International Finance: Putting Theory Into Practice

134 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY

CLPT = 121,000. We discount this,^5 and convert the proceeds of this loan into
Crowns, which are invested. At the same moment we already sell forward the future
Crown balance. The final outcome is:

121 , 000 ×

1

1. 21

×

1

100

× 1. 10 ×110 = 121, 000. (4.9)

So we break exactly even: the forward sale nets us exactly what we need to pay
back the loan.

DoItYourself problem 4.1
Show, similarly, that also the counterclockwise roundtrip exactly breaks even. For
your convenience, start by writing apnwith face valueNOKT= 1100. What is the
path? What is the outcome?

What ifFt,T= too low, say 109? If one price is too low relative to another
price (or set of other prices), we can make money bybuyingat this too-low rate.
The trip where we buy forward is the counterclockwise one. We start as before,
except for the new price in the last step:

1100 ×

1

1. 10

× 100 × 1. 21 ×

1

109

= 1110. 09 > 1100. (4.10)

So the forward purchase nets us 1110.09 Pesos, 10.09 more than the 1100 we need
to pay back loan.

DoItYourself problem 4.2 :
What ifFt,T is too high, say 111? Indicate the path and calculate the arbitrage
profit.

DoItYourself problem 4.3
To generalize these numerical results, we now start withpn’s with face value 1, and
replace all rates by their symbols. One no-arb condition is that the proceeds of the
clockwise trip should not exceed the starting amount, unity. Explain how this leads
to the following expression:

1

1 +rt,T

×

1

St

×(1 +r∗t,T)×Ft,T ≤ 1. (4.11)

(^5) Discounting apnor a T-bill or a trade bill not only means computing itsPV; it often means
borrowing against the claim. In practice, under such a loan the borrower would typically also cede
the claim to the financier, as security. This lowers the lender’s risk and makes the loan cheaper.