Topic 9: Interest Parity Models

Question 1

What are the interest rate parity models?

Answer 1

• Covered Interest Rate Parity (CIP)
• Uncovered Interest Rate Parity (UIP)
• Real Interest Rate Parity (RIP) [we don’t look at this]

Question 2

What is a forward contract?

Answer 2

An agreement to swap a specific amount of currency, at a specific rate, at a specific point in time.

Question 3

What is the definition of CIP?

Answer 3

The condition that the return to similar assets in different countries are equal once we take into account that foreign exchange risk being covered in the forward market.

Question 4

Give the CIP equation.

Answer 4

(1 + i) = F(d/f)/S(d/f) * (1 + i*)

• Right hand side is value of foreign asset in d.c.
• Left hand side is the value of foreign asset.

Question 5

What are the conditions for CIP?

Answer 5

• Assets & forward rate must be of the same period, or converted to such
• Assets must be the same, meaning have the same risk

Question 6

How is CIP derived?

Answer 6

From these conditions:

1. If CIP is violated, there is risk free abitrage profits
2. Exploiting arbitrage opportunities pushes towards the CIP equilibrium
3. If arbitrage occurs fast and readily then we can assume CIP.

Question 7

What are the types of CIP arbitrage?

Answer 7

• Inward: When the domestic interest rate is higher then the foreign. We borrow internationally and invest locally. We also purchase a forward contract that assures us an arbitrage profit.
• Outward: When the foriegn interest rate is higher then the local. We borrow locally and invest in the foriegn, purchasing a forward contract that assures us arbitrage profit.

Question 8

What is the forward margin?

Answer 8

The proportional difference between the current spot and the current forward

f = (F - S)/S

Question 9

What is approximate form of CIP?

Answer 9

i = i* + f(d/f)

Question 10

What evidence is there for CIP?

Answer 10

Lots, it is very strong.

The CIP consistant exchange rate: S = F(1+i*)/(1+i)

The actual exchange rate is indistinguishable, no systemic differences.

Question 11

What is it called when F > S?

What about F < S?

Answer 11

Trading forward at a premium.

Trading foward at a discount.

Question 12

What is the definition of UIP?

Answer 12

The condition that returns to similar assets (i.e. assets with the same risk.) in different countries are equal after taking into account the expected changes in the exchange rate in the absence of forward cover.

Question 13

Give the uncovered interest rate parity condition.

Answer 13

(1+i) = S^e(d/f)/S(d/f) (1 + i*)

• Left hand side represents end of period value of domestic investment
• Right hand side is the expected end of period value of foreign investment in d.c. terms.

Question 14

How do we derive UIP?

Answer 14

1. If UIP is violated, there would be arbitrage
2. The operations of arbitrage should push markets towards the UIP equilibrium.

Question 15

Go through the tedious steps of UIP inward arbitrage.

Answer 15

Start of Period:

1. Borrow at i* internationally.
2. Convert to d.c. at S_0.
3. Invest domestically at i.

End of Period:

1. Receive investment proceeds S₀(1+i) per f.c.
2. Convert enough to f.c. pay off at (1+i*), which is S₁(1+i)
3. Reap proceeds (S₀(1+i) - S₁(1+i*)) per f.c. in d.c. value

Question 16

What is the implication of assuming UIP?

Answer 16

That actors are risk neutral.

Question 17

What is the approximate form of UIP?

Answer 17

(1+i) = (S^e/S) (1 + i*) or

(1+i) = (1 + S(dot)^e) (1+i)

i ~= S(dot)^e + i*

Question 18

What does the variable S(dot)^e denote?

Answer 18

The proportional difference between the expected spot rate and the current spot rate.

(S^e - S) / S = S(dot)^e

Question 19

Are CIP and UIP the same?

Answer 19

Only when F = S^e.

Called forward-market efficiency.

Question 20

Compare the approximate forms of CIP & UIP

Answer 20

CIP: i ~= i* + f(d/f)

UIP: i ~= i* + S(dot)^e (d/f)

Question 21

How can we estimate S^e?

Answer 21

• Surveys (Economists don’t like this. Actions inconsistant with statements.)
• Forecasting model
• Assume rational expectations

Question 22

What are the problems with testing UIP?

Answer 22

• Hard to observe the expected exchange rate.
• None of the methods of observing the expected exchange rate work.
• We can also just test forward market efficiency with some estimage of the expected spot rate. Because if it is, then UIP = CIP.

Question 23

Show how a forecasting model could be used to determine S^e_t+n

Answer 23

Could use something simple, like:

S_{t + n} = α + βS_t + ε_t+n

Or you could do the same, but with S(dot).

Question 24

Show a test of forward market efficiency.

Answer 24

f^t_t+n = ρ₀ + ρ₁S^t_t+n + ε

H₀: ρ₀ = 0 and ρ₁ = 1

Question 25

Show how rational expectations could demonstrate forward market efficiency

Answer 25

• We just straight out assume S^e(dot) = S + ε - i.e. forecasts are perfect.
• Where ε has a zero mean and is uncorrelated.
• This tells us that the futures market should on average predict the spot rate with zero error.

Question 26

What is the evidence for UIP?

Answer 26

Nope nope nope.

The actual exchange rate systemically deviates from the predicted forward market rate.

Called the forward premium puzzle.

Question 27

What can explain the forward premium puzzle?

Answer 27

• Maybe we can’t use rational expectations, or forecasting models.
• Maybe there is a risk premium.
• Transaction costs.

Question 28

How do CIP and UIP fair theoretically as models?

Answer 28

Underdetermined.

There is only one equation.

Question 29

What is a covered margin? uncovered margin?

Answer 29

The percentage profit to an arbitrage opportunity presented by a violation of CIP / UIP.

Question 30

What is the random walk hypothesis?

Answer 30

That stock prices evolve according to a random walk model and thus cannot be predicted. The errors have a zero mean and are not correlated, and represent unpredictable news about the assets value. Hence the best prediction is the previous periods price.