Economics 826 International Finance. Final Exam: April 2007

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1 Economics 826 International Finance Final Exam: April 2007 Answer 3 questions from Part A and 4 questions from Part B. Part A is worth 60%. Part B is worth 40%. You may write in english or french. You may use a hand calculator. Part A: Analytical Answer 3 of the following questions. (20 marks each) 1. Suppose that investors are risk neutral and that returns satisfy: 1 = E t β(1 + i t+1 ) P t P t+1. (a) Suppose i is the nominal return on a riskless Yen bond and Japan is the home country. Let i be the nominal return on a USD bond and S the exchange rate (price of a dollar in yen). Give a formula that would allow you to price an uncovered position in the USD. (b) What sign would the covariance term have in order to be consistent with the puzzle of the yen carry trade? 2. Suppose that a floating nominal exchange rate satisfies this model: s t = α x t + α 1 + α E ts t+1, where s is the log exchange rate and x the log fundamental. The fundamental follows this stochastic process: x t = μ + ρx t 1 + ɛ t, 1

2 with ɛ t iid(0,σ 2 ). (a) Find a solution for the exchange rate. (b) Describe the cross-equation restrictions that make this model testable. (c) Show that adding a speculative bubble b t = ( 1 + α ) t α to your answer in part (a) also is consistent with the original equation for the exchange rate. 3. This question studies the effect of the time path of government spending on a country s current account, in a two-period model. Imagine a small, open economy with endowment Y, consumption C, government spending G, and no investment. Its inherited debt is B 0 = 3. The world, real interest rate is r = Output is Y 1 = Y 2 = 10. The path of government spending is G 1 = 3 and G 2 = 2. Private consumption is smoothed: C 1 = C 2. (a) Write the country s present-value budget constraint and solve for consumption. (b) Solve for the trade balance and the current account in each time period. (c) In this model economy would reductions in government spending lead to the country s paying off its debt faster? 4. This question studies whether consumption loans to sovereign borrowers can be explained by the threat of sanctions. Suppose that a borrower tries to maximize utility of a typical consumer: E 1 ln C 2, and that the borrower s income each period is independently and identically distributed as Y = 1 ± 0.1, where the two outcomes are equally likely. If the borrower defaults next period, then a portion of its output ηy 2 can be seized by competitive lenders. (a) How large must η be for the lenders to offer full insurance? (b) Will any loans be offered at sanction rates lower than the rate you found in part (a)? (c) Find the effect of η on the price of a one-period real discount bond that is a claim to a unit of goods in the sovereign country and is priced by its residents. 2

3 5. A central bank s balance sheet can be approximated as: m = b + r, where b is its holdings of government bonds, r its foreign exchange reserves, and m the monetary base. Bond holdings grow like this: b t+1 = b t. Currently, the exchange rate is fixed at rate s = m. If the central bank runs out of reserves, then the exchange rate will float, and follow the monetary model with fundamental b t and α = 1. (a) If currently r t = 10 then how many periods will the fixed exchange rate last? (b) Suppose that the exchange rate is fixed at s = 30. At what value of the central bank s bond holdings, b T, will a speculative attack occur? What value of reserves will the central bank lose on that day? 6. Suppose that there are no risk premia in the foreign exchange market and that the unbiasedness hypothesis holds (in logs): The exchange rate evolves this way: f t = E t s t+1. s t+1 = s t + ɛ t, where ɛ t is a mean-zero innovation. But actual forecasts are formed with adaptive expectations: E t s t+1 = λs t + (1 λ)e t 1 s t. (a) Find E t s t+1 in terms of current and lagged observable variables. (b) Will an econometrician be able to reject the unbiasedness hypothesis? (c) Are there opportunities for profit in this market? 3

4 Part B: Empirical Discuss 4 of the following statements. (10 marks each) 1. Predictable changes in an exchange rate are inconsistent with market efficiency. 2. Dark matter explains how the US can have positive net foreign investment income. 3. Nontraded goods can explain why international consumption correlations are not unity. 4. An inverted yield curve reflects an anticipated recession. 5. Exchange-rate pass-through is high throughout the world. 6. China s exchange-rate regime is a significant cause of the US current account deficit. 7. Fixed exchange rates and currency boards are impractical because of speculative attacks. 8. There are no good reasons for the fear of floating. 4

5 2007 Answer Guide 1. (a) 1 = (1 + i t) 1 + i t E t S t+1 S t + (1 + i t )cov(β P t P t+1, S t+1 S t ). (b) In the yen carry trade we find that S is greater than F (the USD is at a forward discount or the yen is at a forward premium) so the covariance term must be negative. 2. (a) The solution is: s t = αμ 1 + α αρ α αρ x t (b) The restrictions give four coefficients as functions of three parameters: α, μ, and ρ. (b) Adding this term and substituting for s t and s t+1 shows that the equation still holds. 3. (a) (1 + r)b 0 + Y 1 + Y r = C 1 + C r + G 1 + G r. which gives C = (b) In period 1 tb 1 = and ca 1 = while in period 2 tb2 = and ca 2 = (Remember to check your answer with accounting rules such as Y = C + G + TB, when I = 0, and also B 0 = CA 1 CA 2 so as to avoid mistakes.) (c) I think that reducing G 1 would bring this about. In fact, reducing G 1 and raising G 2 would also bring this about. (Try setting G 1 = G 2 = , which does not change the present value of government spending.) The underlying principles are that (a) the country has to pay off its debt no matter what and (b) the timing of G (but not the overall level) matters to the rate at which the debt is paid off. In the same vein, recall that a temporary change in G affects CA while a permanent one does not.) 5

6 4. (a) Full insurance requires: η ɛ 1 + ɛ = (b) Suppose the contract calls for a payment to the insurer of P in the good state. For incentive compatibility: 1 + ɛ P (1 + ɛ)(1 η), which means that P = η(1 + ɛ) = 1.1η. In the bad state, the country will receive this same amount so that the insurers break even on average. Thus any positive sanction rate can sustain some lending. (c) Since β = 1, with complete insurance h 1 = 1 since C 1 = C 2 = 1. With partial insurance there are two possible bond prices, depending on the current state. The two-point density gives an explicit expression for E 1 (1/C 2 ). Obviously a rise in η reduces consumption variability and so lowers h 1 and raises the interest rate. 5. (a) T t = r t αμ μ = = 19 (b) Clearly b t = 20 so after 19 periods b T = Reserves will drop by 0.5 at that point. 6. (a) E t s t+1 = λ 1 λl s t. (b) s t+1 f t = s t + ɛ t which will be autocorrelated unless λ = 1. λ 1 λl s t, (c) Yes. The forecast error is positively correlated with s t. 6

7 Economics 826 International Finance Final Exam: April 2007 Answer 3 questions from Part A and 4 questions from Part B. Part A is worth 60%. Part B is worth 40%. You may write in english or french. You may use a hand calculator. Part A: Analytical Answer 3 of the following 6 questions. (20 marks each) Part B: Empirical Discuss 4 of the following 8 statements. (10 marks each)