Future f (e.g-, 1Future $ ( e.g. 1yearfromnow)yearfrom now)3.Sell future f withF$(F/S)(1 + iuk)2. Invest inInvest inUSBritain$(1+ius)f (1/S)(1+iuk)1.Buy spot f with Sf 1=$s$1= f(1/S)Present $Present f
6 1.Buy spot ￡ with S ￡1=$s $1=￡(1/S) Future $ ( e.g. 1 year from now) Future ￡ (e.g., 1 year from now) Present $ Present ￡ 2. Invest in Britain ￡(1/S)(1+iUK) 3.Sell future ￡ with F $(F/S)(1 + iUK) Invest in US $(1+iUS)
Arbitragedefined> Since both of these investments have the same risk(suppose: default-free), they must have the samefuture value-otherwise an arbitrage would exist.(F/S)(1 + iuk) = (1 + ius)Arbitrageis the act of simultaneously buying and sellingthesameor equivalentassetsorcommoditiesforthepurposeof making certainguaranteedprofits
7 Arbitrage defined ➢ Since both of these investments have the same risk (suppose: default-free), they must have the same future value—otherwise an arbitrage would exist. (F/S)(1 + iUK) = (1 + ius) Arbitrage is the act of simultaneously buying and selling the same or equivalent assets or commodities for the purpose of making certain guaranteed profits
Covered Interest arbitrage If iRP did not hold. then it would bepossible for an astute trader to makeunlimited amounts of money exploitingthe arbitrage opportunity If (FIS)(1 + iuk) >(1 + ius) →invest in the UK If (FIS)(1 + iuk) <(1 + ius) →invest in the US
8 Covered Interest arbitrage ❖If IRP did not hold, then it would be possible for an astute trader to make unlimited amounts of money exploiting the arbitrage opportunity. ▪ If (F/S)(1 + iUK) ＞(1 + ius) →invest in the UK ▪ If (F/S)(1 + iUK) ＜(1 + ius) →invest in the US
Example:covered interestarbitrageConsider the following set of foreignand domestic interest rates and spotand forward exchange rates.S($/E)$1.25/Spotexchange rateF($/)$1.20/1 yearforward rate一is7.10%U.S.interest rate=igBritishinterestrate11.56%
9 Example: covered interest arbitrage Consider the following set of foreign and domestic interest rates and spot and forward exchange rates. Spot exchange rate S($/£) = $1.25/£ 1 year forward rate F($/£) = $1.20/£ U.S. interest rate i$ = 7.10% British interest rate i£ = 11.56%
A trader with s1.00o to invest could invest in the U.S..in one year his investment will be worth $1,071 =$1,000x(1+is)=$1,000x(1.071) this trader could exchange $1,000 for 800 at theprevailing spot rate (note that 800 = $1,000- $1.25/)② invest 800 at i = 11.56% for one year to achieve892.48. ③Translate 892.48 back into dollars atF($/) = $1.20/, the 892.48 will be exactly $1,071
10 ✓ A trader with $1,000 to invest could invest in the U.S., in one year his investment will be worth $1,071 = $1,000(1+ i$ ) = $1,000(1.071) ✓① this trader could exchange $1,000 for £800 at the prevailing spot rate (note that £800 = $1,000÷$1.25/£) ② invest £800 at i£ = 11.56% for one year to achieve £892.48. ③Translate £892.48 back into dollars at F($/£) = $1.20/£, the £892.48 will be exactly $1,071