lecture 5 (topic 4 international parity relations and forecasting foreign exchane rates

Question 1

International parity relationships

Answer 1

are manifestations of law of one price that must hold to avoid arbitrage opportunities

Question 2

Law of one price (LOP)

Answer 2

prevails when the same or equivalent things are trading at the same price across different locations or markets, precluding profitable arbitrage opportunities

Question 3

Arbitrage

Answer 3

the act of simultaneously buying and selling the same or equivalent assets or commodities for the purpose of making certain, guaranteed profits

Question 4

Interest rate parity

Answer 4

LOP applied to international money market instruments and provides a linkage between interest rates in two different countries

Question 5

Purchasing power parity

Answer 5

LOP applied to a standard consumption basket and provides a linkage between prices in two differnt countries

Question 6

International parity relationships help us understand

Answer 6

how exchange rates are determined and how we can forecast exchagne rates

Question 7

There are two alternative ways of investing your fund

Answer 7

1) invest in the us dollar at the dollar interest rate (rate i$)

2) Invest in a foreign currency a foreign currency denominated security (for example the british pound) at the interest rate ipound and hedge exchange risk by selling the maturity value of the pound investment forward

Question 8

Deriving interest rate parity (invest in the US dollar at the dollar interest rate )

Answer 8

(1 + i$)

Question 9

Deriving interest rate parity (invest in a foreign currency a foreign currency denominated security at the interest rate i pound and hedge exchange risk by selling the maturity value of the pound investment forward

Answer 9

Exchange 1$ for a pound amount, that is pund*(1/S) at the prevailing spot exchange rate (S)

Invest the pound amount at the pound interest rate

Sell the maturity value of the pound investment forward in exchange for a predetermined dollar amount –> $((1/S) * (1 + ipound))*F

simply (F/S)(1+ipound)

Question 10

Deriving interest rate parity formulas equal

Answer 10

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

Question 11

Future dollar proceeds from investing in these two equivalent investments must be the same –>

Answer 11

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

or F = S(1+i$/1+iPound)

Question 12

IRP can also be derived by

Answer 12

constructing an arbitrage portfolio that involves no net investment and no risk

Borrow $S at the dollar interest rate and buy Pound1 at the prevailing spot exchange rate of S

Lend 1 pound at the pound interest rate

Sell the maturity value of the pound investment forward

Since no one should be able to make certain profits by holding this self-financing portfolio, the net cash flow at maturity should be zero in equilibrium

(1+ipound) * F - (1 +i$)S = 0

Question 13

Covered interest arbitrage

Answer 13

When IRP does not hold, the situation gives rise to covered interest arbitrage opportunities, allowing certain profits to be made without the arbitrageur investing any money out of pocket or bearing any risk

Question 14

what if

Answer 14

(1 + i$ > F/S(1+ipound) or (1 + i$ < F/S(1+ipound)

Question 15

Covered interst arbitrage appx

Answer 15

i$ - ipound = F-S/S

Question 16

Reforming the IRP relationship in terms of the spot exchange rate yields (formula)

Answer 16

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

Question 17

Forward exchange rate can be viewed as the expected future spot exchange rate conditional on all revelant information being available (formula)

Answer 17

F = E(St+1 I It)

Question 18

combining forward exchange rate formula and IRP in terms of spot exchange yields:

Answer 18

S = (1+ipound/1+i$) * E * (St+1 I It)

Things that are noteworthy:
1) Expectation plays a key role in exchange rate determination (that is, when people “expect” the exchange rate to go up in the future, it goes up now)

2) Exchange rate behavior will be driven by news events