International Monetary Economics
Mar 16 2004
Lesson 12
By
John Kennes
ASSET MARKETS
A REVIEW
Mar 16 2004
Key Concepts
Mar 16 2004
–
–
–
–
–
–
–
–
–
–
Assets
Arbitrage
Covered interest parity (CIP)
Uncovered interest parity (UIP)
Spot exchange rate
Hedged
Term structure of interest rate
International Fisher Equation
Random walk
Undervaluation, overvaluation
Convenient References
Mar 16 2004
–
Any good macro textbook
•
International Economics: Theory and Policy (2003) by Krugman and
Obstfeld
–
•
chapters 13 and 14
Macroeconomics: A European Text (2001) by Burda and Wyplosz *
–
chapter 19.
What are Asset Markets?
Mar 16 2004
•
•
•
Asset markets put a price tag on the future and risk
They allow households and coorperatons to decide on
savings and borrowing without having to gather a whole
array of information that affects their own future.
Allow savers who are most willing to bear risk to do so,
at minimum cost
Properties of Assets
Mar 16 2004
•
•
•
•
Financial assets are traded with ease in well-organized
financial markets
They are durable, and cheap to store
Finacial markets equate the price of asset stocks, rather
than the flow increments to the stocks that are created
each period.
For these stocks to be held voluntarily, returns among
similar assets – similar in terms of risk and maturity –
must be equalized.
No-profit condition
Mar 16 2004
•
•
•
•
The no-profit condition is a characteristic of efficient
financial markets.
In the absence of risk it takes the form of arbitrage.
A good example is covered interest parity
Covered interest parity (CIP): When capital is
internationally mobile, a higher domestic interest rate is
matched by a forward exchange rate premium.
CIP
Mar 16 2004
•
•
•
Based on the comparison of the return from a domestic
asset with the return from a foreign asset with similar
risk characteristics.
Example, an investor can obtain an annual interest rate i
on riskless British Treasury Bills and i* on equally
riskless assets issued in euros.
The two investments are not equivalent, since the
sterling value of the euro may change over the
investment period.
How to solve for the CIP condition?
Mar 16 2004
•
•
•
•
Let the price of the pound in euros at the start of the
period be St.
By selling one pound at the beginning of the year, a
British investor obtains St euros that she can invest to
receive (1+i*)St at the end of the year.
This is a completely certain return since i* and St are
known at the beginning of the year
But it is in terms of euro and the exchange rate in the
next period is uncertain.
How to eliminate the risk?
Mar 16 2004
•
•
•
The investor can eliminate all risk by signing a forward
contract at the begining of the year to sell (1+i*) St euros
against ponds at the end of the year.
The forward contract specifies the exchange rate at
which this sum will be converted from euros to pounds:
it is the one year ahead forward exchange rate, denoted
Ft .
The forward exchange rate, corresponds to a transaction
which implies a delay date of delivery.
A Perfect Hedge
Mar 16 2004
•
•
•
The forward exchange rate Ft is to be distinguished from
the spot exchange rate, St, which implies immediate
delivery.
Thus the British investor can be certain that for every
pound invested this way, she will receive (1+i*) St/ Ft
pounds at the end of the year
Because all exchange risk is eliminatd, the foreign
investment is said to be covered or hedged.
CIP condition
Mar 16 2004
•
•
•
The investor could have invested her money in the safe
sterling asset and receive (1+i) at the end of the year.
Both strategies are riskless, so arbitrage guarantees that
the returns must be equal. This is the CIP condition:
(1 + i*)St / Ft = (1 + i)
A useful approximation:
i* = i + (Ft - St)/St
Interest rate in Euroland = interest rate in UK + forward premium
Where to look for forward rates
Mar 16 2004
–
–
–
–
Forward rate are quoted in the Financial Times
Currencies are generally sold forward at standardized intervals
(e.g. 1, 3, or 12 months), but in the retail market banks are
willing to customize forward rates.
The price of such a contract is usually stated as a forward
premium or discount with respect to the spot price.
A forward premium on the Danish krone vis-a-vis the US
dollar exists when the forward price of dollars in krone is
lower than the current spot price
Numerical Example
Mar 16 2004
–
–
–
–
–
–
The forward premium is (Ft+1 – St)/St, it is a discount if
negative.
(Ft+1 – St)/St is similar to a rate of interest over the period of a
contract
To obtain its per annum equivalent, we compound it.
For example, for a 3 month contract (1+r)4 which gives
(Ft+1/St)4 since 1 + (Ft+1 – St)/St = (Ft+1/St)
A premium of 2% per annum on the three-month krone/US
dollar forward rate means that (Ft+1/St)4 = 1.02 so that Ft+1/St =
1.00496: Ft+1 is .496% above St.
Check the Financial Times and do such calculations
Numerical Example
Mar 16 2004
DOLLAR SPOT – FORWARD AGAINST THE DOLLAR
(5 May 1992, The Financial Times)
May 1
Day’s
Spread
Close
One
month
% p.a.
Three
months
% p.a
Denmark
6.35256.3925
6.35506.3600
3.553.95
ordeis
7.08
9.4010.10
dis
-6.13
What happens when the investor does
not eliminate risk by engaging in a
forward contract?
Mar 16 2004
–
–
The foreign investment is left open or unhedged, the investor
takes a risk, and this will involve a risk premium
Risk premium depends on two concepts
•
•
Risk Diversification
The Price of Risk
Risk Diversification
Mar 16 2004
–
–
–
–
–
–
–
–
Investments A and B involve independent flips of coins
Heads give €100, tails nothing
The expected value is €50
Compare A and B with a third, C
The expected value of C is €50 but its variability is lower.
To see this list four outcomes HH = €100, HL, LH = €50, LL=
€50.
Diversification reduces risk. Diversifiation even greater when
returns move in opposite directions, less so otherwise.
(negative/positivecorrelation)
Impossible to reduce all risk, macro-risk, policy changes
The Price of Risk
Mar 16 2004
–
–
–
–
–
–
–
A and B have same expected value. How uch are you willing to
pay to aquire either investment?
Most people are risk averse and would rather get €50 than buy
a risk investment with the same expected value
If you are willing to pay € 48 the risk premium is €2 or 4% of
the risk free price.
If Demand and supply are equated, the risk premium
represents the market price of risk
What about investment C, the risk premium might be 2%
Facing less risk the investors prefer the new asset.
Macroeconomic risk cannot be diversified much
Uncovered Interest Rate Parity
(UIP) condition (1)
Mar 16 2004
–
–
–
–
What happens when the investor does not eliminate risk by
engaging in a futures contract
To examine the new situtation, we start by assuming that the
investor is risk neutral, so that the risk premium is zero.
The strategy is the same as before, except the euro investment
will not be sold at the end of the year using the forward
exchange rate Ft aggreed upon earlier, but at the prevailing
spot exchange rate St+1.
Going through the same reasoning, the expected return in
pounds from one pound invested in euros is (1+i*) St/ tSt+1
where tSt+1 is the end-of-year exchange rate expected at the
beginning
Uncovered Interest Rate Parity
(UIP) condition (2)
Mar 16 2004
–
–
A one year investment in pounds still yields (1+i).
The no-profit condition for a risk neutral investor is the
uncovered interest rate parity (UIP) condition:
(1 + i*)(St / tSt+1) = (1 + i)
•
A useful approximation:
i* = i +(tSt+1 - St)/St
Interest rate in Euroland = interest rate in UK + expected appreciation of sterling
Uncovered Interest Rate Parity
(UIP) condition (3)
Mar 16 2004
–
–
The UIP states that rates of return are equalized once expected
exchange rate changes are accounted
Expectations cannot be observed directly, but if rates are
higher than in those of Euroland (i>i*), then the euro is
expected to appreciate, (tSt+1 - St)/St < 0
Modified Uncovered Interest Rate
Parity (UIP) condition
Mar 16 2004
–
The UIP condition can be modified to accomodate risk
aversion by allowing for a risk premium Yt that the British
investor will require to hold euro-denominated assets:
i* = i +(tSt+1 - St)/St + Yt
Interest rate in Euroland= interest rate in UK+expected appreciated of sterling + risk premium on euro
– Turning things around, define risk premium as deviation from
UIP, which can depend on time:
Yt
= (i*- i) - (tSt+1 - St)/St
Risk premium = Interest rate differential - expected appreciation
What form does the Risk Premium
take in the Market?
Mar 16 2004
–
–
–
–
–
–
The risk premium explains how assets which bear a rate of
return can contain compensation for risk
How does this work for foreign exchange, bank deposits used o
demand,etc?
Market makers specialize in buying and selling them
The risk premium typically takes the form of a bid – ask spread
A lower bid price for those who want to exchange and a
higher ask price for buyers. The difference is the market
makers profit, in fact the risk premium
Large bid ask price differences for risk currencies
Information and Market Efficiency
Mar 16 2004
–
–
A precise definition of market efficiency is that prices fully
reflect all available information
Market efficiency requires two things
•
•
Markets use all available information about the future, even at cost
They do not make systematic mistakes
– Efficiency in markets implies an absence of opportunities for
easy profits. Thus the no profit condition that we used.
Examples of the no-profit condition
Mar 16 2004
–
–
–
–
Arbitrage: operations that do not involve additional risk
Yield arbitrage
Spatial arbitrage
Triangular arbitrage (no money pumps)
•
•
if the euro costs one US dollar and one euro cost 8 Danish krone (DKR),
then the DKR/$ rate must be (DKR8/ €)($1/ € )= 8 DKR/$
Otherwise limitless profit would be possible
NEW TOPIC
Mar 16 2004
Linking Asset Markets and
International Monetary Economics
Mar 16 2004
–
–
–
–
–
–
The interest rate is the price of the future
Most borrowers are interested in the real interest rate and in
longer maturities, most commercial loans range from 1 to 10
years
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
The Term Structure
of Interest Rates
Mar 16 2004
–
The interest rate is the price of the future