Yen Forward Premium Analysis: Spot and Forward Rates Explained

Problem 5.3 Yen Forward Use the following spot and forward bid-ask rates for the Japanese yen/U.S. dollar ( ¥ /$) exchange rate from September 16, 2010, to answer the following questions: ¥/$ ¥/$ Period Bid Rate Ask Rate spot 85.41 85.46 1 month 85.02 85.05 2 months 84.86 84.90 3 months 84.37 84.42 6 months 83.17 83.20 12 months 82.87 82.91 24 months 81.79 81.82 a. What is the mid-rate for each maturity? b. What is the annual forward premium for all maturities? c. Which maturities have the smallest and largest forward premiums? Since the exchange rate quotes are indirect quotes on the dollar ( ¥ /$), the proper forward premium calculation is: Forward premium = ( Spot - Forward ) / (Forward) x (360 / days) a. b. ¥ /$ ¥ /$ Calculated Forward Period Days Forward Bid Rate Ask Rate Mid-Rate Premium spot 85.41 85.46 85.43500 1 month 30 85.02 85.05 85.03500 5.6447% 2 months 60 84.86 84.90 84.88000 3.9232% 3 months 90 84.37 84.42 84.39500 4.9292% 6 months 180 83.17 83.20 83.18500 5.4096% 12 months 360 82.87 82.91 82.89000 3.0703% 24 months 720 81.79 81.82 81.80500 2.2187% The forward rates progressively require fewer and fewer Japanese yen per dollar than the current spot rate. Therefore the yen is selling forward at a premium and the dollar is selling forward at a discount. c. Which maturities have the smallest and largest forward premiums? The 24 month forward rate has the smallest premium, while the 1 month forward possesses the largest premium.

Problem 5.7 Asian Pacific Crisis The Asian financial crisis which began in July 1997 wreaked havoc throughout the currency markets of East Asia. a. Which of the following currencies had the largest depreciations or devaluations during the July to November period? b. Which seemingly survived the first five months of the crisis with the least impact on their currencies? Part a. July 1997 November 1997 Percentage Country Currency China yuan Hong Kong dollar Indonesia rupiah Korea won Malaysia ringgit Philippines peso Singapore dollar Taiwan dollar Thailand baht (per US$) 8.40 7.75 2,400 900 2.50 27 1.43 27.80 25.0 (per US$ Change vs dollar 8.40 0.0% 7.73 0.3% 3,600 -33.3% 1,100 -18.2% 3.50 -28.6% 34 -20.6% 1.60 -10.6% 32.70 -15.0% 40.0 -37.5% Part b. The Chinese yuan's value against the US dollar, as a result of the Chinese government maintaining its peg to the dollar, did not change at all during the crisis. The Thai baht, however, fell 37.5% in only five months, with the Indonesian rupiah a close second with a loss of 33.3%.

Problem 5.8 Bloomberg Currency Cross Rates Use the following cross rate table from Bloomberg to answer the following questions. Currency USD EUR JPY GBP CHF CAD AUD HKD 7.7736 10.2976 0.0928 12.2853 7.9165 7.6987 7.6584 AUD 1.015 1.3446 0.0121 1.6042 1.0337 1.0053 0.1306 CAD 1.0097 1.3376 0.0121 1.5958 1.0283 0.9948 0.1299 CHF 0.9819 1.3008 0.0117 1.5519 0.9725 0.9674 0.1263 GBP 0.6328 0.8382 0.0076 0.6444 0.6267 0.6234 0.0814 JPY 83.735 110.9238 132.3348 85.2751 82.9281 82.4949 10.7718 EUR 0.7549 0.009 1.193 0.7688 0.7476 0.7437 0.0971 USD 1.3247 0.0119 1.5804 1.0184 0.9904 0.9852 0.1286 Quote Calculated a. Japanese yen per US dollar? 83.735 b. US dollars per Japanese yen? 0.0119 0.0119 c. US dollars per euro? 1.3247 d. Euros per US dollar? 0.7549 0.7549 e. Japanese yen per euro? 110.9238 f. Euros per Japanese yen? 0.009 0.0090 g. Canadian dollars per US dollar? 1.0097 h. US dollars per Canadian dollar? 0.9904 0.9904 i. Australian dollars per US dollar? 1.015 j. US dollars per Australian dollar? 0.9852 0.9852 k. British pounds per US dollar? 0.6328 l. US dollars per British pound? 1.5804 1.5803 m. US dollars per Swiss franc? 1.0184 n. Swiss francs per US dollar? 0.9819 0.9819 HKD

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Problem 5.9 Dollar/Euro Forwards Use the following spot and forward bid-ask rates for the U.S. dollar/euro (US$/€) exchange rate from December 10, 2010, to answer the following questions: US$/ € US$/ € Period Bid Rate Ask Rate spot 1.3231 1.3232 1 month 1.3230 1.3231 2 months 1.3228 1.3229 3 months 1.3224 1.3227 6 months 1.3215 1.3218 12 months 1.3194 1.3198 24 months 1.3147 1.3176 a. What is the mid-rate for each maturity? b. What is the annual forward premium for all maturities? c. Which maturities have the smallest and largest forward premiums? Since the exchange rate quotes are direct quotes on the dollar (US$/ € ), the proper forward premium calculation is: Forward premium = ( Forward - Spot ) / (Spot) x (360 / days) a) b) US$/ € US$/ € Calculated Forward Period Days Forward Bid Rate Ask Rate Mid-Rate Premium spot 1.3231 1.3232 1.32315 1 month 30 1.3230 1.3231 1.32305 -0.0907% 2 months 60 1.3228 1.3229 1.32285 -0.1360% 3 months 90 1.3224 1.3227 1.32255 -0.1814% 6 months 180 1.3215 1.3218 1.32165 -0.2267% 12 months 360 1.3194 1.3198 1.31960 -0.2683% 24 months 720 1.3147 1.3176 1.31615 -0.2645% The forward rates progressively require less and less U.S. dollars per euro than the current spot rate. Therefore the dollar is selling forward at a premium and the euro is selling forward at a discount. c) Which maturities have the smallest and largest forward premiums? The 1 month forward rate as the smallest premium, while the 12 month forward possesses the largest premium.

Problem 5.10 Swissie Triangular Arbitrage The following exchange rates are available to you. (You can buy or sell at the stated rates.) Mt. Fuji Bank ¥92.00/$ Mt. Rushmore Bank SF1.02/$ Mt Blanc Bank ¥90.00/SF Assume you have an initial SF12,000,000. Can you make a profit via triangular arbitrage? If so, show the steps and calculate the amount of profit in Swiss francs (Swissies). Assumptions Values Beginning funds in Swiss francs (SF) 12,000,000.00 Mt. Fuji Bank (yen/$) 92.00 Mt. Rushmore Bank (SF/$) 1.0200 Matterhorn Bank (yen/SF) 90.00 Try Number 1: Start with SF to $ Step 1: SF to $ 11,764,705.88 Step 2: $ to yen 1,082,352,941.18 Step 3: yen to SF 12,026,143.79 Profit? 26,143.79 A profit. Try Number 2: Start with SF to yen Step 1: SF to yen 1,080,000,000.00 Step 2: yen to $ 11,739,130.43 Step 3: $ to SF 11,973,913.04 Profit? (26,086.96) A loss.

Problem 5.13 Venezuelan Bolivar (A) The Venezuelan government officially floated the Venezuelan bolivar (Bs) in February of 2002. Within weeks, its value had moved from the pre-float fix of BS778/$ to Bs1025/$. a. Is this a devaluation or depreciation? b. By what percentage did its value change? Assumptions Values Fixed rate of exchange, Bs/$ 778 New freely floating rate (2 weeks later), Bs/$ 1,025 a. Is this a devaluation or depreciation? Devaluation This is a case in which a government has changed its currency from a then governmentally determined fixed rate, to a regime in which the currency Depreciation is allowed to change in value based on supply and demand forces in the market. As a result of the move, the currency's value in this case was a "depreciation" against the U.S. dollar. b. By what percentage did its value change? Percentage devaluation is: % Chg = (S1 - S2) / (S2) -24.10%

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Problem 5.14 Venezuelan Bolivar (B) The Venezuelan political and economic crisis deepened in late 2002 and early 2003. On January 1st, 2003, the bolivar was trading at Bs1400/$. By February 1st, its value had fallen to Bs1950/$. Many currency analysts and forecasters were predicting that the bolivar would fall an additional 40% from its February 1st value by early summer 2003. a. What was the percentage change in January? b. Forecast value for June 2003? Assumptions Values Exchange rate, January 1, 2003 (Bs/$) 1,400 Exchange rate, February 1, 2003 (Bs/$) 1,950 Forecast fall in value from Feb 1 to early summer, 2003 -40.0% a) What was the percentage change in January? % chg = (S1 - S2)/(S2) b) Forecast value for June 2003? -28.21% We are actually solving the equation for S2 (Bs/$) S2 = (S1)/(1+%chg) = (1950)/(1-.40) 3,250

Problem 5.16 Direct on the Dollar Calculate the forward discount on the dollar (the dollar is the home currency) if the spot rate is spot rate is $1.5800/£ and the 6-month forward rate is $1.5550/£ Quoted 180-day Percent premium Assumptions Spot rate Forward rate or discount Days forward 180 Exchange rate, US$/ £ 1.5800 $ 1.5550 $ Calculation formula for the direct quote on the dollar: Percent premium = ( Forward - Spot ) / ( Spot ) x ( 360 / 180 ) -3.1646% The forward rate requires fewer US dollars in exchange for pounds than the current spot rate. The dollar is therefore selling forward at a premium against the pound (and the pound is simultaneously selling forward at a discount versus the US dollar). Check calculation Inverting the quotes ( £ /US$) £0.6329 £0.6431 Percent forward premium = ( Spot - Forward ) / ( Forward ) x ( 360 / 180 ) -3.1646%

Problem 5.17 Mexican Peso - European Euro Cross Rate Calculate the cross rate between the Mexican peso (Ps) and the euro (€ ) from the following two spot rates: Ps12.45/$ and € 0.7550/$. Assumptions Exchange rate Mexican peso, pesos/dollar (Ps/$) 12.45 European euro, euros/dollar (€/$) 0.7550 Calculated cross rate, pesos/euro 16.4901 pesos/euro = (Ps/$) / (€/$) or equivalently, euros/peso (€/Ps) 0.0606

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