Week 9 - Elements of international finance

Question 1

Forward premium, FP_t,T

Answer 1

= (F_t,T - S_t)/St
= the annualised percentage difference between the forward rate and the spot rate
-> captures the TRADEOFF between buying today vs buying forward

1. If FP > 0, then it takes more £ to buy $1 in the future than now
   => £ is at a discount and $ is at a premium
2. If FP < 0, then it take fewer £ to buy $1 in the future than now
   => £ is at a premium and $ is at a discount

Question 2

How are Forward rates priced?

Answer 2

By INTEREST ARBITRAGE
- If there is no arbitrage, borrowing in one country and then lending in the other country should NOT be PROFITABLE after eliminating exchange rate risk using currency forwards

Question 3

No-arbitrage pricing implies the Covered Interest Parity (CIP).
1. What is the formula for CIP?
2. Can investors trust the CIP theory?

Answer 3

F = S x (1+r)/(1+r*)

where r = interest rate in the home country UK
and r* = interest rate in the foreign country US

If F < or >, then we can have an ARBITRAGE strategy

2. This is a no-arbitrage pricing relationship, and thus it holds as long as capital is free to flow across markets.
   - We CAN TRUST this theory, since arbitrage trades are possible in these foreign currency markets and money markets.
   - All the quotes/rates are assumed to be risk free and are known today.

Question 4

2 strategies of the Covered Interest Parity (CIP)

Answer 4

• agree today t, executed in future (t+k)
• how much £ to deposit in bank at t today to get $1 at (t+k)
  » strategy 1: deposit PV of F pounds in UK bank account to get enough, F pounds at time (t+k) to buy $1
  » strategy 2: convert 1/(1+r*) pounds to dollars at time t to deposit in US bank account to buy $1
• commonality between strategies 1 and 2 is getting $1 at (t+k)
  » so no-arbitrage implies that both values of £ have to be equal at time t (Law of One Price)

Question 5

Unbiased Expectations Hypothesis (UEH)

Answer 5

If investors have identical expectations and are risk neutral (ie. do not require risk premium),
F_t,t+1 will rise or fall to E_t[S_t+1]

UEH: F_t,T = E_t[S_T]

Question 6

Unbiased Expectations Hypothesis (UEH) - What to do if F_t,t+1 > E_t[S_t+1]? What about if < ?

(see slides for example with numbers)

Answer 6

1. Buy pounds forward at time t
2. Expect to sell at time t+1

If F_t,t+1 < E_t[S_t+1],
1. Sell pounds forward at time t
2. Expect to buy pounds at time t+1

Question 7

Uncovered Interest Parity (UIP) which now has EXPECTATION

*obtained from CIP and UEH

Can investors trust the UIP theory?

Answer 7

• does not need to hold from no-arbitrage, unlike CIP
  E_t[S_T] = S_t x (1+r_t,T)/(1+r_t,T*)
• when it holds, it implies that the Expected change in interest rates is approx. = to the difference between domestic and foreign interest rates
  E_t[(S_T - S_t)/S_t] ≈ r_t,T - r_t,T*
• Investors cannot trust UIP b/c empirically UIP does not hold
• UIP is derived from CIP and UEH
  > UEH ASSUMES that investors are RISK NEUTRAL. In reality, however, investors are risk averse.

Question 8

Testing the Expectations theory - regression formula and results

Answer 8

See slides for formula

1. If UEH is true -> alpha = 0
2. UIP does NOT hold b/c alpha ≠ 0
3. One explanation is RISK
   - in well-functioning markets, risk will be rewarded to the extent that it cannot be diversified away (rmb CAPM)
   - E[return] = rf rate + RISK PREMIUM
   - coefficient a in the formula is the estimate of the risk premium

Question 9

Commodity Price Parity (CPP)

Answer 9

~ Law of One Price
- we cannot make profits from buying individual goods in USD and selling in JPY

Question 10

Absolute purchasing power parity (Absolute PPP)

Answer 10

P_t = P_t* St

where P_t is the price of basket of goods in the home country at time , P_t* is for foreign country

= {same} basket of goods should cost the same in the UK and in the US
- absolute PPP relates differences in prices of goods across countries to differences in inflation across countries

Question 11

Absolute PPP may fail because CPP may not hold -> so represent Deviations from PPP, R_t
How do we relate R_t to relative PPP?

Answer 11

S_t = R_t P_t / P_t*
If systematic deviations from PPP (R_t) are constant over time, we can look at RELATIVE MOVEMENTS in EXCHANGE RATES & PRICE LEVELS OVER TIME

[see slides for formulas and equations]

then, relative PPP is s_t,T ≈ π_t,T - π_t,T*
ie. the change in spot exchange rate from t and T can be attributed to the INFLATION RATE differential between domestic and foreign
» related to UIP and the small s_t,T

Question 12

Does Relative PPP and Absolute PPP hold?

Answer 12

1. Relative PPP fails in the short run (1 day to 5 years)
2. Absolute PPP holds better in long horizon (10-20 years)

Question 13

Real exchange rate, R_t

Answer 13

• a measure that tells us about the relative purchasing power of money in the 2 countries

R_t = (S_t x P_t*)/P_t

• intuition: you can buy a number R of UK baskets for every foreign basket purchased
• if investors can trade freely across countries and the absolute PPP is satisfied, then R = 1

Question 14

Real interest rate, rho_t,T

Answer 14

• the nominal interest rate r adjusted for inflation π

[see slides for formula]

• for small rates, we have the approximation rho_t,T ≈ r_t,T - π_t,T