IFM&KE CAU MBA Fall 2015 Answers to Problem Set (Due on October 13th, 2015) Suppose that a Cadillac costs E 45,000 in Germany and that the current USD/EUR exchange rate is 0.7624 Calculate the dollar price of the Cadillac 45,000 × 0.7624 = $34,308 Consider the following exchange rates: EUR/USD = 1.2500 ($/Euro) USD/CAD = 1.1000 (CAD/$) EUR/CAD = 1.3550 (CAD/Euro) How could you use this information to make money in the currency markets? EUR  USD × USD = 1.25 × 1.10 = 1.375 > 1.3550 = EUR/CAD CAD EUR USD × USD CAD 1.375 × = >1 CAD 𝐸𝐸𝑈𝑈𝑈𝑈 1.3550 The above calculations tell that we can get arbitrage profits by converting 1Euro as follows EuroCADUSDEUR Hence, the FX markets are not in equilibrium now Suppose that you took a short position on 12,500,000 Japanese Yen future (remember, a short position involves selling Yen) at a price of 104.5 Yen/$ If the spot rate on the contract's expiration date was 103.45 Yen/$, calculate your profit/loss from the futures contract IFM&KE CAU MBA Fall 2015 This is the case in which Yen is appreciated contrary to your anticipation Compared with the current exchange rate, you should sell yen at a cheaper price So, you will suffer loss amounting to USD 1,214.095 = 12,500,000 × ( 1 − ) 103.45 104.5 Suppose that the annualized inflation in the US is 3% while annual inflation in Europe is 1% If the current exchange rate is $1.40 per Euro, what would you expect the exchange rate to be in one year? If the exchange rate one year from now turns out to be $1.50 per Euro, what has happened to the real exchange rate? From the UIP, iUS = 𝑖𝑖𝐸𝐸𝐸𝐸𝑅𝑅 + 𝐸𝐸 𝑒𝑒 $ −𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸 0.03 = 0.01 + 𝐸𝐸 𝑒𝑒 −1.4 1.4  𝐸𝐸 𝑒𝑒 = 1.428 Next, the real exchange rate is defined as follows 𝜀𝜀 = 𝜀𝜀𝑃𝑃𝑈𝑈𝑈𝑈 Rearranging the above, 𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑃𝑃 𝐸𝐸𝑈𝑈𝑈𝑈 𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸 × 𝑃𝑃𝐸𝐸𝑈𝑈𝑈𝑈 𝑃𝑃𝑈𝑈𝑈𝑈 So, assuming there is no change in the price levels of the two countries, the appreciation (depreciation) of the Euro (USD) exceeding the expectation (1.50>1.40) is in line with real appreciation (real depreciation) of the Euro(USD) (From the textbook) Consider two countries, Japan and Korea In 1996, Japan experienced relatively slow output growth (1%), whereas Korea had relatively robust output growth (6%) Suppose the Bank of Japan allowed the money supply to grow by 2% each year, whereas the Bank of Korea chose to maintain relatively high money growth of 12% per year For the following questions, use the simple monetary model (where L is constant) It will be easier to treat Korea as the home country and Japan as the foreign country A What is the inflation rate in Korea? In Japan? πKor = 𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑔𝑔𝐾𝐾𝐾𝐾𝐾𝐾 = 12% − 6% = 6% πJap = 𝜇𝜇𝐽𝐽𝐽𝐽𝐽𝐽 − 𝑔𝑔𝐽𝐽𝑎𝑎𝑎𝑎 = 2% − 1% = 1% IFM&KE CAU MBA Fall 2015 B What is the expected rate of depreciation in the Korean won relative to the Japanese yen? According to the PPP, E𝐾𝐾𝐾𝐾/𝑌𝑌𝑌𝑌𝑌𝑌 = 𝑃𝑃𝐾𝐾𝐾𝐾𝐾𝐾 𝑃𝑃𝐽𝐽𝐽𝐽𝐽𝐽 Hence, ∆E𝐾𝐾𝐾𝐾 𝑌𝑌𝑌𝑌𝑌𝑌 E𝐾𝐾𝐾𝐾 𝑌𝑌𝑌𝑌𝑌𝑌 Hence, 5% depreciation of Korean Won is expected ≈ πKor − πJap = 6% − 1% = 5% C Suppose the BOK increases the money growth rate from 12% to 15% If nothing in Japan changes, what is the new inflation rate in Korea? Using time series diagrams, illustrate how this increase in the money growth rate affects the money supply, Korea’s interest rate, prices, real money supply, and the exchange rate over time (Plot each variable on the vertical axis and time on the horizontal axis.) πKor = 𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑔𝑔𝐾𝐾𝐾𝐾𝐾𝐾 = 15% − 6% = 9% For diagrams, see Appendix A D Suppose the BOK wants to maintain an exchange rate peg with the Japanese yen What money growth rate would the Bank of Korea have to choose to keep the value of the won fixed relative to the yen? To keep the exchange rate constant, the Bank of Korea must lower its money growth rate We can figure out exactly which money growth rate will keep the exchange rate fixed by using the fundamental equation for the simple monetary model πKor − πJap = (𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑔𝑔𝐾𝐾𝐾𝐾𝐾𝐾 ) − �𝜇𝜇𝐽𝐽𝐽𝐽𝐽𝐽 − 𝑔𝑔𝐽𝐽𝑎𝑎𝑎𝑎 � = (𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 6%) − 1% = 𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 = 7% Therefore, if the Bank of Korea sets its money growth rate to 7%, its exchange rate with Japan will remain unchanged E Suppose the Bank of Korea sought to implement policy that would cause the Korean won to appreciate relative to the Japanese yen What ranges of the money growth rate (assuming positive values) would allow the Bank of Korea to achieve this objective Using the same reasoning as previously, the objective is for the won to appreciate: ∆E𝐾𝐾𝐾𝐾 𝑌𝑌𝑌𝑌𝑌𝑌 E 𝐾𝐾𝐾𝐾 𝑌𝑌𝑌𝑌𝑌𝑌 < This can be achieved if the Bank of Korea allows the money supply to grow by less than 7% IFM&KE CAU MBA Fall 2015 each year (From the textbook) This question uses the general monetary model, in which L is no longer assumed constant and money demand is inversely related to the nominal interest rate Consider the same scenario described in the beginning of the previous question In addition, the bank deposits in Japan pay 3% interest A Compute the interest rate paid on Korean deposits Fisher effect: iKor − iJap = πKor − πJap iKor − 3% = 6% − 1% iKor = 8% B Using the definition of the real interest rate (nominal interest rate adjusted for inflation), show that the real interest rate in Korea is equal to the real interest rate in Japan (Note that the inflation rates you calculated in the previous question will apply here.) 𝑟𝑟𝐾𝐾𝐾𝐾𝐾𝐾 = iKor − πKor = 8% − 6% = 2%, 𝑟𝑟𝐽𝐽𝐽𝐽𝐽𝐽 = iJap − πJap = 2% − 1% = 1% C Suppose the Bank of Korea increases the money growth rate from 12% to 15% and the inflation rate rises proportionately (one for one) with this increase If the nominal interest rate in Japan remains unchanged, what happens to the interest rate paid on Korean deposits? We know that the inflation rate in Korea will increase to 9% We also know that the real interest rate will remain unchanged Therefore: iKor = 𝑟𝑟𝐾𝐾𝐾𝐾𝐾𝐾 + πKor = 1% + (6% + 3%) = 10% D Using time series diagrams, illustrate how this increase in the money growth rate affects the money supply, Korea’s interest rate; prices, real money supply; and the exchange rate over time (Plot each variable on the vertical axis and time on the horizontal axis.) See the Appendix for diagrams IFM&KE CAU MBA Fall 2015 Diagrams for Q5-C IFM&KE CAU MBA Fall 2015 Diagrams for Q6-D ... πKor =