FINANCIAL MANAGEMENT
4.3 T HE F ISHER E FFECT
The interest rates that are quoted in the financial press are nominal rates. That is, they are expressed as the rate of exchange between current and future dollars. For example, a nominal interest rate of 8% on a one-year loan means that $1.08 must be repaid in one year for $1.00 loaned today. But what really matters to both parties to a loan agreement is the real interest rate, the rate at which current goods are being converted into future goods.
Looked at one way, the real rate of interest is the net increase in wealth that people expect to achieve when they save and invest their current income. Alternatively, it can be viewed as the added future consumption promised by a corporate borrower to a lender in return for the latter’s deferring current consumption. From the company’s standpoint, this exchange is worthwhile as long as it can find suitably productive investments.
However, because virtually all financial contracts are stated in nominal terms, the real interest rate must be adjusted to reflect expected inflation. The Fisher effect states that the nominal interest rateris made up of two components: (1) a real required rate of returnaand
(2) an inflation premium equal to the expected amount of inflation i. Formally, the Fisher effect is
1+Nominal rate= (1+ Real rate)(1+ Expected inflation rate) 1+r=(1+a)(1+i)
or
r=a+i+ai (4.11)
Equation 4.11 is often approximated by the equationr=a+i.
The Fisher equation says, for example, that if the required real return is 3% and expected inflation is 10%, then the nominal interest rate will be about 13% (13.3%, to be exact). The logic behind this result is that $1 next year will have the purchasing power of $0.90 in terms of today’s dollars. Thus, the borrower must pay the lender $0.103 to compensate for the erosion in the purchasing power of the $1.03 in principal and interest payments, in addition to the
$0.03 necessary to provide a 3% real return.
Application
Brazilians Shun Negative Real Interest Rates on SavingsIn 1981, the Brazilian government spent $10 million on an advertising campaign to help boost national savings, which dropped sharply in 1980. According to theWall Street Journal(January 12, 1981, p. 23), the decline in savings occurred ‘‘because the pre-fixed rates on savings deposits and treasury bills for 1980 were far below the rate of inflation, currently 110%.’’ Clearly, the Brazilians were not interested in investing money at interest rates less than the inflation rate.
The generalized version of the Fisher effect asserts that real returns are equalized across countries through arbitrage—that is, ah=af, where the subscripts h and f refer to home and foreign real rates, respectively. If expected real returns were higher in one currency than another, capital would flow from the second to the first currency. This process of arbitrage would continue, in the absence of government intervention, until expected real returns were equalized.
In equilibrium, then, with no government interference, it should follow that the nominal interest rate differentialwill approximately equal the anticipated inflation differential between the two currencies, or
rh−rf =ih−if (4.12)
where rh andrf are the nominal home and foreign currency interest rates, respectively. The exact form of this relationship is expressed by Equation 4.13:7
1+rh
1+rf = 1+ih
1+if (4.13)
In effect, the generalized version of the Fisher effect says thatcurrencies with high rates of inflation should bear higher interest rates than currencies with lower rates of inflation.
For example, if inflation rates in the United States and the United Kingdom are 4%
and 7%, respectively, the Fisher effect says that nominal interest rates should be about 3%
7Equation 4.13 can be converted into Equation 4.12 by subtracting 1 from both sides and assuming thatrf andif are relatively small.
Exhibit 4.8 The Fisher Effect
–2
–2 –1 1 2 3 4 5
–3 –4 –5
–3 –4 –5 –1 1 2 3 4 5
Parity line
C D
Inflation differential, home country relative to foreign country (%) Interest differential,
in favor of home country (%)
higher in the United Kingdom than in the United States. A graph of Equation 4.12 is shown in Exhibit 4.8. The horizontal axis shows the expected difference in inflation rates between the home country and the foreign country, and the vertical axis shows the interest differential between the two countries for the same time period. The parity line shows all points for which rh−rf =ih−if.
Point C, for example, is a position of equilibrium because the 2% higher rate of inflation in the foreign country (ih−if = −2%) is just offset by the 2% lower HC interest rate (rh−rf = −2%). At point D, however, where the real rate of return in the home country is 1%
lower than in the foreign country (an inflation differential of 2% versus an interest differential of 3%), funds should flow from the home country to the foreign country to take advantage of the real differential. This flow will continue until expected real returns are again equal.
Empirical Evidence
Exhibit 4.9 illustrates the relationship between interest rates and inflation rates for 28 countries as of May 2007. It is evident from the graph that nations with higher inflation rates generally have higher interest rates. Thus, the empirical evidence is consistent with the hypothesis that most of the variation in nominal interest rates across countries can be attributed to differences in inflationary expectations.
The proposition that expected real returns are equal between countries cannot be tested directly. However, many observers believe it unlikely that significant real interest differentials could long survive in the increasingly internationalized capital markets. Most market partic- ipants agree that arbitrage, via the huge pool of liquid capital that operates in international markets these days, is forcing pretax real interest rates to converge across all the major nations.
To the extent that arbitrage is permitted to operate unhindered, capital markets are integrated worldwide.Capital market integrationmeans that real interest rates are determined by the global supply and global demand for funds. This is in contrast to capital market segmentation, whereby real interest rates are determined by local credit conditions. The
Exhibit 4.9
Fisher Effect: Nominal Interest Rate versus Inflation Rate for 28 Developed and Developing Countries as of November 2007
25%
Money market interest rate
20%
15%
10%
5%
0%0% 2% 4% 6%
Inflation rate (measured as the change in the CPI over the past 12 months)
8% 10% 12%
Regression line
Brazil
South Africa
Colombia India
Pakistan
Hungary
Russia
Argentina Turkey
Mexico Australia
Philippines
Japan Switzerland
Israel France
Taiwan Singapore Sweden
New Zealand Britain United States
China Thailand
Czech Republic Canada
Germany
Indonesia
Inflation=Change in 2007 consumer price.
Nominal Rate=3-Month Money Market Rate.
Source:The Economist, May 17, 2007.
difference between capital market segmentation and capital market integration is depicted in Exhibit 4.10. With a segmented capital market, the real interest rate in the United States,aus, is based on the national demandDusand national supplySusof credit. Conversely, the real rate in the rest of the world,arw, is based on the rest-of-world supplySrwand demandDrw. In this example, the U.S. real rate is higher than the real rate outside the United States, oraus>arw.
Once the U.S. market opens up, the U.S. real interest rate falls (and the rest-of-world rate rises) to the new world rate aw, which is determined by the world supply Sw(Sus+Srw)
Exhibit 4.10
The Distinction Between Capital Market Integration and Capital Market Segmentation
Sus
Srw
Drw Dus
aus arw
Credit
Real interest rate
(a) Capital Market Segmentation
Dw =Dus + Drw Sw =Sus + Srw aus
arw aw
Credit
Real interest rate
(b) Capital Market Integration
and world demandDw(Dus+Drw) for credit. The mechanism whereby equilibrium is brought about is a capital inflow to the United States. It is this same capital flow that drives up the real interest rate outside the United States.8
As shown by Exhibit 4.10, in an integrated capital market, the domestic real interest rate depends on what is happening outside as well as inside the United States. For example, a rise in the demand for capital by German companies to finance investments in Eastern Europe will raise the real interest rate in the United States as well as in Germany. Similarly, a rise in the U.S. savings rate, other things being equal, will lower the real cost of capital both in the United States and in the rest of the world. Conversely, a fall in U.S. inflation will lower the nominal U.S. interest rate (the Fisher effect), while leaving unchanged real interest rates worldwide.
Capital market integration has homogenized markets around the world, eroding much, although not all, of the real interest rate differentials between comparable domestic and offshore securities, and strengthening the link between assets that are denominated in different currencies but carry similar credit risks.9To the extent that real interest differentials do exist, they must be due to either currency risk or some form of political risk.
A real interest rate differential could exist without being arbitraged away if investors strongly preferred to hold domestic assets in order to avoid currency risk, even if the expected real return on foreign assets were higher. The evidence on this point is somewhat mixed. The data indicate a tendency toward convergence in real interest rates internationally, indicating that arbitrage does occur, but real rates still appear to differ from each other.10Moreover, the estimated currency risk premium appears to be highly variable and unpredictable, leading to extended periods of apparent differences in real interest rates between nations.11
These differences are displayed in Exhibit 4.11, which compares real interest rates (measured as the nominal interest rate minus the past year’s inflation rate as a surrogate for the expected inflation rate) as of May 2007 versus nominal rates for the same 28 countries shown in Exhibit 4.9. According to this exhibit, countries with higher nominal interest rates (implying higher expected inflation and greater currency risk) tend to have higher real interest rates, resulting in large real rate differentials among some countries.
In addition to currency and inflation risk, real interest rate differentials in a closely integrated world economy can stem from countries pursuing sharply differing tax policies or imposing regulatory barriers to the free flow of capital.
In many developing countries, however, currency controls and other government policies impose political risk on foreign investors. In effect, political risk can drive a wedge between the returns available to domestic investors and those available to foreign investors. For example, if political risk in Brazil causes foreign investors to demand a 7% higher interest rate than they demand elsewhere, then foreign investors would consider a 10% expected real return in Brazil to be equivalent to a 3% expected real return in the United States. Hence, real interest rates in developing countries can exceed those in developed countries without presenting attractive arbitrage opportunities to foreign investors. The combination of a relative shortage of capital
8The net gain from the transfer of capital equals the higher returns on the capital imported to the United States less the lower returns forgone in the rest of the world. Returns on capital must be higher in the United States prior to the capital inflow because the demand for capital depends on the expected return on capital. Thus, a higher real interest rate indicates a higher real return on capital.
9An offshore security is one denominated in the home currency but issued abroad. They are generally referred to as Eurosecurities.
10See, for example, Frederick S. Mishkin, ‘‘Are Real Interest Rates Equal Across Countries? An International Investigation of Parity Conditions,’’Journal of Finance(December 1984): 1345–1357. He finds that, although capital markets may be integrated, real interest rates appear to differ across countries because of currency risk. His findings are consistent with those of Baghar Modjtahedi, ‘‘Dynamics of Real Interest Rate Differentials: An Empirical Investigation,’’European Economic Review 32, no. 6 (1988): 1191–1211.
11Adrian Throop, ‘‘International Financial Market Integration and Linkages of National Interest Rates,’’Federal Reserve Bank of San Francisco Economic Review, no. 3 (1994): 3–18, found that exchange risk caused persistent real interest rate differentials among developed nations for the years 1981 to 1993.
Exhibit 4.11
Real Interest Rate versus nominal Interest Rate for 28 Developed and Developing Countries as of May 2007
12%
Real interest rate (measured as the money market interest rate— the change in the CPI over the past 12 months) 10%
8%
6%
4%
2%
0%
–2%0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
Nominal money market interest rate
11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21%
Regression line Turkey
Brazil
South Africa
Colombia Mexico Philippines
Japan Switzerland
Israel
Taiwan
SingaporeSwedenGermany China Czech Republic New Zealand Australia Canada
Thailand France
Britain
India Hungary Russia
Pakistan
Argentina
Inflation=Change in 2007 consumer price.
Nominal Rate=3-Month Money Market Rate.
Source:The Economist, May 17, 2007.
Application
France Segments Its Capital MarketThroughout the European Monetary System’s September 1992 crisis, the French franc managed to stay within the ERM. Exhibit 4.12 suggests why. It plots two interest rate differentials: (1) the gap between three-month domestic money market rates and the corresponding Eurofranc rate, which is the rate on francs deposited in London in the Eurocurrency market (to be discussed in Chapter 13) and (2) the gap between the domestic money market rate and the bank prime rate.
Exhibit 4.12
France Segments its Money Market to Defend the Franc
Weekly figures Daily figures 5
4 3 2 1 0 –1 –2
%
Jan Feb Mar Apr May Jun Jul Aug Sep 1992
Oct Three-month Eurofranc deposit rate minus
three-month domestic franc money market rate Three-month domestic franc money market rate minus domestic prime lending rate
France supposedly has ended capital market controls, so arbitrage should ensure that the first of these interest differentials (shown by the solid black line) should be approximately zero—as it was until the crisis that began in mid-September. Once trouble began, however, the Euromarket rate exceeded the domestic rate by a big margin for almost two weeks, indicating that the French government was impeding the flow of capital out of France.
The other series sheds more light on what was going on during this period. Until pressures began building in the spring, the prime lending rate slightly exceeded the money market rate, as you might expect because money market rates help determine the banks’ cost of funds. In May, however, the money market rates rose above the prime lending rate, widening to more than 4 percentage points at the height of the crisis.
The obvious conclusion is that the French government was using high money market rates to defend the franc, while forcing banks to lend money at a loss in order to avoid the adverse impact of high interest rates on the French economy.
and high political risk in most developing countries is likely to cause real interest rates in these countries to exceed real interest rates in the developed countries. Indeed, the countries in Exhibit 4.11 with the highest real rates of interest tend to be developing countries.
Investors’ tolerance of economic mismanagement in developed nations also has fallen dramatically, as financial deregulation, abolition of foreign exchange controls, and the process of global portfolio diversification have swollen the volume of international capital flows. With modern technology enabling investors to move capital from one market to another at low cost and almost instantaneously, the pressure on central banks to seem to ‘‘do the right thing’’ is intense. Conversely, those nations that must attract a disproportionate amount of global capital to finance their national debts and that have no credible policies to deal with their problems in a noninflationary way will be forced to pay a rising risk premium. ‘‘Canada’s High Real Interest Rate Comes Down’’ provides a good example of both these trends.
Application
Canada’s High Real Interest Rate Comes DownIn early 1995, the Canadian dollar slipped to an 81/2 -year low against the U.S. dollar. At the same time, with Canada’s inflation rate under 1% and its 10-year government bonds yielding 9.3% (about 1.5 percentage points more than 10-year U.S. Treasury bonds), Canada had the highest real long-term interest rates in the world. The weak Canadian dollar and high real interest rates stemmed from the same source—a lack of confidence in Canada’s longer-term inflation prospects.
Canada had a large current-account deficit, driven by large budget deficits, political uncertainty, and other structural problems that led to investor worries that the current low rate of inflation was only temporary. The persistently high budget deficits, in turn, reflected big spending on generous social welfare programs and overly rigid labor markets, along with a lack of political will to attack these problems. At the same time, investors feared that the government would rely more on tax increases than on spending cuts to reduce the deficit. Further increases in the already high Canadian tax rates would likely drive more of the economy underground and aggravate capital flight. Investors were concerned that if higher tax rates did not reduce the deficit, and the government would not cut spending, Canada might be tempted at some point to monetize its deficits, reigniting inflation.
Adding fuel to these fears was the resignation of John Crow, the highly respected head of the Bank of Canada, Canada’s central bank, and a strong advocate of price stability. Some analysts contended he was forced out by government officials who opposed his tough low-inflation targets. His successor as head of the Bank of Canada followed a relatively lax monetary policy. Investors responded to these worries by driving down the value of the Canadian dollar and by demanding higher interest rates. In the background was the ever-present fear that Quebec separatists would manage to secede from Canada.
By late 1995, Quebec’s separatists had lost their referendum for independence, the federal and provincial governments began slashing their budget deficits and planned even bigger cuts in the future, and Canada’s largest province, Ontario, announced large tax cuts as well. Perceived political risk declined, and investors began focusing on Canada’s low inflation rate. As a result of these favorable trends, the Canadian dollar strengthened and, in early 1996, short-term Canadian interest rates fell below U.S.
rates, after having stayed above U.S. rates for more than a decade. But the yield on 10-year Canadian government bonds stayed about 1 percentage point above that on U.S. Treasuries. With continued low inflation, however, by late 1997, Canada paid about 0.5 percentage pointslessfor 10-year money than did the United States.
Before we move to the next parity condition, a caveat is in order. We must keep in mind that there are numerous interest differentials just as there are many different interest rates in a market. The rate on bank deposits, for instance, will not be identical to that on Treasury bills.
In computation of an interest differential, therefore, the securities on which this differential is based must be of identical risk characteristics save for currency risk. Otherwise, there is the danger of comparing apples with oranges (or at least temple oranges with navel oranges).
Adding Up Capital Markets Internationally. Central to understanding how we can add yen and euro and dollar capital markets together is to recognize that money is only a veil: All financial transactions, no matter how complex, ultimately involve exchanges of goods today for goods in the future. As we will see in Chapter 5, you supply credit (capital) when you consume less than you produce; you demand credit when you consume more than you produce. Thus, the supply of credit can be thought of as the excess supply of goods and the demand for credit as the excess demand for goods. When we add up the capital markets around the world, we are adding up the excess demands for goods and the excess supplies of goods. A car is still a car, whether it is valued in yen or dollars.