Question

Challenge Problem. Following are currency exchange “crossrates” between pairs of major currencies. Currency crossrates include both direct and indirect methods for expressing relative exchange rates. Currency crossrates include both direct and indirect methods for expressing relative exchange rates.

      U.S.  U.K.  Swiss  Japanese  European

              Dollar  Pound  Franc  Yen  Euro

      EMU      1.1406      ?  0.6783  0.0087  ---

      Japan       130.66  185.98  77.705     ---  114.60

      Switzerland      1.6817  2.3936     ---  0.0129     ?

     United Kingdom         ?      ---  0.4178     ?  0.6162

     United States         ---  1.4231      ?  0.0077  0.8767

a.    Fill in the missing exchange rates in the crossrates table.

b.    If the inflation rate is expected to be 3 percent in the European Monetary Union

       (EMU) and 4 percent in the United States next year, estimate the forward rate of one euro in U.S. dollars one year from now.

c.     If the one-year government interest rate is 6 percent in Japan and 4 percent in the United Kingdom, estimate the amount of Yen that will be needed to purchase one British pound one year from now.

d.    Based solely on purchasing power parity (PPP), calculate the expected one-year inflation rate in the U.S. if the Swiss inflation rate is expected to be 3.5 percent next year, and the one-year forward rate of a Swiss franc is $.6100.

e.   Assume the U.S. dollar is expected to depreciate by 15 percent relative to the euro at the end of one-year from now and the interest rate on one-year government securities in the EMU is 5.5 percent. What would be the current U.S. one-year government security interest rate based solely on the use of interest rate parity to forecast forward currency exchange rates?

U.S. U.K. Dollar Pound 1.1406 7 130.66 185.98 1.6817 2.3936 Swiss Franc 0.6783 77.705 EMU Japan Switzerland United Kingdom United States Japanese European Yen Euro 0.0087 --- 114.60 0.0129 0.6162 0.0077 0.8767 0.4178 2 --- 1.4231

> Please provide answer to part d and e of the question. Thank You

Answer 1

a) let's start with the first blank.

GENERALLY CROSS RATE IS EXPRESSED BASED ON US DOLLARS AS FOLLOWS

CROSS RATE = ( CURRENCY1 / USD ) * ( USD / CURRENCY 2 )

FOR QN MARK1,

We have to find out cross rate between POUND and EURO .

thus , CROSS RATE = ( POUND / USD ) * (USD / EURO )

Directly substituting values from the table

cross rate = 1.4231 * 1.1406

= 1.62318 ans.

similarly for second qn mark,

CROSS RATE = ( EURO / USD ) * ( USD / FRANC ) FOR euro v/s franc

= 0.8767 * 1.6817

= 1.4743

for third qn mark ,  

CROSS RATE = ( USD / USD ) * ( USD / POUND ) FOR usd v/s pound

= USD / POUND

= 1 / 1.4231 = 0.7026 ( RECIPROCAL OF POUND TO USD RATIO )

for fourth qn mark , CROSS RATE = ( YEN / USD ) * ( USD / POUND ) FOR yen v/s pound

= 0.0077 * 0.7026

= 0.0054

for last qn mark , CROSS RATE = ( FRANC / USD ) * ( USD / USD ) FOR franc v/s usd

= FRANC / USD

= 0.5946 ( RECIPROCAL OF USD TO FRANC )

b)

Forward rate can be directly calculated using the formula

FR = ( ( 1 + int rate 1 )n1 / ( 1 + int rate 2 )n2 ) - 1

substituting values = (( 1 + 0.004 ) / ( 1 + 0.003 )) - 1

= 0.099%v

c)

value of japaneese yen based on usd now = 0.0077

after accounting interest rate the value will be 0.0077 * 1.06 = 0.00816

value of uk pound based on usd now = 1.4231

afterr accounting interest rate the value will be 1.4231 * 1.04 = 1.48

thus amount of yen needed to purchase 1 british pound = 1.48 / 0.00816 = 181.37