Creating Synthetic FX Forward Contracts
Team Latte
Sep 08, 2005

Suppose we want to create a synthetic forward on Dollar-Yen. Very simple, to synthesize a two year USD-JPY forward contract we need to:

1. Borrow Japanese Yen for two years;
2. Convert the Yen into US Dollars at the spot FX rate; and finally
3. Deposit the Dollars in a deposit account for two years.

Actually, the above is easier said than done. This is for the simple reason the 2-year borrowing and the 2-year deposit in the above scheme must be both zero-coupon transactions, i.e. zero-coupon borrowing and zero-coupon deposit. Though, it may be easy to find zero-coupon deposits (Certificates of Deposit) it is very difficult for most companies to get access to zero-coupon borrowings. Most borrowings would be either with fixed rate coupons or LIBOR based floating coupons.

Therefore, to engineer a synthetic FX forward contract one has to first engineer a zero coupon borrowing. To engineer a zero coupon borrowing the treasurer (of a company) has to go through the following process:

• The company needs to borrow A₁ for one year at an interest rate of l₂ which is the 1-year forward LIBOR rate, which can be easily deduced from the forward curve.
• At the same time, the company enters into a vanilla 1-year fixed-for-floating interest rate swap with a notional amount of N₁ in which the company receives floating annual cash flows determined 1-year LIBOR rate and make fixed annual payments determined by the 1-year swap rate s₁, which is also know today;
• Also, at the same time the company enters into a 2-year fixed-for-floating swap as well with a notional of N₂ in which the company receives floating annual cash flows determined by the 1-year LIBOR rate and it makes fixed annual payments to the bank determined by the 2-year swap rate s₂ which is also know today.

At the end of the first year, however, the company needs to roll the loan over for another year. This means that:

• The company needs to borrow A₁ for one year at an interest rate of l₂ which is the 1-year forward LIBOR rate, which can be easily deduced from the forward curve.

Thus the company has to determine four variables - A₀, A₁, N₁ and N₂ - and if we choose a principal repayment amount of $100 (for benchmark) then there would be four equations corresponding to the four transactions above. So the four variables can be easily determined, because one can solve a system of four equations with four variables.

Once the zero coupon loan is synthesized the company can easily synthesize the forward FX contract. But the million dollar question is: when FX contracts are so readily available in the market why does the treasurer of a company have to go to all this trouble to create a synthetic forward contract. The main reason for this is cost savings. Long dated forward contracts, 2 years or more can cost a lot given the big bid-ask spreads. However, the bid-ask spread for LIBOR borrowings, for standard interest rate swaps and for spot FX are quite small. According to the treasurer of one multinational corporate the cost can be cut by half to two-thirds if a synthetic forward is created.

Acknowledgement: The above is inspired by the experience of Jacques Tierney who was at one time responsible for group treasury management in a multinational company and as reported in Managing Financial Risk.

Disclaimer
"Risk Latte uses proprietary and non-proprietary mathematical and empirical models to measure the volatility and estimate the direction of the market. There is no guarantee of any particular outcome happening and readers must exercise caution while interpreting the conclusions of this article. Risk Latte Company is not a registered stock broker or an SFC registered entity and readers must take advise from their financial advisors, stock brokers, research analysts and bankers while making any buying or selling decisions. Risk Latte Company is not in the business of making stock or asset forecasts whether explicitly or implicitly and shall not be responsible for and/or liable for any losses arising out of any trading decisions based on the above article."

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