If the US nominal interest rate is 5 percent, the foreign nominal interest rate
ID: 2761610 • Letter: I
Question
If the US nominal interest rate is 5 percent, the foreign nominal interest rate is 3 percent, and the current nominal exchange rate (domestic currency price of foreign exchange] is 2, what is the equilibrium forward rate set by banks and the equilibrium forward premium according to covered interest rate parity? Explain your answer carefully. Assume that absolute purchasing power parity holds. If the domestic country inflation rate is 5%, and the rate of nominal exchange rate depreciation is 2%, what is the foreign country's inflation rate? Suppose asset A and asset B have equal expected returns, asset A has a variance of 2, asset B has a variance of 4, and the covariance between asset A and asset B is -6. If you are risk averse, and hold 50% of your portfolio in asset A and 50% in asset B, are you better off than if you hold asset A only? Suppose you discover that the dollar price of a Big Mac is $2.50 in the US, the UK pound price of a Big Mac is one pound and 50 pence, and the dollar price of a pound is 2. According to the law of one price, is the dollar overvalued or undervalued compared to the relative price of Big Macs? Is there any reason to expect the exchange rate - or the prices of Big Macs - to adjust? Why or why not? If the expected inflation rate is 5 percent, and the nominal interest rate is 2 percent, what does the Fisher Equation tell you is the ex-ante real interest rate? What does this mean, exactly? If markets forecast that next month's dollar/pound exchange rate will be $2 per pound, and the one month nominal interest differential between the US and UK is 10%, in an efficient market what should be the equilibrium nominal exchange rate be?Explanation / Answer
a) According to Interest rate parity: F = S*(1+iD)/(1+iP) = 2*(1+0.05)/(1+0.03) = $2.04 where iD is the interest rate of domestic currency and iP is the interest rate of price currency.
b) According to Purchasing rate parity: Depreciation rate = (1+iD)/(1+iP) - 1 = (1+0.05)/(1+0.03) - 1 = 0.0194 or 1.94% where iD is the inflation rate of domestic currency and iP is the inflation rate of price currency.
c) Since the investor is risk averse it will be always better for him to hold Asset A only because A and B have same return with lesser variance and thus, the portfolio with A and B will also have the same return, because the return of the portfolio is the weighted average return of the assets. Thus, it is better to hold only A.
d) Dollar price on the basis of Big Mac = 2.5/1.5 = $1.67 per pound
Current spot rate = $2 per pound
The $ is under-valued because the intrinsic price is less than the current spot rate. It is expected that the Big-Mac price in the UK will rise.
e) Real Interest rate = (1+0.02)/(1+0.05) - 1 = -2.86% This means that the investor is in loss when the time value of the money is considered because the interest rate the investor is receiving is less than the inflation rate which means not compensating the investor even for the inflation.
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