Solution: Currency Conversion Problem

1. $3,000,000can be converted into ??? British pounds

3,000,000 x0.75 = BP 2,250,000

2. SF1,500,000 can be into ???? USD

1,500,000 x0.50 = $ 750,000

3. MP 600,000can be converted into ??? Swiss Francs

MP 600,000 /10 = $ 60,000

$ 60,000 /0.50 = SF 120,000

4a. How manySF does it take to buy 1 BP ?

BPDQ = 1 /0.75 = 1.33 ; SFDQ = 0.50

BPDQ / SFDQ =1.33 / 0.50 = SF 2.67

4b. How manyBP does it take to buy 1 SF?

SFDQ / BPDQ =0.50/1.33 = BP 0.375

Bid-Ask Spread Problem

The followingtable presents bid and ask quotes for BP from currency dealers in New York andLondon:

1. Assume thatyou dealt with the New York currency dealer only. You converted $100,000 intopounds, and immediately afterwards sold the pounds for dollars. Estimate thedollar amount you lost in this round trip transaction.

$100,000 /1.68= BP 59,523.81; BP 59,523.81 * 1.58 = $94,047.62

$94,047.62 -$100,000 = $5,952.38

2. Assume thatyou dealt with the London currency dealer only. What is the percentage bid-askspread for this dealer?

[(1.70 - 1.65)/ 1.70] * 100 = 2.94%

3. Whichdealer (s) would you buy from, and sell to ?

Buy from thelowest ask = New York

Sell to thehighest bid = London

1. The following exchangerates are available to you.

Swiss franc/dollar                SFr1.5971/$

Australian dollar/U.S.dollar       A$1.8215/$

Australian dollar/ Swissfranc      A$1.1450/SFr

Assume you have an initial$10 million.

a. Can you make a profitvia triangular arbitrage? Explain.

b. If so, show steps andcalculate the amount of profit in U.S. dollars.

ANS:

a.Since S^SFr/$ S^$/A$S^A$/SFr = 1.5971 x 1/1.8215x 1.1450 = 1.00394 > 1, there is an arbitrage opportunity.

因为S^SFr/$S^$/A$S^A$/SFr = 1.5971 x 1/1.8215 x 1.1450 = 1.00394 >1，所以有套汇获利机会。

b.Steps套汇路径:

① Sell $ to buy SFr: 10 million x SFr 1.5971/$= SFr15.971m

卖出美元买进瑞郎：10million x SFr 1.5971/$ = SFr15.971m 

② Sell SFr to buy A$: SFr15.971m xA$1.1450/SFr = A$18.286795m

卖出瑞郎买进澳元：SFr15.971mx A$1.1450/SFr = A$18.286795m

③ Sell A$ to buy $: A$18.286795m÷A$1.8215/$ =$10.0394153m

卖出澳元买回美元：A$18.286795m÷A$1.8215/$= $10.0394153m

Profit(ignoring transaction fees)套汇利润（不计交易费用）:

  $10.0394153 – $10 = $0.0394153 million =$39,415.3 

1. That’s the information ofthe selected items from country A’s balance of payments in 2010.

a. Calculate country A’s BOT.

b. How many millions dollarCountry A’s current account balance is?

c. Suppose the changes incountry A’s official reserves are zero in 2010, calculate its capital andfinancial account balance.

d. If country A’s officialreserves are recorded on the credit side by $10 million in 2010, calculate itscapital and financial account balance.

e. Based on the assumption ofquestion d, country A has BOP deficit or surplus in 2010? Explain.

ANS:

a. BOT=719-1,145=-426                                

b. CA=719-1,145+279-210-269+284-49=-391                                 

c. KA=-(CA+Errors)=380                                  

d. KA=-(CA+Errors+OR)=370                                  

e. deficits逆差.                              

Because the official reservesreduced by $10 million.

因为官方储备减少了$10 million。              

2. List of transactions

1. Purchase of $35 million in Japanese bonds by Vangaurd(USA).

2. A $25 million US aid to Bosnia

3. $45 million sales by All State Insurance in France

4. Purchase by HP of components valued at $65 millionfrom Hyndai, in Korea.

5. Payment of $10 million in dividends by GE to itsinvestors in Frankfurt

6. A $120 million stock issue in Frankfurt by GE

7. Purchase of $50 million French Francs by the USFederal Reserve

8. Purchase of $60 million in Japanese Govt Bonds by theUS Federal Reserve

9. Foreign tourists spending $15 million in New Orleans

10. Sale of Star Wars DVD, valued at $55 million, in China

Please enter the alphabetsassociated with each transaction listed above in the proper cells in thefollowing table.

2. Based on the transactionamounts, please calculate the following Balance of Payment accounts:

Balanceof Trade [55] - [65] =-10

CurrentAccount Balance [55 + 15] - [65+ 45+ 10 + 25] = -75

CapitalAccount Balance [35+25+45+120+65+10+50] -[35+ 60+120+15+55] = 65

Overall Balance

OR=60 - 50 = 10

So, Overall Balance=-10

1. Samuel Samosir trades currencies for Peregrine Funds in Jakarta, Indonesia. He focuses nearly all of his time and attention on the U.S. dollar/British pound ($/₤) exchange rate. The current spot rate is$1.5950/₤. After considerable study this week, he has concluded that the British pound will depreciate versus the U.S. dollar in the coming 90 days. A British pound option quoted on PSE as the following:

a. Should Samuelbuy a put option on British pound ora call option on British pound?

b. Using youranswer to part a, what is Samuel’s break-even price?Label your axes and plot the break-even price. Draw a profit/loss graph for this currency option at expiration.

c. Using youranswer to part a, and assume he buys 100contracts, what is Samuel’s gross profit and net profit (includingthe premium) if the spot rate at the end of the 90 days is indeed $1.5600/₤? And what if the spot rate atthe end of the 90 days is indeed $1.6000/₤?

ANS:

a. Samuel should buy a put option on British pound.

  Samuel应该买进英镑看跌期权。 

b. Break-even exchange rate for a put option = strike price - premium

                                    = 1.5900 - 0.0174= $1.5726/₤     

  看跌期权的盈亏平衡汇率=执行汇率-期权费

                        = 1.5900 - 0.0174= $1.5726/₤ 

c. Gross profit =($1.5900/₤- $1.5600/₤) ×₤31,250×100=$93,750

  毛利= ($1.5900/₤- $1.5600/₤) ×₤31,250×100=$93,750

  Net profit = ($1.5900/₤- $1.5600/₤- $0.0174/₤)×₤31,250×100 = $39,375 

净利润=($1.5900/₤-$1.5600/₤- $0.0174/₤) ×₤31,250×100 = $39,375

Gross profit = $0                               

毛利= $0                                     

  Net profit =-($0.0174/₤ ×₤31,250×100) = -$54,375

净利润=-($0.0174/₤×₤31,250×100) = -$54,375    

2. Let’s consider a Swiss franc futures contract traded in the United States. On February 19, the March contract closed at 0.7049 dollar per Swissfranc. The size of the contract is 125,000 Swiss francs. The initial margin is $2,600 per contract and the maintenance margin is $1,600. Assume that you buy one March contract on February 19 at 0.7049 $/SFr and you deposit, in cash, an initial margin of $2,600. Listed below are the futures quotations (settlement prices) observed on three successive days:

 What are the cash flows associated with the marking-to-market procedure?

Answer:

Feb. 19: Deposit $2,600 inyour account to hold a Sfr contract. The value of this contract is 125,000×0.7049=$88,112.5.

Feb. 20: Thesettlement price is 0.7009.The value of thiscontract now is 125,000×0.7009=$87,612.5.You lose $500 per contract. Your margin now is equal to $2,100, which is abovethe maintenance margin $1,600. You needn’t reconstitute the initial margin.

Feb. 21: Thesettlement price is 0.6949.The value of thiscontract now is 125,000×0.6949=$86,862.5.You lose an additional $750 per contract. Your margin now is equal to $1,350,which is below the maintenance margin. You will get the margin call toreconstitute the initial margin up to $2,600 by transferring $1,250 to yourmargin account.

Feb. 22: Thesettlement price is 0.7089.The value of thiscontract now is 125,000×0.7089=$88,612.5.You gain $1,750 per contract. You can use this $1,750 as you like.

If youdecide to sell this contract at Feb. 22, you have a net gain of $500 whichcomes from the initial margin of $2,600.

1. Akira Numata, a foreignexchange trader at Credit Suisse (Tokyo), is exploring covered interestarbitrage possibilities. He wants to invest $5,000,000 or its yen equivalent,in a covered interest arbitrage between U.S. dollars and Japanese yen. He facedthe following exchange rate and interest rate quotes:

Spot rate: ¥118.60/$

180-day forward rate:¥117.80/$

180-day dollar interestrate: 4.8% per year

180-day yen interest rate:3.4% per year

The bank does not calculatetransaction costs on any individual transaction because these costs are part ofthe overall operating budget of the arbitrage department.

a. Explain the specificsteps Akira must take to make a covered interest arbitrage profit.

b. Calculate the arbitrageprofit.

c. Using the supply anddemand model to illustrate the effect on spot exchange market, forward exchangemarket, U.S. capital market, and Japan capital market.

ANS:

a. According to IRP 按照利率平价定理:

  i$–i￥= 4.8%/2–3.4%/2 = 0.7% = 0.007

  (F￥/$–S￥/$) / S￥/$ = (117.8–118.6) / 118.6 = - 0.006745

 (F￥/$–S￥/$) / S￥/$+ (i$–i￥)¬=0.000255>0

Akira should invest hismoney in the U.S., because interest rate differential is greater thanforward-spot exchange rate differential.

Akira应在美国进行投资，因为利率差高于远期汇率和即期汇率差。

  Step 1: Since Akira decides to invest$5,000,000, so he borrow yen equivalent.

第一步：因为Akira决定在美国投资$5,000,000，所以在日本借入等值的日元。

       $5,000,000 x ¥118.6/$ = ¥593,000,000

     Akira’s obligation: ¥593,000,000 x (1 +1.7%) = ¥603,081,000

Akira借入日元，负债为：¥593,000,000 x (1 + 1.7%) = ¥603,081,000  

Step 2: Sell yen for dollarat the spot market.

第二步：在即期外汇市场卖出日元买进美元。

     ¥593,000,000 / ¥118.6/$ = $5,000,000                 

Step 3: invest in U.S.market.

第三步：投资于美国市场。

       $5,000,000 x (1 + 2.4%) =$5,120,000               

Step 4: sell dollar for yenat the forward market.

第四步：交割卖出的美元远期换回日元。

        ($5,120,000) x (¥117.8/$) =¥603,136,000          

b. Akira’s net profit:¥603,136,000 –¥603,081,000 = ¥55,000

Akira 取得的净利润：¥603,136,000 –¥603,081,000 = ¥55,000

1. Use the informationpresented in table to answer the following questions.

1. What was the real exchange rate of the dollaragainst the euro in 2009?

2. What was the real exchange rate of the dollaragainst the peso in 2009?

3. Was the dollar appreciated or depreciatedagainst the euro in nominal term? By how many percent?

4. Was the Mexican peso appreciated ordepreciated against the dollar in nominal term? By how many percent?

5. What was the volume of the German foreign tradewith the U.S.?

6. What was the volume of the Mexican foreigntrade with the U.S.?

7. Assume the U.S. trades only with the Germanyand Mexico. Now if we want to calculate the dollar effective exchange rate in2009 against a basket of currencies of euro and Mexican peso, what should bethe weight assigned to the euro?

8. What should be the weight assigned to thepeso?

9. Assume the 2008 is the base year. What wasthe dollar effective exchange rate in 2009?

10. Was the dollar generally stronger or weakerin 2009 according to your calculation? Why?

ANS:

1. 0.70 x (105.3/102.5) = 0.7 x1.0273 = 0.7191

2. 12.2 x (105.3/110.5) = 12.2x .9529 = 11.6259

3. (0.7 /.75)–1 = -6.67%        depreciated

(0.7 /.75)–1 = -6.67%        贬值

4. (1/12.2)/(1/11.8)–1 = -3.28%  depreciated

  (1/12.2)/(1/11.8)–1 = -3.28%  贬值

5. Trade with theGermany is(200 + 350) = 550

与德国的贸易额为(200 + 350) = 550

6. Trade with the Mexicois(120 + 240) =360

与墨西哥的贸易额为(120 + 240) =360

7. The weight assigned to the euro is 550/910 = 60.44%

分配给欧元的权重为 550/910 = 60.44%

8. The weight assigned to the peso is 360/910 = 39.56 %

分配给比索的权重为360/910= 39.56 %

9. Because the base year is 2008, the 2008 EER is 100. The value of the 2009 EER is: [(0.70/0.75)(60.44%)+ (12.2/11.8)(39.56%)] x 100 = (0.5641+0.4090) x 100 = 97.31

因为基年为2008年，2008年的有效汇率为100。2009年的有效汇率为：

[(0.70/0.75)(60.44%) +(12.2/11.8)(39.56%)] x 100 = (0.5641+0.4090) x 100 = 97.31

10. weaker, because97.31-100=-2.69, dollar depreciated by 2.69%.

变弱，因为97.31-100=-2.69，美元贬值2.69%。

2. Based on the informationpresented below:

Current price of abarrel of crude oil (BCL) in the US: $105

Current price ofBCL in Mexico: MXN 1,480

Current exchangerate: 1 USD = MXN 12.70

applying the Big Mac type analysis to determine thefollowing:

a) The price of BCL in Mexico in terms of US dollars(based on the going exchange rate)

b) What should the exchange rate be for the Mexican pesosso that the price of BCL is the same in both countries?

c) Based on the current price of BCL in both countries,what is the percentage overvaluation or undervaluation of the Mexican pesoagainst the USD?

d) Suppose the price of BCL increased by 17% in the USand 11% in Mexico. At the end of the year the exchange rate is MXN 12.25 perUSD. Which currency appreciated in “real terms” USD or MXN?

Solutions

a) The price of BCL in Mexico in terms of US dollars(based on the going exchange rate)

1480 / 12.70 = $116.54

b) What should the exchange rate be for the Mexican pesosso that the price of BCL is the same in both countries?

1480 / 105 = MXN 14.095 = I USD

c) Based on the current price of BCL in both countries,what is the percentage overvaluation or undervaluation of the Mexican pesoagainst the USD?

(14.095 – 12.70) / 12.70 = 10.986% overvaluation of MXNagainst the USD

d) Suppose the price of BCL increased by 17% in the USand 11% in Mexico. At the end of the year the exchange rate is MXN 12.25 perUSD. Which currency appreciated in “real terms” USD or MXN?

According to PPP, the expected percentage change in the exchange rate for USD is 

πMEXICO ­-πUS =11%-17%=-6%

The actual percentage change in the exchange rate is 

%△S^MXN/USD=(12.25-12.7) / 12.7= -3.54%

So in “real terms”USD appreciated.

3. Below are the Big Mac prices and actualexchange rates for select Latin American countries as printed in previouseditions. Use the data to complete the calculation of the implied PPP value ofthe currency versus the U.S. dollar and the calculation as to whether thatcurrency is undervalued (-%) or overvalued (+%) versus the U.S. dollar.

Solution:

4. In January 2000, the spot exchange rate for theeuro was 1.05$/euro. In September 2009 that rate was 1.43$/euro. In January2000, the euro area CPI was 107.5, and the US CPI was 112.7. In September 2009,the euro are CPI was 120 and the US CPI was 125. Based on this information,answer the following questions:

a) Innominal terms, did the euro appreciate or depreciate against the dollar? Whatwas the rate of appreciation / depreciation?

b) Usingthe information on question a), calculate the real exchange rate for the euroin January 2000 and September 2009.

c) Inreal terms, did the euro appreciate or depreciate against the dollar? What wasthe rate of appreciation / depreciation?

d) Accordingto absolute purchasing power parity (PPP), was the euro undervalued or overvaluedrelative to the dollar in September 2009? By what percent?

e) Accordingto relative PPP, what is the predicted value for the euro for September 2009?Was the euro over or undervalued relative to the dollar in September 2009? By whatpercent?

ANS:

a) Therate of nominal depreciation (appreciation) of the dollar (euro) was: (1.43−1.05)/ 1.05 ×100 = 36.19%

b) RER2000 = 1.05 × 107.5/112.7 = 1.0015

RER2009= 1.43 × 120/125= 1.3728

c) Theeuro also appreciated in real terms by 37%.

d) S = P^d/P^f=125/120 = 1.0416 The euro is overvalued because the impliedrate is below the market rate. 37.5% rate of overvaluation.

e)%△S =%△P^d − %△P^f= 10.91%-11.62%=- 0.71% So, with S in 2000 equal to 1.05, S in 2009should have equaled 1.042525 according to relative PPP. Thus, the euro seems tohave been overvalued, with an overvaluation rate of 37.16%.