Question

The nominal yield on 6-month T-bills is 7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5%. In the spot exchange market, 1 yen equals $0.011. If interest rate parity holds, what is the 6-month forward exchange rate? Round the answer to five decimal places. Do not round intermediate calculations.

Answer 1

Interest rate parity holds that investors should earn the same return on interest-bearing investments in all countries aftere adjusting for risk. It recognizes that when you invest in a country other than your home country, you are affected by two forces- return on the investment itself and changes in the exchange rates. It follows that your overall return will be higher than the investment's stated return if the currency in which your investment is denominated appreciates relative to your home currency. Likewise, your overall return will be lower if the foreign currency you receive declines in value.

The relationship between spot and forward exchange rates and interest rates, which is known as interest rate parity, is expressed in the following equation:

Forward exchange rate / Spot exchange rate = (1 + rh)/ (1+rf)

where rf is the default free interest rate
rh is the interest rate of the home country

rf is calculated as

rf = 5.0%/2
= 2.50% (Because 180days is one-half of 360-day year)
rh = 7% / 2
= 3.5% (Because 180 days is one-half of 360-day year)

Given that the spot exchange rate is $0.011

Substituting the values in the above equation, we get

Forward exchange rate/ $0.011 = (1+ 0.035) / (1+0.025)
Forward exchange rate = [(1.035) / (1.025)] * $0.011
Forward exchange rate = 1.009756 * $0.011
= $0.0111073

Therefore, the forward exchange rate (ft) = $0.01111