International Financial Management Vicentiu Covrig 1 International Parity Relationships International Parity Relationships (chapter 5)

International Financial Management Vicentiu Covrig 2 The following topics or sections in chapter 5 are not required for the exam: - The real exchange rate (p ) -The Fisher effect (p. 113 to 114)

International Financial Management Vicentiu Covrig 3 Interest Rate Parity Defined Suppose you have $100,000 to invest for one year. You can either 1. invest in the U.S. at i $. Future value = $100,000(1 + i $ ) or 2. trade your dollars for yen at the spot rate, invest in Japan at i ¥ and hedge your exchange rate risk by selling the future value of the Japanese investment forward. The future value = $100,000(F/S)(1 + i ¥ ) Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist, therefore (F/S)(1 + i ¥ ) = (1 + i $ ) Both the spot and forward rate are defined as $/FC

International Financial Management Vicentiu Covrig 4 Interest Rate Parity Defined Formally, (F/S)(1 + i ¥ ) = (1 + i $ ) or if you prefer, IRP is sometimes approximated as 1 + i ¥ 1 + i $ = S F i $ – i ¥ = S F – S

International Financial Management Vicentiu Covrig 5 IRP and Covered Interest Arbitrage If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example. Consider the following set of foreign and domestic interest rates and spot and forward exchange rates. Spot exchange rateS($/£)=$1.25/£ 360-day forward rateF 360 ($/£)=$1.20/£ U.S. discount ratei$i$ =7.10% British discount rate i £ =11.56%

International Financial Management Vicentiu Covrig 6 IRP and Covered Interest Arbitrage 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) Alternatively, this trader could exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) invest £800 at i £ = 11.56% for one year to achieve £ Translate £ back into dollars at F 360 ($/£) = $1.20/£, the £ will be exactly $1,071.

International Financial Management Vicentiu Covrig 7 Interest Rate Parity & Exchange Rate Determination According to IRP only one 360-day forward rate, F 360 ($/£), can exist. It must be the case that F 360 ($/£) = $1.20/£ Why? If F 360 ($/£)  $1.20/£, an astute trader could make money with one of the following strategies:

International Financial Management Vicentiu Covrig 8 Arbitrage Strategy I If F 360 ($/£) > $1.20/£ (For example F 360 ($/£) = 1.30$/£ ) i. Borrow $1,000 at t = 0 at i $ = 7.1%. ii. Exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) invest £800 at 11.56% (i £ ) for one year to achieve £ iii. Translate £ back into dollars, if F 360 ($/£) = 1.30$/£, £ x 1.3 $/£ = $1,160 will be more than enough to repay your dollar obligation of $1,071.

International Financial Management Vicentiu Covrig 9 Arbitrage Strategy II If F 360 ($/£) < $1.20/£ (For example F 360 ($/£) =1.1 $/£ ) i. Borrow £800 at t = 0 at i £ = 11.56%. ii. Exchange £800 for $1,000 at the prevailing spot rate, invest $1,000 at 7.1% for one year to achieve $1,071. iii. Translate $1,071 back into pounds, if F 360 ($/£) = 1.10$/£, $1,071/1.1 = £974 will be more than enough to repay your £ obligation of £

International Financial Management Vicentiu Covrig 10 Absolute Purchasing Power Parity The exchange rate between two currencies should equal the ratio of the countries’ price levels: S($/£) = P£P£ P$P$ The Law of one price: Identical goods sell for the same price, in the same currency, worldwide. Theoretical basis: if the price after exchange-rate adjustment were not equal, arbitrage in the goods worldwide ensures eventually it will. Arbitrage: simultaneously purchase and sale of the same assets on different markets to profit from price discrepancies

International Financial Management Vicentiu Covrig 11 Relative Purchasing Power Parity Relative PPP states that the rate of change in the exchange rate is equal to the differences in the rates of inflation: e = (1 +  £ ) (  $ –  £ ) ≈  $ –  £ If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 2.78% or around 3% PPP says that currencies with high rates of inflation should devalue relative to currencies with lower rates of inflation

International Financial Management Vicentiu Covrig 12 Evidence on PPP PPP doesn’t hold precisely in the real world. Why? Relative PPP is used in practice as a exchange rate forecasting tool

International Financial Management Vicentiu Covrig 13 Forecasting Exchange Rates Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters

International Financial Management Vicentiu Covrig 14 Efficient Markets Approach Financial Markets are efficient if prices reflect all available and relevant information. If this is so, exchange rates will only change when new information arrives F t = E[S t+1 | I t ] Market efficiency requires that investors process information and form reasonable expectation; doesn’t require the above relation to hold In reality the forward rate is a biased and poor predictor of the future spot rate Predicting exchange rates using the efficient markets approach is affordable and is hard to beat.

International Financial Management Vicentiu Covrig 15 Fundamental Approach Involves econometrics to develop models that use a variety of explanatory variables. This involves three steps: - step 1: Estimate the structural model. - step 2: Estimate future parameter values. - step 3: Use the model to develop forecasts. The downside is that fundamental models do not work any better than the forward rate model or the random walk model.

International Financial Management Vicentiu Covrig 16 Technical Approach Technical analysis looks for patterns in the past behavior of exchange rates. Clearly it is based upon the premise that history repeats itself. Thus it is at odds with the Efficient Markets Hypothesis

International Financial Management Vicentiu Covrig 17 Performance of the Forecasters Forecasting is difficult, especially with regard to the future. As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate. The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it.”

International Financial Management Vicentiu Covrig 18 Learning outcomes Calculate a forward rate under the assumptions of covered Interest Rate Parity Determine whether an arbitrageur can profit from given interest rates, and spot and forward rates. If yes, explain in detail the arbitrage strategy and calculate the profits. Define and discuss the law of one price; absolute and relative PPP Forecasting models Recommended end-of-chapterquestions: 3, 4, 7, 10, 11 problems: 1, 2, 3, 4