Question 1: (40 points) Consider two currencies: US dollar and Euro. In period t = 1, the nominal interest rate for

risk-free bonds in US dollars is 2% and the nominal interest raise for risk-free bonds in

Euros is 3%. The nominal exchange rate is such that 1 US dollar is exchanged for 1 Euro. In period t = 2, it can be either sunny or rainy with probability 112 each. if sunny the

nominal exchange rate is S_2 = .98 and if it is rainy S_2 = 1.02 where S_2 are how many

dollars for 1 euro. i) Deﬁne what a forward rate is. ii) Calculate the forward rate that will prevail if international ﬁnancial markets are

perfectly integrated. Provide an intuitive argument why such value should prevail. Do

you need information about the possible realizations of S_2 to answer this question? iii) Calculate the expected return of investing in Euros for a US investors (i.e. in terms of

US dollars). Is the expected return higher than investing in risk free US dollar bonds?

How expected returns differ from realized returns? Calculate also the realized returns

when it is sunny and when it is rainy. iv) Does the fact that expected returns of risk free bonds in Euros and US dollars differ

imply that there are proﬁtable arbitrage opportunities? Or that international credit

markets are not integrated? Please explain as carefully as you can. v) Consider two alternative scenarios: A and B. In scenario A, consumption of US

investors is high when it is sunny and low when it is rainy. In scenario 8, consumption

of US investors is low when it is sunny and high when it is rainy. Which scenario is

more plausible in light of your answer to part iv assuming that US investors are risk

averse. Deﬁne what risk neutral means. Deﬁne what risk averse means. vi) Suppose now that there are no capital controls imposed by the US and that the

forward rate, F, is equal to 1. Is this evidence that the European Union is imposing

capital controls? If so, it is limiting inflows or outﬂows? Please explain.