International Monetary Economics
Mar 18 2004
Lesson 13
By
John Kennes
Asset Markets and International
Money
Mar 18 2004
Asset Markets and International
Money
Mar 18 2004
– To have an impact on economic conditions, monetary policy
must also affect real interest rate
– The other channel of monetary policy is the exchange rate
– We will examine the links between short-term nominal rates,
the exchange rates, the longer-term interest rate, and the value
of shares and bonds, all of which are determined on f. Markets
– A central theme is the no-profit condition of efficient markets
Short and Long-term interest rates
Mar 18 2004
–
–
–
–
–
Short-term interest rates change frequently, because monetary
policy can change.
If short-term interest rates are expected to increase over the
next two years, the longer term interest rates will also rise.
A two year loan can be arranged in a number of ways: one
loan of two years maturity, or two succesive loans one year
loans.
The no-profit condition implies that these combinations are
equivalent
Therefore, if the interest rate is expected to increase next year,
then the two-year rate must also increase, today
More generally
Mar 18 2004
–
–
–
–
Consider a long-term interest rate of L years maturity.
Ignoring the maturity and risk premia, it is equivalent to a
succesion of one year loans which are rolled over
If the annualized interest rate on the long-term loan is iL, the
return is (1+ iL)L(by the rule of compound interest rates). If the
one-year interest rate expected to prevail t years from now is
ite, where the superscript e denotes an expectation, the return
from such loans is (1+i1)(1+ i2e)...(1+ ite)... (1+ iLe)
The no-profit condition implies that these returns should be
equal
More Generally (2)
Mar 18 2004
–
As a first approximation, this equality states that the long rate
at time t, itL is an average of expected future short rates, plus a
possible risk premium, YtL
itL= (1/L) S it+ie + YtL
•
–
summed over L periods
Note: The risk premium explains the general tendency of the term
structure of interest rates to be upward sloping
A Basic Conclusion: Central Bank’s actions, both current and
anticipated, affect interest rates of all maturities.
How do interest rate changes affect
Bond Prices?
Mar 18 2004
–
–
–
–
Loans can be directly arranged by large borrowers in fancial
markets.
They take the form of bonds, i.e recognition of debt by
borrower along with a schedule of payments concerning both
interest and principal.
Bonds can be traded like any other asset
What determines the price at which bonds sell?
Pricing Bonds (1)
Mar 18 2004
–
–
–
–
–
The bond price represents the present dscounted value of the
payments agreed upon at the time the bond was issued.
Consider the simplest case of a bond which pays € 100 in one
year’s time. (A pure discount bond)
If the interest rate is 5%, what is the value of the bond today?
It is the amount B invested that yields 100 next year.
B(1+0.05)=100
So that B= € 90.70.
Pricing Bonds (2)
Mar 18 2004
–
A payment at in a future year t, n years from today is worth
an/(1+r)n
–
The present value, p, of a consul, a bond that promises an
infinite stream of payments, a, per year is worth
p = a/r
–
–
The price of a consul is clearly inversely related to the interest
rate. Other bonds have finite maturity so the formula is a bit
more complicated.
General principal: higher real interest rates imply lower bond
prices
Pricing Bonds (2)
Mar 18 2004
–
A payment at in a future year t, n years from today is worth
an/(1+r)n
–
The present value, p, of a consul, a bond that promises an
infinite stream of payments, a, per year is worth
p = a/r
–
–
The price of a consul is clearly inversely related to the interest
rate. Other bonds have finite maturity so the formula is a bit
more complicated.
General principal: higher real interest rates imply lower bond
prices
Bond Prices and Yields
Mar 18 2004
Description of the payment
stream
Price in euros
given yield i
Yield given price P
One year pure discount bond
paying 1 euro
1/(1+i)
1/P-1
Ten-year pure discount bond
paying 1 euro in 10th year
1(1+i)10
1/P1/10-1
Bond paying a coupon each year
of C euros for two years plus a
payment of 1 euro in 2nd year
(C<1)
C/(1+i)+(1+C)(1+i)2
(4P(C+1)+ C2)1/2/2P-(1-C/2P)
Consul paying 1 euro per annum,
forever
1/i
1/P
Computer needed for complicated
bonds
Real interest rate arbitrage in the
long run
Mar 18 2004
•
•
•
•
The UIP conditions, with and without risk aversion,
link nominal interest rate at home and abroad
Does the arbitrage argument extend to real interest
rates, which is decisive for intertemporal decisions
It turns out that a purchasing power parity condition
(PPP) implies real interest rate at home and abroad will
be roughly equal
However, like PPP, this is likely to hold only in the
medium to long run.
PPP and the Real Exchange Rate
Mar 18 2004
•
•
•
To compare prices of goods produced at home with
those produced abroad, we need to express them in a
common currency.
If S denotes the exchange rate (say dollars per €1) and P*
is the price of the foreign goods expressed in the foreign
currency (say $) then the domestic price of the foreign
good is P*/S.
Conversely, if P is the price of domestic goods in
domestic currency, their price in the foreign currency is
SP.
PPP and the Real Exchange Rate
Mar 18 2004
•
The real exchange rate, the relative price of foreign gods
in terms of domestic good, is
s
= P/(P*/S)
Both prices in domestic currency
–
=
SP/P*
both prices in foreign currency
As long as goods prices P* and P remain unchanged or move
together, the nominal and real exchange rates move together.
PPP and the Real Exchange Rate
Mar 18 2004
•
•
•
Over short horizons, the nominal and real exchange
rates tend to fluctuate in tandom
In the longer run, nominal and real exchange rates seem
to have lives of their own
Notes:
–
–
Real exchange rates are much more volatile in the short run
It might be worth studying how real exchange rates are
measured in practice. Big Mac index at the Economist, etc
The Real Exchange Rate
Mar 18 2004
–
–
–
The real interest rate parity condition follows from the
assumption that UIP holds: the inflation differential is the
expected rate of appreciation of domestic currency
In the medium and long run, relative PPP implies that the
future rate of depreciation is equal to the future inflation
differential
(St+1-St)/St = p*t+1-pt+1
If forecasts of inflation at home and abroad are consistent with
PPP, the definition of the real interest rate rt= i - tpt+1 and r*t= i –
*
tp t+1 implies the international Fisher equation
rt = r*t
Stock Prices
Mar 18 2004
–
–
–
–
Shares in firm (stocks) are held by households (and their
intermediaries) and are issued by firms to aquire resources for
capital expenditure.
Stocks are risky assets because they represent a claim to a share
of future profits after costs - wages, interest payments, rent,
and other expenses - are paid
How are stocks valued?
Once again, we make use of a no-profit condition, comparing
now a riskless treasury bill paying a constant yield r per
annum with a traded share in a company that pays all its
profits out at the end of each period as dividends, dt .
Stock Prices
Mar 18 2004
–
–
The hitch is that while the T bill pays a fixed yield, the stock
investment consists of the dividend plus possible capital gains
or losses when the share price changes.
If qt is the share price at the beginning of period t, the rate of
retrun on the company shares is the dividend yield dt/qt plus
the anticpated capital gain (qt+1-qt)/qt. The no-profit condition
implies
r = dt/qt + (qt+1- qt)/qt
Yield on T Bill = dividend yield + capital gain
– Which means stock prices depend inversely on r
qt = (dt + qt+1)/(1+r)
Rational Pricing of Stock Prices
Mar 18 2004
–
–
–
–
–
If qt depends on qt+1 and qt+1 depends on qt+2 will such an
endless repitition converge to anything sensible?
If stock prices dont grow faster than the real interest rate r,
the current stock price is well defined
qt = S(1/(1+r))i dt+i summed over i=0 to infinity
Which expresses the current stock price as the present value of
future earnings only.
The role of the future price disappears. Market value is based
on what it expects to earn now and in the indefinite future
Formula called fundamental valuation of an asset. Do stock
prices reflect rational pricing of future company profits?
Nominal Exchange Rates and
National Money Markets
Mar 18 2004
–
–
–
–
The exchange rate can be thought of as the realtive price of
national monies
Much as share price changes affect the return on stock, the
exchnage rate affects the opportunity cost of holding various
currencies, and assets denominated in these currencies
The interest rate parity condition UIP bears a telling
resemblence to the share price equation
We want to relate this the financial integration line in IS-LM
analysis: i.e the required foreign rate of return i*
Nominal Exchange Rates and
National Money Markets (2)
Mar 18 2004
–
–
–
–
–
The UIP condition without risk aversion is given by
St = ((1+i*t) / (1+i*t)) (tSt+1)
The current spot exchange rate St is now determined by the
domestic and foreign interest rates and by the market’s current
expectation of next period’s interest rate, tSt+1
Like all asset prices, the nominal exchange rate is forward
looking.
What happened in the past are bygones. The exchange rate is
totally free to jump (a non-predetermined variable)
An appreciation in the future shows up immediately in the
current exchange rate.
Nominal Exchange Rates and
National Money Markets (3)
Mar 18 2004
–
–
–
–
–
As with stock prices St is driven by expectation of St+1 which is
driven by expectation of St+2 and so on.
To keep thngs simple, ignore uncertainty, we get
St = ((1+i*t) / (1+i*t)) ((1+i*t+1) / (1+i*t+1)) (tSt+2)
And repeat n times
St = ((1+i*t) / (1+i*t)) ((1+i*t+1) / (1+i*t+1)) ... ((1+i*t) / (1+i*t))(tSt+n+1)
As with stock prices, the current exchange rate reflects all
current and future interest rates at home and abroad, and its
own long run value
It shows how tight monetary in the future (i is expected to
rise) can lead to an appreciation today (S increases).
Resolving an apparent contradiction
Mar 18 2004
–
–
–
Suppose interest rates at home rise unexpectedly. According to
our equation, an appreciation should result.
Yet we know from UIP that higher interest rates at home
should be associated with a depreciation of our currency (S
falling)
Is this a contradiction?
Resolving an apparent contradiction
(2)
Mar 18 2004
–
–
The contradiction is only apparent, once we recognize that we
are implicitly assuming that the exchange rate does not rise in
the long run.
The two ways of reasoning are reconciled in the following
figure
An increase in the domestic interest
rate
Mar 18 2004
i
i*,i
S
Time
Resolving an apparent contradiction
(2)
Mar 18 2004
–
–
–
–
As the domestic interest rate rises above the world rate i* the
exchange rate appreciates temporary, but is expected to
depreciate back to its initial value
As required by UIP, an expected depreciation of the domestic
currency (a capital loss) offsets the interest rate advantage at
home.
Holding the future expected exchange rate constant, the only
way for the current exchange rate to depreciate in future
periods is to appreciate now.
Capital movements are not necessary as long as asset returns
are equalized. The outcome of integrated efficient fin. markets.
Next class
Mar 18 2004
–
–
How do fundamentals determine the nominal exchange rate?
Market efficieny or Speculative mania? Implications for
international money
•
•
Noise traders
Bubbles
– Exchange rate determination in the short run
•
•
•
•
•
Mussa stylized facts and the asset behaviour of exchange rates
Money and goods market equilibrium: Mt /Pt =L(Y, it )
Insert UIP for it
Overshooting: Basic Dornbusch (1976) result.
IS-LM interpretation