# Chapter 12 - Selected Quantitative Problems & Solutions

Chapter 12 - Selected Quantitative Problems & Solutions

Question 1

A German sports car is selling for 70,000 euros. What is the dollar price in the United States for the German car if the exchange rate is 0.90 euros per dollar?

Solution:

70,000 euros  (\$1/0.90 euros)  \$77,777.77.

Question 2

An investor in England purchased a 91-day T-bill for \$987.65. At that time, the exchange rate was \$1.75 per pound. At maturity, the exchange rate was \$1.83 per pound. What was the investor’s holding period return in pounds?

Solution:The bond cost \$987.65/\$1.75  £564.37.

At maturity, the \$1,000 is worth \$1,000/\$1.83  £546.45.

The holding period return is (546.45  564.37)/564.37 0.0317.

Question 3 (Useful)

An investor in Canada purchased 100 shares of IBM on January 1st at \$93.00/share. IBM paid an annual dividend of \$0.72 on December 31st. The stock was sold that day as well for \$100.25. The exchange rate is \$0.68/Canadian dollar on January 1st and \$0.71/Canadian dollar on December 31st. What is the investor’s total return in Canadian dollars?

Solution:The price of each share is \$93.00/\$0.68  136.76 Canadian dollars.

The dividend is \$0.72/\$0.71  1.014 Canadian dollars

The sale price is \$100.25/\$0.71  141.20 Canadian dollars

The return  (141.20  1.014  136.76)/136.76  0.03988

Question 4

The current exchange rate is 0.93 euros per dollar, but you believe the dollar will decline to 0.85 euros per dollar. If a euro-denominated bond is yielding 2%, what return do you expect in U.S. dollars?

Solution:% change in currency  (0.85 – 0.93)/0.93 0.086

Total investment return  0.02  (0.086)  10.6%

Chapter 13 - Selected Quantitative Problems & Solutions

2.Again, the Federal Reserve purchases \$1,000,000 of foreign assets. However, to raise the funds,
the trading desk sells \$1,000,000 in T-bills. Show the effect of this open market operation using
T-accounts.

Solution:

Federal Reserve System
Assets / Liabilities
Foreign assets / \$1 million / Currency in circulation / 
(international reserves)
Government bonds / \$1 million

3.\$1.274 per euro. Note that since the exchange rate is quoted as \$ per euro, the euro is the domestic currency. The interest parity equation is as follows:

0.04  0.02 

 0.02 0.04 0.02 

 1.30 1.3 (0.02)  1.30  0.026  \$1.274 per euro

Another way to get the answer is to recognize that the interest rate differential between implies that the euro is expected to depreciate by 2% which implies a decline of 2% of 1.30 which is 0.026 over the year to \$1.274 per euro.

4.\$1.287 per euro. Note that since the exchange rate is quoted as \$ per euro, the euro is the domestic currency. From the previous problem,  \$1.274 per euro and the interest rate on euro deposits rises to 5%.Again using the interestparityequation:

0.05  0.02  (1.274 Et)/Et

(1.274 Et)/Et 0.02  0.05 0.03 

Et1.274  0.03 Et

0.97 Et 1.274 

Et 1.274/0.97  \$1.287 per euro

Another way to get the answer is to recognize that when the interest rate on euro deposits rises by 1%, the euro must have an additional expected depreciation of 1% which means that the initial level of
the euro must fall by 1% from 1.30 to 1.287 per euro.

5.If the balance in the current account increases by \$2 billion while the capital account is off \$3.5 billion, what is the impact on governmental international reserves?

Solution:Current account  capital account  international reserves 2  3.5 1.5

Governmental international reserves are down by \$1.5 billion.