2 Learning ObjectivesDescribe and calculate covered interest arbitrage. ▪Discuss reasons for a deviation from interest rate parity.▪
3 Interest Rate Parity (IRP) Recall, for no arbitrage, the following relationship must hold:This is the interest rate parity (IRP) requirement.FIRP is the forward rate predicted by IRP.Both in American Terms
5 Two Connections (cont’d) The Two Connection:In wordsIf the dollar is depreciating (FIRP($/x) > S($/x)), the dollar interest return must be higher (i$ > ix).If the dollar is appreciating (FIRP ($/x) < S($/x)), the dollar interest return must be lower (i$ < ix).
6 FX/Interest Rate Relationships If dollar is at a forward discount, i.e.,FIRP ($/£) > S ($/£)There will be less demand for the dollar,It will cost more dollars to buy one poundThe dollar will depreciate against the poundTheni$ > i£The interest rate on dollars must be higher to offset the depreciation.Otherwise the two strategies would not yield the same dollar value.
7 Example 1 RevisitedTo capture the arbitrage opportunity, do you borrow or lend dollars?If the FX market is efficient, what should happen to the rates in example 1?S(£/$) =F12(£/$) = (→ F12($/£) = )i£ = 9%i$ = 10%
8 Example 1: An Arbitrage Opportunity Strategy Strategy 2≠$1.10$1.13£0.6540F12($/£) =i$ = 10%i£ = 9%S(£/$) =$1.00$1.00£0.6000
9 Practice Is arbitrage possible if... Exercise: S($/€) = , so S(€/$) =F($/€) =i$ = 6%i€ = 7%Exercise:Calculate the two strategies.Does the IRP requirement hold?
10 Practice (cont’d)We could tell that covered interest arbitrage is possible, sinceThe dollar is at a forward discountFIRP ($/£) > S ($/£)>But the dollar interest is lessi$ < i€6% < 7%
11 Capturing the Arbitrage Profit If arbitrage is possible,To capture the profitGo short in the less valuable strategyHere, borrow at the lower returnGo long in the more valuable strategyHere, lend (invest) at the higher returnNet the difference
12 Practice (same numbers) We now know arbitrage is possible if...S($/€) = , so S(€/$) =F($/€) =i$ = 6%i€ = 7%How do you exploit covered interest arbitrage?Borrow at the lower return (i$ = 6%)Lend (Invest) at the higher return (i€ = 7%)Do it.
13 Implications Recall the IRP requirement: So, if there is no arbitrage, the forward rate is strictly a function of...The spot rateThe two risk free rates of interest
14 Key Idea: Differentials Forward rates are determined by differentials in the risk free return (i).If the risk free rates are equal, i$ = i€,FIRP($/€) = S($/€)FIRP(€/$) = S(€/$)If the risk free rates are not equal, i$ ≠ i€,FIRP($/€) ≠ S($/€)FIRP(€/$) ≠ S(€/$)
16 Transaction CostsTransaction costs are central in we can, in practice, get an arbitrage profit.Arbitrage is only practical if the arbitrage profit exceeds the transaction costs required to get it.You cannot exploit small deviations from IRP.▪Arbitrage Practical▪
17 Capital ControlsIf governments limit the flow of capital across political borders,There are capital controls.If the demand for a currency increasesThe currency appreciatesBut capital controls may limit the supply of the currency.