonian Subsidiary

unhedged cash flows

boom: CF∗= 150 bust : CF∗= 100 E(V ̃T|ST)

ST= 1. 2 150 × 1 .2 = 180 100 × 1 .2 = 120^180 × 00 ..15+015+120. 35 ×^0.^35 =gbp 138

p= 0. 15 p= 0. 35 p= 0. 50

ST= 0. 8 150 × 0 .8 = 120 100 × 0 .8 = 80^120 × 00 ..35+035+80. 15 ×^0.^15 =gbp 108

p= 0. 35 p= 0. 15 p= 0. 50

hedged cash flows

ST= 1. 2 180 −18 = 162 120 −18 = 102^162 ×^00 ..15+015+102. 35 ×^0.^35 =gbp 120

ST= 0. 8 120 + 12 = 132 80 + 12 = 92^132 × 00 ..35+035+92. 15 ×^0.^15 =gbp 120

180 CF in HC

80

exposureline

120

138

108

ST

0.8 1.2

o o

o

o

180 CF in HC

80

120

ST

0.8 1.2

o

o

o

o

of the economy (and, therefore, the cash flow) is not fully know once the exchange
rate is observed, so there is only an imperfect correlation between thehccash flow
and the exchange rate. Table 13.2 repeats the Freedonia data and then shows the
hedged cash flows. To find the hedged cash flows we of course need the exposure.
In the case with just two possible values ofS ̃T, the regression line runs through the
points representing the conditional expectations. We identified these expectations
as 138 whenST= 1.20 and 108 whenST= 0.80. So the exposure now equals

Bt,T=

138 − 108

1. 20 − 0. 80

=

30

0. 4

=fdk 75. (13.6)

Note, in passing, that even though the cash flow, infc, is either 150 or 100, the
exposure is not even in the range [100, 150]: it equals 75. The only way to come
with a meaningful exposure number again is to compare the two scenarios; neither
scenario in itself gives you a reliable answer, nor does any accounting number. Let’s
show that ourfc75 does make sense. Assuming the forward rate is 0.96, the pay-offs
from the hedges would be

whenST= 1.20: −Bt,T(ST−Ft,T) =− 75 ×(1. 20 − 0 .96) = − 18 ,

whenST= 0.80: −Bt,T(ST−Ft,T) =− 75 ×(0. 80 − 0 .96) = +12.

From the table, we see that now not all uncertainty is gone: the deviations between