Determination of FX Rate: Financial Investment Theory J.D. Han King’s College UWO.

Determination of FX Rate: Financial Investment Theory

J.D. HanKing’s College

UWO

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• International Trade and Price Level->Purchasing Power ParityExchange rates depend on relative price ratio or inflation differentials

• International Financial Investment Theory-> Interest Parity Theorem

1. Overview Revisited: Three TheoriesThere are three theories which link the economic fundamental to the Long-run Equilibrium FOREX rate

• Real Factor Real AnalysisReal FOREX rate changes due to real factors such as Demand and Supply of Goods

•Monetary Approach -> “Money Supply affects interest rates and inflation rates; Thus this encompasses the above two.

2. Summary: Four theories for determination of equilibrium FX rate

1) International Investment Theory

- Differences in Rates of Returns

2) Purchasing Parity Theory

- Relative Prices

3) Monetary Approach- Money affects i and P; thus

Money affects FOREX rates

4) Real Factor Analysis

-S (Technical Innovation)/ D(changes in demand)

3.International Financial Investment involving FOREX

- Who are the Players ? International Investors Arbitrageurs

- What are they focusing on? Differences in Rates of Returns across countries with

different currencies

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Interest (Rate) Arbitrageurs

• Arbitrage means the following two activities:

1) Solely based on spot FOREX: If dollars are cheaper in New York than in London, people will buy them in New York and stop buying them

in London.

If triangular FOREX rate is in such a way that Canadian dollar is undervalued with respect to U.S. dollar, but not to Euro, What would the arbitrageur do?

You borrow U.S. dollar, buy Canadian dollars (with the U.S. dollars), and exchange them into Euro, covert the Euro revenue into U.S. dollar, and pay back the U.S. loans. You will have some profits.

2) Based on spot FOREX rate, future expectations, Forward Rate and international interest rate differentials: moving capital across countries for a higher return:

4. Arbitrage, Capital Flows, and Changing FX rates

• Bottom Line International Capital Flows determine FOREX

rates in such a way that Capital Inflows increase the receiving

country’s external value; -> Capital Inflows lowers S for the receiving

country

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5. Arbitrage for Rates of Returns on Domestic versus Foreign Investments

• What influences the demand for (willingness to buy) domestic or foreign currency for investors?

• If we assume that risk is the same between the two countries

• The return on domestic investment versus the return on investment in foreign country

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International Investors are faced with two options:

• Return on Domestic Asset = interest on Canadian dollar asset = i$

• Return on Foreign Investment

= interest on foreign (country) interest rate

+ capital gains or loss due to expected changes in FOREX rates

= i€ + (Se$/€ - S$/€)/S$/€

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Two Rates of Returns

• The difference in the rate of return on dollar deposits and euro deposits is

i$ versus i€ + (Se$/€ - S$/€)/S$/€

expected rate of return = interest rate on dollar deposits

interest rateon euro deposits

expected rate of return on euro deposits

expected exchange rate

currentexchange rate

expected rate of appreciation of the euro

The Equilibrium in International Investmet

-is obtained whendomestic ROR = Foreign ROR;

-no more arbitrage

-capital flows stop

-equilibrium FX rate S* is determined

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“Uncovered Interest (Rate) Parity”

is achieved at the equilibrium of financial investment.

Then, domestic and foreign investment earn the same rate of return.

Explanation of the terminology

• What does Interest Parity Mean? The rate of returns get at par between the two

countries. * Note that the ‘interest(s) ’ is only an

approximate description, not an exact description, of the rate(s) of returns.

• Why ‘uncovered’?It is subject to ‘expectation errors’.

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Formula of the Uncovered Interest Parity Theorem

• At equilibrium of international capital flows

i$ = i€ + (Se$/€ - S$/€)/S$/€

expected rate of return = interest rate on dollar deposits

interest rateon euro deposits

expected rate of return on euro deposits

expected exchange rate

Current exchange rate in finan. Mkt.

expected rate of appreciation of the euro

5. Dynamics Suppose that initially FOREX market is in

equilibrium and UCIP holds.What will happen to S if there is a change in

the following Exogenous Variables? 1) If i rises, S falls (class example).1) If if rises, S rises.2) If Se rises, S rises.3) If M increases, S rises.4) If Mf increase, S falls.

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1)Domestic Interest Rates rise.

– We start from the long-run equilibriumi$ = i€ + (Se

$/€ - S$/€)/S$/€ .– Suppose the Canadian interest rate is raised: Thus i$ > i€ + (Se

$/€ - S$/€)/S$/€ . - Disequilibrium of Uncovered Interest parity

- Capital Inflows to Canada- In Canada, Supply of FX up and D for Canadian Dollars Up.- The Canadian dollar appreciates and the euro depreciates- FOREX rate or S falls for Canada.

– i$ = i€ + (Se$/€ - S’$/€)/S’$/€ is restored.

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• How was the Canadian interest rate raised?

• It is thought the Canadian government’s contractionary Monetary Policy (Ms down).

Thus, when the govern tightens Ms(down), i goes up and, S goes down (domestic curreny appreciates; foreign currency depreciates).

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2) Expected Appreciation of euro or Se

• If people expect the euro to appreciate in the future, then the expected return on euros therefore increases.

• Investment will pay off in a valuable (“strong”) euro. So people start buying Euro now, and the demand for Euro rises.

• The Price of Euro in terms of Dollars rises.

An expected appreciation of a currency leads to an actual appreciation

-> “self-fulfilling prophecy”

– We start from the long-run equilibriumi$ = i€ + (Se

$/€ - S$/€)/S$/€ .– Suppose Se is raised: Now i$ < i€ + (Se

$/€ - S$/€)/S$/€ . - Disequilibrium of Uncovered Interest parity

- Capital Outflows from Canada- In Canada, D for euros Up.- The Canadian dollar depreciates and the euro appreciates- FOREX rate or S rises for Canada.

– i$ = i€ + (Se$/€ - S’$/€)/S’$/€ is restored.

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3)The effect of changing domestic/Canadian money supply on S

• (Domestic/Canadian) Money supply rises-> (Domestic/Canadian) Interest Rate falls-> Rate of Returns on domestic /Canadian financial

investment falls-> Capital Outflows from Canada-> Demand for FX/euro rises-> FX rate or S rises.

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4)The Effect of changing foreign/European money supply on S

• In the short-run, if falls in Europe.-> For Canadians, ROR for foreign investment

falls-> In Canada, Demand for FX(euros) falls-> In Canada, Price of FX(euro) or FX rate S falls.

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6. Efficient FX Market:Unbiased-Forward-Rate Theory

• Forward FX rate is the FX rate set today for a future delivery; thus it is based on today(time t)’s expectations of what S might be at time t+1.

Thus “the expected future spot FX rate is equal to the Forward FX rate”.

t Se t+1 = Ft+1

• The difference between Forward Rate of t+1 and Actual Rate(realized) of t+1 is Random Errors

Ft+1 = St+1 + random errors

Forward Premium tells the expected change in S:

• Δ% Se = (Se – S)/S

If FOREX market is efficient, then Se = F • Δ% Se = (F- S)/ S Forward premium or discount is equal to the

market’s expected change in the spot rate.

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*Test of FOREX Market Efficiency

• t Se t+1 = St+1+ e

Note that F has replaced Se

• Thus, Ft+1 = St+1 + e

Forward Rate is the best predictor for the future spot rate.

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7. ‘Covered’ Interest Parity• Covered interest parity :

i $ = i€ + (F$/€ - S$/€)/S$/€ at eq.

where F$/€ is the Forward Exchange Rate.

• Alternatively, i $ - i€ = (F$/€ - S$/€)/S$/€ at eq.

where (F$/€ - S$/€)/S$/€ is Forward Premium (+) or Forward Discount (-)

At Disequilibrium,

• When i $ - i€ > (F$/€ - S$/€)/S$/€,

Capital inflows occur, and S falls if and only if the domestic and foreign

investment are perfect substitutes. .

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Dynamics

• If the FOREX market revises expectations of FOREX upwards, then what will happen to the spot rate S$/€ ?

• i• If

• M• Mf

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• At equilibrium, the rates of return on domestic (dollar) deposits, and the return on the non-risk or “covered” foreign investment are the same.– How could you make easy, risk-free money in the foreign exchange

markets if covered interest parity did not hold?– Covered positions using the forward rate involve little risk.

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7. Limitations of CIP and UCIP:

• Even when i $ < i€ +(F$/€ - S$/€)/S$/€,

Capital may not flow out and S may not rise.

• CIP and UCIP assume that domestic and foreign investments are perfect substitutes.

• UCIP and CIP do consider other FX risk: In reality, i€ may simply rises due to an

increased risk premium.

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What will be the true Parity Equation?

i $ = i€ +(Se$/€ - S$/€)/S$/€ - Other Relative Risk Premium of Foreign Investment