SUGGESTED READINGS
4.4 LESS RELIABLE INTERNATIONAL PARITY CONDITIONS
−15%
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10%
15%
−2% −1% 0% 1% 2%
Percentage change in the spot rate (S1¥/$/S0¥/$) − 1
Inflation differential (1 + p¥)/(1 + p$) − 1
FIGURE 4.5 RPPP: Japanese Yen versus U.S. Dollar.
Source:Monthly changes in exchange rates and relative inflation over 2001 – 2010 from International Monetary Fund (IMF) Statistics (www.imf.org).
In the long run, inflation differences do prevail eventually. Figure 4.6 graphs the mean annual change in the spot rate against inflation differentials relative to the U.S. dollar for several currencies over 5-year and 10-year forecast horizons. As predicted by RPPP, the dollar rose against currencies with high inflation. Moreover, the influence of inflation is more pronounced over 10-year than over 5-year horizons as RPPP begins to exert itself. RPPP holds in the long run, but is of little use in predicting daily or even quarterly changes in the spot exchange rate.
Forward Rates as Predictors of Future Spot Rates
Forward parityasserts that forward exchange rates are unbiased predictors of future spot rates; that is, Ftd/f=E[Std/f].
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This figure displays average annual changes in the spot rate sf/$ = (S1f/$ − S0f/$)/S0f/$ against average annual inflation differentials relative to the dollar (1 + pf)/(1 + p$) − 1 over 5-year (2006–2010) and 10-year (2001–2010) forecast horizons for Argentina, (S1f/$ − S0f/$), Australia, Canada, Colombia, Egypt, the Eurozone, India, Indonesia, Japan, S. Korea, Malaysia, Mexico, New Zealand, Pakistan, Philippines, Singapore, South Africa, Sri Lanka, Switzerland, and the United Kingdom.
Percentage change in the spot rate
Percentage change in the spot rate
Inflation
differential Inflation
differential 5-year horizon
2006–2010
10-year horizon 2001–2010
FIGURE 4.6 RPPP in the Long Run.
Source:Exchange rates and inflation from IMF Statistics (www.imf.org).
Forward rates should predict future spot rates.
If forward parity holds, then forward premiums should reflect the expected change in the spot exchange rate according to
Ftd/f
S0d/f = E[Std/f]
S0d/f (4.6)
Like the inflation differential in Equation 4.5, forward rates are poor predictors over short horizons. Figure 4.7 plots actual spot rate changes st¥/$ = (Std/f/St – 1d/f)
−1 against the forward premium FPt¥/$ =(Ftd/f/St – 1d/f)−1 for 1-month intervals. If forward parity accurately predicts future spot rates, then the actual and predicted changes in the spot rate should lie along a 45-degree line
s¥t/$=α+βFP¥/$t +et (4.7) withα=0 andβ=1. Contrary to theory, there is no obvious relation between spot rate changes and forward premiums in Figure 4.7. The 1-month forward rate clearly is not a good predictor of the following month’s spot exchange rate. Over longer forecast horizons, the forward parity relation gradually gains credence and begins to look more like the relations in Figure 4.6.
Froot and Thaler review 75 studies of this relation over short forecasting horizons and find a mean slope coefficient in Equation 4.7 of−0.88.4 This finding is referred to as theforward premium anomalyand often is interpreted as evidence of a bias in forward rates. However, this bias (if it exists) is small in magnitude and
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Percentage change in the spot rate (S1¥/$/S0¥/$) − 1
Percentage forward premium (F1¥/$/S0¥/$) − 1
FIGURE 4.7 Forward Parity: Japanese Yen versus the U.S. Dollar.
Source:This figure displays monthly yen-per-dollar forward premiums and spot rate changes over the period 2001 – 2010 based on spot and forward exchange rates from Bloomberg (www.bloomberg.com.)
unreliable as an exchange rate predictor. Moreover, some of the bias is caused by other factors, such as persistence in exchange rate volatility.5
Forward premiums reflect relative opportunity costs of capital.
In this book, we’ll often use forward exchange rates as predictors of future spot rates. At the very least, the forward premium reflects the relative opportunity cost of capital in the two currencies through the interest rate parity relation. The good news is that the forecasting performance of forward rates improves considerably over longer horizons. Indeed, the long-run performance of forward rates as predictors of future spot rates is similar to the long-run performance of inflation differentials in Figure 4.6. For these reasons, forward rates are useful predictors of future spot rates in capital budgeting and other long-horizon forecasting problems.
The International Fisher Relation
The Fisher Equation If investors care about real (inflation-adjusted) returns, then they will set nominal required returns to compensate them for real required returns and expected inflation. The Fisher equation relates the nominal interest rate i to inflation p and a real interest rate .
(1+nominal interest rate)=(1+inflation rate)(1+real interest rate) or (1+i)=(1+p)(1+ )
Real interest rates are inflation-adjusted.
For example, if Chinese inflation is expected to be 5 percent and investors require a real return of 2 percent on a 1-year government discount bond, then the nominal required return on the bond will be iCNY = (1 + E[pCNY])(1 + CNY) − 1 = (1.05)(1.02)−1=0.071, or i=7.1 percent.6 If the discount bond has a par value of 1 million Chinese new yuan, then it would sell for (CNY1,000,000/1.071) = CNY933,707.
Realized real return is determined by the nominal return earned during the period and realized inflation. For example, if a 1-year Chinese government bond yields i =7.1 percent and realized inflation during the year is 3 percent, then the realized real return on the bond is =[(1+i)/(1+p)]−1=(1.071)/(1.03)−1≈ 0.0398, or 3.98 percent.
The Fisher equation can be written alternatively as i=(1+p)(1+ )−1=p+ +p . If real interest and inflation rates are low, then the cross-product term p is small and the approximation i≈p+ is close to the actual value. If p=0.05 and
=0.02, this approximation suggests a nominal required return of i≈0.05+0.02
=7 percent, which is close to the exact answer of 7.1 percent.
Use the exact form of Equation 4.8 when real returns or inflation is high. For example, if expected inflation is 70 percent and required real return is 30 percent, the approximation suggests a nominal return of i ≈0.30 +0.70 = 1.00, or 100 percent. The true nominal required return is i =(1.30)(1.70)−1 =1.21, or 121 percent, which is quite a bit more than the approximation.
Real Interest Parity and the International Fisher Relation
Real interest parity requires d = f.
The Fisher equation has an important consequence for nominal interest rates in an international setting. In particular, substituting the Fisher equation into the ratio of nominal interest rates in Equation 4.4 leads to
(1+id)/(1+if)=[(1+E[pd])(1+ d)] \ [(1+E[pf])(1+ f)] (4.8) According to the law of one price, real (inflation-adjusted) required returns on comparable assets should be equal across currencies so that d = f. This equality is calledreal interest parity.If real interest parity holds, then the (1+ d) and (1+ f) terms cancel and the nominal interest rate differential merely reflects the expected inflation differential. Over t periods, the relation is
(1+id) (1+if)
t
=
(1+E[pd]) (1+E[pf])
t
(4.9)
Equation 4.9 is called theinternational Fisher relation.
Like other parity conditions based on nontraded assets, these two parity relations are unreliable over short horizons. The unreliability of these parity relations over short horizons is further confounded by volatility in realized inflation. Figure 4.8 illustrates the volatility of inflation relative to nominal interest rates with 1-month Euroyen and Eurodollar London Interbank Offer Rate (LIBOR) contracts over 1990 – 2010. The difference between the Eurocurrency yield and realized inflation is
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1990 1995 2000 2005 2010
Realized monthly $ inflation 1-month $ LIBOR rate
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1990 1995 2000 2005 2010
Realized monthly ¥ inflation 1-month ¥ LIBOR rate
U.S. dollar Japanese yen
FIGURE 4.8 Nominal Eurocurrency Interest Rates and Inflation.
Expected change in the spot exchange rate Expected inflation differential
t
Interest rate differential
(1 + id)t (1 + E[pd])
(1 + E[pf])
E[Std/f] S0d/f (1 + if)
Forward-spot differential
International Fisher relation
Unbiased forward expectations Interest rate parity Uncovered RPPP
interest parity
Ftd/f S0d/f
FIGURE 4.9 The International Parity Conditions.
the realized real return in each currency. Real interest parity and the international Fisher relation do not hold over short horizons largely because of inflation volatility.
Real rates are seldom equal across currencies.
Uncovered Interest Parity
Figure 4.9 summarizes the international parity conditions. Note that the ratios that lie diagonally across the figure also must be equal in equilibrium. Because interest rates are tied to the forward premium and the forward premium is a (long-run) predictor of changes in spot rates, then
E[Std/f] S0d/f =
(1+id) (1+if)
t
(4.10) This is calleduncovered interest parityand relates nominal interest rates to expected spot rate changes, and vice versa.7
Similarly, the other diagonal in Figure 4.9 should hold in equilibrium.
Ftd/f S0d/f =
(1+E[pd]) (1+E[pf])
t
(4.11) The inflation differential should predict future changes in the spot rate of exchange.
This completes the circuit of international parity conditions.