Question

2. Synthetic Forward a) Explain how deposits and spot transactions in the foreign exchange rate can be used to create the same payoff as a forward contract. Illustrate with an example. b) Assume the US interest rate on a 1 year deposit is 1% and the Japanese rate on an identical deposit is / and the spot rate is 100 yen/US$. Compute the forward rate and the forward premium. Show calculations

Answer 1

Answer 2a)

Let us assume that we borrow US Dollar (USD) from US for 1 year, bring it to Japan and convert it into Japanese Yen (JPY) to deposit in Japan for 1 year.

We assume,

a) the deposit interest rates for 1 year time period in US and Japan are iUS and iJPY respectively.

b) Current conversion rate of US dollar to Japanese Yen is Spot Rate (S)

c) Conversion rate of US dollar to Japanese Yen after 1 year is Forward Rate (F)

• If we borrow 1 US Dollar (USD) from any US Bank for 1 year then I will return (1+1*iUS) to that same Bank. This amount can be converted into JPY by multiplying with the forward rate F i.e F (1+1*iUS)
• If we borrow that 1 USD from any US Bank for (1 year), bring it to Japan and convert it into Japanese Yen (JPY) to deposit in any Japanese Bank for 1 year then in that case, 1 USD will be converted to JPY at current Spot rate S. The amount S will be invested to Japanese Bank at interest rate iJPY to get a return of (S + S*iJPY) after 1 year.

To ensure the above two transactions does not result into any risk free profit, should matches each other in JPY terms.

F (1+1*iUS) = S (1+1*iJPY)

or F = S*{(1+1*iJPY) / (1+1*iUS)}

Hence this formula suggests how deposits and spot transactions in the foreign exchange rate can be used to create the same pay-off as a forward contract.

Answer 2b)

As per the assumptions given,

1 year US deposit interest rate = 1% = 0.01 = iUS

1 year JPY deposit interest rate = 1/2% = 0.005 = iJPY

The Spot Rate = 100 Yen/$ = S

Hence applying the formula to calculate the forward rate for 1 year derived above,

F = S*{(1+1*iJPY) / (1+1*iUS)}

F = 100{(1+0.005)/(1+0.01)}

F = 100{1.005/1.01} = 99.50

Hence the forward rate is computed as 99.50 Yen/$.

And Forward premium = Forward Rate - Spot Rate = 99.50 - 100 = -0.50 Yen/$

Therefore 1 year forward rate for USDJPY is 99.50 whereas the current SPOT price for USDJPY is 100 Yen/$. It means that USD is at discount to JPY.

Conclusion: Therefore in any currency pair, future value of a currency with high interest rate is at a discount (in relation to spot price) to the currency with low interest rate.