128 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY
Suppose you sell forwardusd100,000 ateur/usd0.75 for December 31. (Note that
the quote defines the euro as thehc.) Then
- you commit to deliverusd100,000, which is similar to signing a promissory
note (pn) with face valueFCT=usd100,000 on Dec 31, and handing it over
to the bank; - the bank promises to pay youeur75,000, which is similar to giving you a
signedpnwith face valueHCT=eur75,000 for that date.
Intimately linked to the exchange markets are the money markets for the home
and foreign country, that is, the markets for short-term deposits and loans. A home-
currency deposit ofgbp1m “spot”^3 for one year at 4 percent means that you pay an
amount ofgbp1m to the bank now, and the bank pays you an amountgbp1.04m
at timeT. This is similar to handing over the spot money amount ofHCt=1m in
return for apnwith face valueHCT=1.04m. Likewise, if you borrowgbp10m at 6
percent over one year, this is tantamount to you receiving a cheque with face value
HCt=gbp10m in return for a promissory note with face valueHCT=gbp10.6m.
Graphical Representation of Chains of Transactions: an Example
For the remainder of this section, we take the Chilean Peso (clp) as our home
currency and the Norvegian Crown (nok) as the foreign one. Suppose the spot
rate isSt=clp/nok100, the four-year forward rateFt,T=clp/nok110, theclp
four-year risk-free rate of return isrt,T=21 percent effective, and thenokone equals
r∗t,T=10 percent. Very often we will discuss sequences of deals, or combinations of
deals. Consider, for example, an Chilean investor who hasclp100,000 to invest.
He goes for anokdeposit “swapped intoclp”, that is, anokdeposit combined
with a spot purchase and a forward sale. Let us see what the final outcome is:
Example 4.6
The investor converts hisclp100,000 into an amountNOKt, deposits these for four
years, and sells forward the proceedsNOKTin order to obtain a risk-free amount
ofclpfour years from now. The outcome is computed as follows:
- Buy spotnok: the input given to the bank isclp100,000, so the output of
the spot deal, received from the bank, is 100, 000 × 1 /100 = 1,000 Crown. - Invest thesenokat 10 percent: the input into the money market operation
isNOKt= 1,000, so after four years you will receive from the bank an output
equal to 1, 000 × 1 .10 = 1,100 Crowns.
(^3) A spot deposit or loan starts the second working day. For one-day deposits, one can also define
the starting date as today (“overnight”), or tomorrow (“tomorrow/next”), but this must be made
explicit, then. In all our examples, the deals are spot—the default option in real life, too.