Dozier Hedging Alternatives Forward Market Hedge:
Dozier would purchase U.S. dollars dollars under a forward contract. The contract would obligate obligate Dozier to pay £1,05,500 in e!change for £1,05,500 ! 1."1#$ %&£ ' %1,501,"($.50 assu)ing the transaction was at the *uoted (+)onth forward rate in !hibit ". -elatie to the alue of the contract at the current e!change rate, £1,05,500 ! 1."(0 %&£ ' %1,51#,/.50 Dozier would accepting a reduction in the reenue fro) the contract of %1,51#,/.50 + %1,501,"($.50 ' %1$,1#$.00
or
%1$,1#$ & %1,51#,/.50 ' 1.0 Money Market Hedge:
2n this case, Dozier would borrow an a)ount of 3ritish pounds that would obligate Dozier to a principal and interest pay)ent in three )onths that would e!actly e*ual the a)ount that Dozier e!pects to receie. 4t an interest rate of 15 per year (.5 for three )onths, the a)ount to borrow e*uals £1,05,500 & 1.0(56 ' £1,01#,.11 Dozier would i))ediately e!change e!change the pounds into dollars at the current e!change rate. So Dozier would hae £1,01#,.11 ! 1."(0 %&£ ' %1,"/",01.1 The proble) with this alternatie is that we hae dollars today if you want to consider that a proble)6 and we need to co)pare the results with the forward hedge which gies us dollar three )onths fro) now. So, we need a way to co)pare dollars today with dollars in three )onths7 i.e., we need an interest rate. rate. So we as8, what can Dozier do with with dollars today9 :ell they could inest inest the )oney in a safe inest)ent, inest)ent, proiding an $.0 annual interest rate. 2f we assu)e that the co)pany;s opportunity cost of funds is inest)ent inest)ent at $.0 for three )onths6, we can calculate how )uch )oney they would hae in three )onths ti)e. %1,"/",01.1 ! 1.06 ' %1,"#(,##5.( -elatie to the alue of the contract at the current e!change rate, £1,05,500 ! 1."(0 %&£ ' %1,51#,/.50 Dozier would accepting a reduction in the reenue fro) the contract of %1,51#,/.50 + %1,"#(,##5.( ' %5,/(.
or
%5,/(. & %1,51#,/.50 ' 1./# That is a bigger reduction in the alue of the contract than the forward )ar8et hedge. So if that is Dozier;s Dozier;s use of funds, the co)pany would be better off using the forward )ar8et. U> borrowing would proide oer the ne!t three )onths, the co)pany )ight be better off with the U> loan than it would with the forward rate contract. ?ere the choice also depends on whether they can actually borrow at a fi!ed rate of interest for three )onths and other considerations including accounting issues. :e could calculate a @brea8eenA interest rateBthe aerage USD rate that )ust apply to the dollars receied fro) U> borrowing for Dozier to be indifferent between the two hedging )ethods. %1,"/",01.1 ! 1 = i 6 ' %1,501,"($.50 1 = i 6 ' %1,501,"($.50&%1,"/",01.1 ' 1.050$
which is an annual rate of 10.0(. 2f haing cash in the US is worth )ore than 10, U> borrowing would be a better hedging )ethod. Shortcut Formulas
2t;s a bit of a pain to do these calculations. Cortunately there is a shortcut. Cirst, for the forward hedge, the following for)ula can be used Eost of forward hedge
' Corward F Spot6 & Spot ' 1."1#$ F 1."(06 & 1."(0 ' F0.010 or F1.0
The negatie nu)ber shows that it is a GcostG. 2f the result is positie, you are GbenefitingG fro) the hedge relatie to the alue of the contract at current spot e!change rate. Cor the )oney )ar8et hedge, the shortcut for)ula is Eost of HH hedge
' % interest rate F £ interest rate6 & 1. = £ interest rate6 ' 0.0 F 0.0(56 & 1.0(56 ' F0.01/# or F 1./#
2f you want to assure yourself that the for)ulas are correct, set up the calculations we did before algebraically and see how the currency nu)bers cancel out. The )ain proble) with these for)ulas is 8eeping trac8 of which interest rate goes where. There is a handy rule for this. Ta8e the e!change rate *uote that you are using, here %&£. Thin8 of this in general as I&J. So, the )oney )ar8et for)ula is, in general, I interest rate F J interest rate6 & 1. = J interest rate6 or, in shorthand, I F J6 &1 = J6 So if you were using a yen&dollar *uote for the e!change rate, you would hae yen rate )inus dollar rate diided by one plus dollar rate. Kote that none of this really soles Dozier;s proble)7 but there is a theory that in well functioning )ar8ets, the results fro) the two for)ulas should be e*ual. 2n other words, it shouldn;t )a8e a difference whether you hedge in the forward )ar8et or in the )oney )ar8et. ?oweer this theory is based on co)paring apples to apples. ?ere the apples are the financial instru)ents whose interest rates we are co)paring. ban8 loan to Dozier co)pared to rate on a ban8 ED. The theory wor8s a bit better if you use the urodollar rate and the uropound rate in !hibit ", but een these are not precisely si)ilar instru)ents. ?oweer, there is another use for the for)ulas. 3an8s use the) in pricing forward contractsL Suppose that we set the two for)ulas e*ual to each other and do so)e rearrange)ents using )y I&J approach to stay general and to re)ind us what we are doing. :e can get the following result, soling for the forward rate Corward rate ' Spot rate ! 1 = I interest rate6 & 1 = J interest rate6 -e)e)ber the rule is I oer J. :hen the ban8ers get up in the )orning, they turn on their screens, chec8 for spot e!change rates and interest rates, and plug the nu)bers into the for)ula. That deter)ines essentially their forward rate *uote in a gien currency. The ti)e period of the interest rate used deter)ines the ti)e period of the forward rate e.g. for one+)onth forward, use one+)onth interest rates6. So, what does the forward rate tell you9 -elatie to the spot rate it tells you whether interest rates in one currency are higher or lower than those in the other currency and that;s about all. So, the reason that the historical forward rates in the Dozier case are consistently below the spot rates is that interest rates in the US hae been consistently below U> rates and the relationship between the relatie interest rates hae not been changing )uch either since the forward+spot difference has been fairly stable.
