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September 12, 1980

I n terest Rates and Exchan ge Rates: I

The Relationship
Conventional wisdom says that a rise in U.S.
interest rates relative to abroad strengthens
the dollar on the foreign exchanges by attracting international capital to our shores. This
argument appears so commonsensical that
market commentators cite interest rates more
frequently than any other factor' when explaining day-to-day changes in exchange
rates.

u.s.

And yet, whenever
interest rates have
increased in recent years, the dollar has
depreciated as often as it has appreciated.
True, the dollar has moved closely with U.S.
interest rates this year, but it fell fairly steadily
during 1977 and 1978, when
interest
rates rose above foreign rates. This pattern is
evident for the dollar and the German mark
(Chart 1), and also for the dollar relative to
other major currencies.

u.s.

This ambiguous relation seems all the more
puzzling because the difference between
and foreign interest rates has moved virtually in "lock-step" with the forward discount on the dollar -that is, the current value
ofthe dollar minus its forward (futures) value
(Chart 2). This means that if interest-rate differences across countries do not cause a
change in the current value of the dollar, they
must lead to a change in its futures value.
Thus we should examine the circumstances
under which a change in relative interest
rates will cause the current value of the dollar
to vary, versus those circumstances under
which its forward value will be affected.

u.s.

Paradox?
Two basic factors can cause interest rates to
rise-but they have very different impacts
upon exchange rates. In effect, every interest
rate is composed of a real yield plus an inflation premium. The real part ofthe interest
rate is simply the compensation in terms of
goods and services paid to the lender for the

use of his money; this is equal to the difference between the purchasing power of the
amount repaid and the purchasing power of
the original loan. In addition, part of each
interest payment is designed to compensate
the lender for the erosion in the purchasing
powerofthe asset due to inflation. This part of
the interest payment is the "inflation premium". For example, suppose that the interest rate on a one-year loan is 12 percent wh i Ie
inflation is expected to average 10 percent
over the year. The purchasing power of the
principal thus declines by 10 percent during
the year, so that 10 of the 12 percentage
points of the interest charge represents an
inflation premium -leaving a real interest
payment of 2 percentage points.
As its name implies, the inflation-premium
part of market interest rates reflects the inflation anticipated over the life ofthe loan.
Hence, so long as the real yield remains fixed,
market interest rates will rise or fall as expected inflation waxes or wanes. For that
reason, interest rates generally tend to be
highest in those nations with relatively high
inflation rates.
The real interest-rate portion of market yields,
on the other hand, reflects in the long run the
productivity of a nation's economy. Short-run
fluctuations in the real yield usually result
from cyclical fluctuations or changes in liquidity. For example, in view of the substantiallag between money changes and price
changes, sudden reductions in money growth
tend to reduce liquidity and hence (all other
factors equal) to raise the real interest rate.
Likewise, business-cycle variations in real income can affect real interest rates by changing the real demand for money.

Arbitrage ...
In contrast to its ambiguous relation with exchange rates, the interest differential

With this exchange risk "covered", arbitragers are encouraged to move funds between
countries until the interest-rate differences
equal the forward discount on the dollar. Actual or prospective capital controls of course
can impede such international transfers of
funds and so "break" this linkage. However,
such controls have not been significant in
major industrial countries in recent years.

the U.S. and abroad usually varies closely
and consistently with the forward discount on
the dollar. The forward discount vis-a-vis
(say) the German deutschemark (OM) is simply the percentage difference between the
amount of marks one dollar wi II buy now and
the forward (futures) price of marks (Chart 2).
The forward price is the amount of OM an
individual can contract to buy now with a
dollar at some future date.

The forward value of the dollar tends to reflect market expectations about what the
(spot) price of the dollar will be in the future.
Suppose, for example, that the one-year forward priceof marks was 20M/dollar, butthat
the price expected one year hence was only
1 .800M/dollar. Then an individual who purchased 2 OM now for one dollar cou Id expect
to sell them later for about $1.10. The potential profit from such "speculation", although
involving some risk, tends to make the forward and anticipated future values of the dollar move together.

In the absence of capital controls, profitseeking investors will seek to obtain roughly
the same dollar yield from comparable
and foreign securities ("comparable" in
terms of maturity, liquidity, and default risk).
A U.S. citizen, for example, can purchase
marks in the spot exchange market and use
the proceeds to purchase a German security.
Moreover, he can hedge the return against a
fall in the mark (relative to the dollar) by
selling now the OM (that he will receive at
maturity) in the forward-exchange market.
Thus he knows immediately what his return
in dollars will be; and he knows that this
return will not be affected by any future
changes in the value of the OM against the
dollar.

u.s.

... and exchange
rates
Taken together, these facts largely explain the
"paradoxical" variations in exchange rates
vis-a-vis interest rates. Basically, increases in
real interest rates tend to raise the current
value of the dollar, while interest-rate increases due to inflationary expectations tend
to lower the forward rate. Consider, for example, a situation where
money growth
decelerates, but presumably only ona temporary basis. The likely consequence is a
temporary shortage of liquidity, along with a
rise in real U.S. interest rates. Foreigners thus
find it attractive to purchase
securities.
The resulting increase in the demand for dollars then pushes up the spot exchange value
ofthe dollar. But without a change in inflation
expectations (and thus in the expected level

u.s.

u.s.

2

Percent

Chart

Chart 1

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12
10

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8

,

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2.3

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4

2

2:1

U. S.lGe!man Interest
Rate Differential

__
1976

.1..- _

_

1977

..1-

_

8
6
4

2.0

2 ......
/

2,2

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o
-4'-

12

2.4 10

6

-2

2,5

D M/ Dollar Exchange Rate

2

V/\"v\
.
.

_

1978

-1 .-_-:----'-

1979

U. S.l German
('
Forward Discount. /

A. ::-2
_

_

1980

,

..
/"

.

-'1.7 -4 L- _ _
1976

t/ \,
U. S.lGerman
Interest Rate Differential
1_

_

_

1977

..L- _

_

1978

-1.- _

_

1979

...1

-_---1

1980

inflation here relative to abroad. In this case,
U.s. interest rates rose because of increases in
the inflation premium, and the dollar fell as a
result.

of U.S. prices), the future value of the dollar
will not change. In this case the interest-rate
differential will equal the forward discount,
because the higher U.S. interest rate will lead
to a higher spot rate for the dollar.

In fact, since the beginning of the floating
exchange-rate regime in 1973, prolonged interest-rate increases have more often than not
been associated with a depreciation of the
currency. Interest-rate changes thus largely
reflect variations in expected inflation. This is
not surprising, in view ofthe substantial variations in money-growth rates here and abroad
since 1973. But this observation also illustrates the crucial importance of monetary
policies in determining the relations observed between interest rates and exchange
rates. In particular, to the extent that the
recent Federal Reserve change in moneycontrol procedures leads to steadier money
growth and less inflation variability, U.S. interest rates and the foreign-exchange value of
the dollar may move together more often in
the future than they have in the past. This
point is discussed further in our next article.

On the other hand, a rise in U.S. interest rates
due to an increase in anticipated inflation will
not attract foreign investment into U.s securities. That is, the higher u.s. rates will just
compensate investors for the expected increase in inflation, and so thecurrentvalue of
the dollar will not necessarily rise. However,
because of the anticipated rise in the level of
u.s. prices, the future value of the dollar will
be expected to fall, driving down the forward
exchange value of the dollar. In this case the
interest-rate differential will equal the forward discount on the dollar, because the
higher U.s. interest rate will be associated
with a fall inthe forward value of the dollar.
Furthermore, the spot value of the dollar will
subsequently fall as U.S. prices rise above
those abroad. Indeed, because exchange
rates often move ahead of current trends, the
dollar's spot value may even fall somewhat
immediately.

MichaelKeran& CharlesPigott

It should now be clear why the dollar has
moved closely with U.S. interest rates this
year, after moving in the opposite direction in
1977 and 1978.The increase in U.s. interest
rates early in 1980 largely reflected a rise in
real yields, due to the liquidity squeeze
caused by reduced U.S. money growth and'
the Federal Reserve's credit-restraint program. Hence the dollar rose during this period. Butthen thedollardeclined in the spring,
in the wake of recession-caused declines in
market and real interest rates. On the other
hand, during the 1977-78 period, increasing
money growth in the u.s. led to accelerating

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BANKING DATA-TWELFTHfEDERAL
RESERVE
DISTRICT
(Dollaramounts millions)
in
Selected
Assets Liabilities
and
largeCommercialDanks
Loans
(gross,
adjusted) investments*
and
Loans
(gross,
adjusted) total#
Commercial industrial
and
Real
estate
Loans individuals
to
Securities
loans
U.s. Treasury
securities*
.
Other securities*
Demanddeposits total#
Demanddeposits adjusted
Savings
deposits total
Timedeposits total#
Individuals,
part.& corp.
(Large
negotiable
CD's)
WeeklyAverages
of Daily Figures
MemberBani,Reserve
Position
Excess
Reserves )/Deficiency - )
(+
(
Borrowings
Net freereserves )/Netborrowed- )
(+
(

Amount
Outstanding

Change
from
yearago
Dollar
Percent

Change
from

8/27/80

8/20/80

138,499
116,778
33,812
47,427
23,532
872
6,337
15,384
42,288
31,106
29,393
62,830
54,647
23,567

384
341
194
213
45
16
47
4
-1,299
- 431
8
241
247
198

-

Weekended

Weekended

8/27/80

8/20/80

86
24
110

41
36
5

-

4.9
7.2
6.4
18.4
1.8
- 56.7
- 15.6
1.1
0.5
0.1
3.7
19.1
23.3
23.0

6,520
7,864
2,039
7,376
422
1,143
1,174
170
194
20
1,118
10,056
10,310
4,404

Comparable
year-ago
period

-

33
146
114

* Excl,udes
tradingaccountsecurities.
# Includesitemsnot shownseparately.
Editorialcomments
maybe addressed theeditor (William 8url(e)or to the author.... Free
to
copies this
of
andother Federal
Reserve
publications beobtained callingor writing thePublicInformation
can
by
Section,
Federal
Reserve
Bank-of Francisco, Box7702,SanFrancisco
San
P.O.
94120.Phone
(415)544-2184.