Mar 16 2004

Lesson 12

By

John Kennes

International Monetary Economics

Mar 16 2004

ASSET MARKETS A REVIEW

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

Key Concepts

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.

Convenient References

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

What are Asset Markets?

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.

Properties of Assets

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.

No-profit condition

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.

CIP

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 solve for the CIP condition?

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.

How to eliminate the risk?

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.

A Perfect Hedge

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

CIP condition

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

Where to look for forward rates

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)

Numerical Example

May 1 Day’s Spread

Close One month

% p.a. Three months

% p.a

Denmark 6.3525-6.3925

6.3550-6.3600

3.55-3.95

ordeis

7.08 9.40-10.10

dis

-6.13

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

What happens when the investor does not eliminate risk by engaging in a forward contract?

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

Risk Diversification

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

The Price of Risk

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 (1)

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 (2)

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

Uncovered Interest Rate Parity (UIP) condition (3)

Mar 16 2004

– The UIP condition can be modified to accomodate risk aversion by allowing for a risk premium t that the British investor will require to hold euro-denominated assets:

i* = i +(tSt+1 - St)/St + tInterest 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:

t = (i*- i) - (tSt+1 - St)/St Risk premium = Interest rate differential - expected appreciation

Modified Uncovered Interest Rate Parity (UIP) condition

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

What form does the Risk Premium take in the Market?

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.

Information and Market Efficiency

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

Examples of the no-profit condition

Mar 16 2004

NEW TOPIC

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

Linking Asset Markets and International Monetary Economics

Mar 16 2004

– The interest rate is the price of the future

The Term Structure of Interest Rates