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International Parity Conditions CHAPTER 6 181 Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium (or expected change in the spot rate), invest in the higher interest yielding currency. If the difference in interest rates is less than the forward premium (or expected change in the spot rate), invest in the lower interest yielding currency. Using this rule of thumb should enable Fye Hong to choose in which direction to go around the box in Exhibit 6.7. It also guarantees that he will always make a profit if he goes in the right direction. This rule assumes that the profit is greater than any transaction costs incurred. This process of CIA drives the international currency and money markets toward the equilibrium described by interest rate parity. Slight deviations from equilibrium provide opportunities for arbitragers to make small riskless profits. Such deviations provide the supply and demand forces that will move the market back toward parity (equilibrium). Covered interest arbitrage opportunities continue until interest rate parity is reestablished, because the arbitragers are able to earn risk-free profits by repeating the cycle as often as possible. Their actions, however, nudge the foreign exchange and money markets back toward equilibrium for the following reasons: 1. The purchase of yen in the spot market and the sale of yen in the forward market narrows the premium on the forward yen. This is because the spot yen strengthens from the extra demand and the forward yen weakens because of the extra sales. A narrower premium on the forward yen reduces the foreign exchange gain previously captured by investing in yen. 2. The demand for yen-denominated securities causes yen interest rates to fall, and the higher level of borrowing in the United States causes dollar interest rates to rise. The net result is a wider interest differential in favor of investing in the dollar. Uncovered Interest Arbitrage (UIA) A deviation from covered interest arbitrage is uncovered interest arbitrage (UIA), wherein investors borrow in countries and currencies exhibiting relatively low interest rates and convert the proceeds into currencies that offer much higher interest rates. The transaction is uncovered, because the investor does not sell the higher yielding currency proceeds forward, choosing to remain uncovered and accept the currency risk of exchanging the higher yield currency into the lower yielding currency at the end of the period. Exhibit 6.8 demonstrates the steps an uncovered interest arbitrager takes when undertaking what is termed the yen carry-trade. The yen carry-trade is an age-old application of UIA. Investors, from both inside and outside Japan, take advantage of extremely low interest rates in Japanese yen (0.40% per annum) to raise capital. Investors exchange the capital they raise for other currencies like U.S. dollars or euros. Then they reinvest these dollar or euro proceeds in dollar or euro money markets where the funds earn substantially higher rates of return (5.00% per annum in Exhibit 6.8). At the end of the period a year, in this case they convert the dollar proceeds back into Japanese yen in the spot market. The result is a tidy profit over what it costs to repay the initial loan. The trick, however, is that the spot exchange rate at the end of the year must not change significantly from what it was at the beginning of the year. If the yen were to appreciate significantly against the dollar, as it did in late 1999, moving from 120/$ to 105/$, these uncovered investors would suffer sizable losses when they convert their dollars into yen to repay the yen they borrowed. Higher return at higher risk. The Mini-Case at the end of this chapter details one of the most frequent carry trade structures, the Australian dollar/japanese yen cross rate.
182 CHAPTER 6 International Parity Conditions EXHIBIT 6.8 Uncovered Interest Arbitrage (UIA): The Yen Carry Trade Investor borrows yen for 360 days at 0.40% per annum Start End 10,000,000 1.004 10,040,000 Repaid 10,500,000 Earn Japanese Yen Money Market 460,000 Profit Investor converts yen to dollars at spot rate Spot: 120.00 = $1.00 360-day period Expected Spot: 120.00 = $1.00 Investor converts dollars back to yen at expected spot rate U.S. Dollar Money Market $83,333.33 1.05 $87,500.00 Investor deposits dollars in U.S. dollar money market at 5.00% per annum Equilibrium between Interest Rates and Exchange Rates Exhibit 6.9 illustrates the conditions necessary for equilibrium between interest rates and exchange rates. The vertical axis shows the difference in interest rates in favor of the foreign currency, and the horizontal axis shows the forward premium or discount on that currency. The interest rate parity line shows the equilibrium state, but transaction costs cause the line to be a band rather than a thin line. EXHIBIT 6.9 Interest Rate Parity and Equilibrium 4 3 2 1 Percentage premium on foreign currency ( ) 4.83 6 5 4 3 2 1 1 2 3 4 5 6 Percentage difference between foreign ( ) and domestic interest rates 1 2 3 4 X Y Z If market interest rates were at point U, covered interest arbitrage profits are available, and would be undertaken until the market drove interest rate differences back to point X, Y, or Z. U
International Parity Conditions CHAPTER 6 183 Transaction costs arise from foreign exchange and investment brokerage costs on buying and selling securities. Typical transaction costs in recent years have been in the range of 0.18% to 0.25% on an annual basis. For individual transactions, like Fye Hong s covered interest arbitrage (CIA) activities illustrated in Exhibit 6.7, there is no explicit transaction cost per trade; rather, the costs of the bank in supporting Fye Hong s activities are the transaction costs. Point X in Exhibit 6.9 shows one possible equilibrium position, where a 4% lower rate of interest on yen securities would be offset by a 4% premium on the forward yen. The disequilibrium situation, which encouraged the interest rate arbitrage in the previous CIA example of Exhibit 6.7, is illustrated in Exhibit 6.9 by point U. Point U is located off the interest rate parity line because the lower interest on the yen is 4% (annual basis), whereas the premium on the forward yen is slightly over 4.8% (annual basis). Using the formula for forward premium presented earlier, we calculate the forward premium on the Japanese yen as follows: 106.00/$ - 103.50/$ 103.50/$ * 360 Days 180 Days * 100 = 4.83% The situation depicted by point U is unstable, because all investors have an incentive to execute the same covered interest arbitrage. Except for a bank failure, the arbitrage gain is virtually risk-free. Some observers have suggested that political risk does exist, because one of the governments might apply capital controls that would prevent execution of the forward contract. This risk is fairly remote for covered interest arbitrage between major financial centers of the world, especially because a large portion of funds used for covered interest arbitrage is in eurodollars. The concern may be valid for pairings with countries not noted for political and fiscal stability. The net result of the disequilibrium is that fund flows will narrow the gap in interest rates and/or decrease the premium on the forward yen. In other words, market pressures will cause point U in Exhibit 6.9 to move toward the interest rate parity band. Equilibrium might be reached at point Y, or at any other locus between X and Z, depending on whether forward market premiums are more or less easily shifted than interest rate differentials. Uncovered interest arbitrage takes many forms in global financial markets today, and opportunities do exist for those who are willing to bear the risk (and potentially pay the price). Global Finance in Practice 6.2 describes one such speculation, foreign-currency home mortgages in Hungary, which as described, can turn an innocent homeowner into a foreign currency speculator. GLOBAL FINANCE IN PRACTICE 6.2 Hungarian Mortgages No one understands the linkage between interest rates and currencies better than Hungarian homeowners. Given the choice of taking mortgages out in local currency (Hungarian forint) or foreign currency (Swiss francs for example), many chose francs because the interest rates were lower. But regardless of the actual interest rate itself, the fall in the value of the forint against the franc by more than 40% resulted in radically increasing mortgage debt service payments in Hungarian forint. These borrowers are now trying to have their own mortgages declared unconstitutional in order to get out from under these rising debt burdens. (continued)
184 CHAPTER 6 International Parity Conditions Hungarian forint/swiss francs (monthly, January 2000 January 2014) 260 240 Rising to HUN 240 = 1.00 CHF 220 +41% 200 180 160 140 Jan-00 Jun-00 Nov-00 Apr-01 Sep-01 Feb-02 Jul-02 Dec-02 Averaging about HUN 170 = 1.00 CHF May-03 Oct-03 Mar-04 Aug-04 Jan-05 Jun-05 Nov-05 Apr-06 Sep-06 Feb-07 Jul-07 Dec-07 May-08 Oct-08 Mar-09 HUN/CHF spot rate Aug-09 Jan-10 Jun-10 Nov-10 Apr-11 Sep-11 Feb-12 Jul-12 Dec-12 May-13 Forward Rate as an Unbiased Predictor of the Future Spot Rate Some forecasters believe that foreign exchange markets for the major floating currencies are efficient and forward exchange rates are unbiased predictors of future spot exchange rates. Exhibit 6.10 demonstrates the meaning of unbiased prediction in terms of how the forward rate performs in estimating future spot exchange rates. If the forward rate is an unbiased predictor of the future spot rate, the expected value of the future spot rate at time 2 equals the present forward rate for time 2 delivery, available now, E 1 (S 2 ) = F 1,2. Intuitively, this means that the distribution of possible actual spot rates in the future is centered on the forward rate. The fact that it is an unbiased predictor, however, does not mean that the future spot rate will actually be equal to what the forward rate predicts. Unbiased prediction simply means that the forward rate will, on average, overestimate and underestimate the actual future spot rate in equal frequency and degree. The forward rate may, in fact, never actually equal the future spot rate. The rationale for this relationship is based on the hypothesis that the foreign exchange market is reasonably efficient. Market efficiency assumes that (1) All relevant information is quickly reflected in both the spot and forward exchange markets; (2) Transaction costs are low; and (3) Instruments denominated in different currencies are perfect substitutes for one another. Empirical studies of the efficient foreign exchange market hypothesis have yielded conflicting results. Nevertheless, a consensus is developing that rejects the efficient market hypothesis. It appears that the forward rate is not an unbiased predictor of the future spot rate and that it does pay to use resources to attempt to forecast exchange rates. If the efficient market hypothesis is correct, a financial executive cannot expect to profit in any consistent manner from forecasting future exchange rates, because current quotations in the forward market reflect all that is presently known about likely future rates. Although future exchange rates may well differ from the expectation implicit in the present forward market Oct-13
International Parity Conditions CHAPTER 6 185 EXHIBIT 6.10 Forward Rate as an Unbiased Predictor of Future Spot Exchange Rate S 2 F 2 S 1 Error Error F 3 F 1 S 3 Error S 4 t 1 t 2 t 3 t 4 Time The forward rate available today (t) for delivery at a future time (t + 1) is used as a forecast or predictor of the spot rate at time t + 1. The difference between the spot rate which then occurs and the forward rate is the forecast error. When the forward rate is termed an unbiased predictor of the future spot rate it means that the errors are normally distributed around the mean future spot rate (the sum of the errors equal zero). quotation, we cannot know today in which way actual future quotations will differ from today s forward rate. The expected mean value of deviations is zero. The forward rate is therefore an unbiased estimator of the future spot rate. Tests of foreign exchange market efficiency, using longer time periods of analysis, conclude that either exchange market efficiency is untestable or, if it is testable, that the market is not efficient. Furthermore, the existence and success of foreign exchange forecasting services suggest that managers are willing to pay a price for forecast information even though they can use the forward rate as a forecast at no cost. The cost of buying this information is, in many circumstances, an insurance premium for financial managers who might get fired for using their own forecast, including forward rates, when that forecast proves incorrect. If they bought professional advice that turned out wrong, the fault was not in their forecast! If the exchange market is not efficient, it is sensible for a firm to spend resources on forecasting exchange rates. This is the opposite conclusion to the one in which exchange markets are deemed efficient. Prices, Interest Rates, and Exchange Rates in Equilibrium Exhibit 6.11 illustrates all of the fundamental parity relations simultaneously, in equilibrium, using the U.S. dollar and the Japanese yen. The forecasted inflation rates for Japan and the United States are 1% and 5%, respectively a 4% differential. The nominal interest rate in the U.S. dollar market (1-year government security) is 8% a differential of 4% over the Japanese nominal interest rate of 4%. The spot rate is 104/$, and the 1-year forward rate is 100/$. Relation A: Purchasing Power Parity (PPP). According to the relative version of purchasing power parity, the spot exchange rate one year from now, S 2, is expected to be 100/$: S 2 = S 1 * 1 + p 1.01 = 104/$ * $ 1 + p 1.05 = 100/$. This is a 4% change and equal, but opposite in sign, to the difference in expected rates of inflation (1% - 5%, or -4%).