Question

Please answer both questions

1) Suppose a bank quotes $/€ = 1.1045-1.1506. What is the bid-ask spread in percentage? Do not write any symbol. Express your answers as a percentage. Make sure to round your answers to the nearest 100th decimal points. For example, write 12.34 for 12.34%.

2)Suppose a bank quotes S = $1.1045/€. The annualized risk-free interest rates are 4% and 6% in the U.S and Germany, respectively. Find the approximate forward rate for the euro. Do not write any symbol. Make sure to round your answers to the nearest 100th decimal points. For example, write 1.2345 for $1.2345/€.

Answer 1

Solution 1:

The formula for calculating the Bid ask spread in percentage is

Bid ask spread (%) = [ ( Ask price – Bid price ) / Ask price ] * 100

As per the information given in the question a bank quotes $/€ = 1.1045-1.1506

Here the Bid price of the Euro is = $ 1.1045

Ask price of the Euro is = $ 1.1506

= [ ( $ 1.1506 – $ 1.1045 ) / $ 1.1506 ] * 100

= ( $ 0.0461 / $ 1.1506 ) * 100

= 0.040066 * 100

= 4.0066 %

= 4.01 % ( when rounded to the 100^th decimal point )

Thus the Bid – Ask spread in percentage = 4.01

Solution 2 :

As per the Interest rate Parity model

Exchange rate differential = Interest rate differential

( Forward Rate / Spot Rate ) = [ ( 1 + Risk free Interest Rate in Currency A ) / ( 1 + Risk free Interest Rate in Currency B ) ] ⁿ

Where n = No. of years

As per the Information given in the question we have

Annualized Risk free Interest rate in US = 4 % = 0.04                        ( Currency A )

Annualized Risk free Interest rate in Germany = 6 % = 0.06             ( Currency B )

Spot rate of the Euro is = $ 1.1045

Thus A/ B = $ / € = $ 1.1045

Applying the above values in the formula / Equation we have

Forward Rate / 1.1045 = [ ( 1 + 0.04 ) / ( 1 + 0.06 ) ] ¹

Forward Rate = [ 1.04 / 1.06 ] *1.1045

Forward Rate = 0.981132 * 1.1045

Forward Rate = $ 1.083660

Forward Rate = $ 1.0837

Thus the forward rate of the Euro in US Dollars = 1.0837