chapter 6 (1)

Question 1

Interest rate parity (IRP)

Answer 1

An arbitrage condition that must hold when international finance markets are in equilibrium.

Suppose that you have 1$ to invest over, say, a one year period. Consider two alternative ways of investing your fund: (i) invest domestically at the US interest rate, or, alternatively (ii) invest in a foreign country, say, the UK at the foreign interest rate and hedge the exchange risk by selling the maturity value of the foreign investment forward. It is assumed here that you want to consider only default free investments. If you invest 1$ domestically at the US interest rate (is) the maturity value will be 1$(1+i$)

Question 2

To invest in the UK you carry out the following transaction

Answer 2

1. Exchange 1$ for a pound amount that is pound pound(1/S), at the prevailing spot exchange rate (S)^2
2. Invest the pound amount at the UK interest rate (ipound) with the maturity value of Pound(1/S)(1+ipound)
3. Sell the maturity value of the UK investment forward in exchange for a predetermined dollar amount, that is, $((1/S)(1+ipound)F where F denotes the forward exchange rate

Question 3

The effective dollar interest rate from the UK investment alternative is given by

Answer 3

F/S*(1+ipound) -1

arbitrage equilibrium then would dictate that the future dollar proceeds (or, equivalently, the dollar interest rate) from investing the two equivalent investments must be the same, implying that

(1+is)=F/S(1+Ipound) or alternatively

F= S((1+is)/(1+ipound))

Question 4

IRP (interest rate pairity) can be derived by constructing an arbitrage portfolio which involves

Answer 4

(i) no net investments
(ii) no risk and then

Question 5

Consider an arbitrage portfolio consisting of three separate positions

Answer 5

1. Borrowing $S in the united states which is just enough to buy 1ound at the prevailing spot exchange rate (S)
2. Lending 1pound in the UK at the UK interest rate
3. Selling the maturity value of the UK investment forward

Question 6

The Interest rate pairity relationship is sometimes approximated as follows

Answer 6

(i$-ipound) = (F-S)/S *(1+ipound) == (F-S)/S

It can be seen clearly from equation 6.1 IPR provides a linkage between interest rates in two different countries. Speciffically, the interest rate will be higher in the united states than in the UK when the dollar is at a forward discount, that is F>S.

Question 7

When the dollar is at a forward discount, this implies

Answer 7

That the dollar is expected to depreciate against the pound. If so the US interest rate should be higher than the UK interest rate to compensate for the expected depreciation of the dollar

Question 8

When IRP holds you will be

Answer 8

Indifferent between investing your money in the united states and investing in the UK with forward hedging.

Question 9

When IRP is violated

Answer 9

you will prefer one investment country to another. you will be better off by investing in the United states (if (1 +i§) is greater than (F/S)(1+ipound) When you need to borrow on the other hand, you will choose to borrow where the dollar interest is lower. When IRP doesnt hold, the situation also gives rise to covered interest arbitrage opportunities

Question 10

How long will an arbitrage opportunity last

Answer 10

A simple answer is for a short while only. As soon as deviations from IRP are detected, informed traders will immediately carry out CIA transactions. As a result of these arbitrage activities, IRP will be restored quite quickly.

Question 11

Currency carry trade

Answer 11

involves buying a high yielding currency and funding it with a low yielding currency, without any hedging.

Question 12

Reasons for deviatio from IRP

Answer 12

Transaction costs

capital controls imposed by governments

Question 13

Purchasing power parity

Answer 13

This theory states that the exchange rate between currencies of two countries should be equal to the ratio of the countries price levels.

Question 14

P$=the dollar price of the standard consumptions basket in the united states

Ppound the price of the same basket in the UK

PPP states that the exchange rate between the dollar and the pound should be

Answer 14

S = P$/Ppound

Where S is the dollar price of one pound

If the price of the commodity basked in the US is 225 and 150 in the UK the exchange rate should be

$1.5/pounds = 225/150

alternatively

P$ = S * Ppound

Question 15

the real exchange rate q which measures deviations from PPP can be defined as

Answer 15

q = 1+pi$/(1+ e) (1+pipound)

First note that if PPP holds, that is, (1+e) = (1 + pi$)/(1+pipound)

the exchange rate will be unity q = 1

e = The rate of change in exchange rate ≈ inflation differential