FX Contracts

# CHAPTER 3: FOREIGN EXCHANGE

### FX Swap Contract

FX swap is a contract with two transactions – a sale (or purchase) of one currency on spot date and purchase (or sale) of the same currency at a forward date. In the case of USD/MYR currency pair, it is a sale of USD in exchange for MYR for value spot date and a purchase of USD and sale of MYR for value forward, or vice versa. Both transactions are agreed on deal date and is a single contract. Diagram 3-3 illustrates a sell-buy swap whereby the first leg is a sale of USD and purchase of MYR while the forward leg is a purchase USD and a sale of MYR.

###### Diagram 3-3

A buy-sell swap, on the other hand is a purchase of USD and sale of MYR for value spot, and sale of USD in exchange for MYR for value forward. The term ‘sell-buy’ and ‘buy-sell’ refers to the transaction of the base or commodity currency. In most instances, traders tend to refer only on the forward leg of the transaction i.e a buy or a sell of the forward leg.

In Example 3-2, the exporter decides to sell USD2 million forward to a bank to cover the expected USD inflow in one month (from spot date). From the perspective of the bank, it is a forward purchase of USD, shown in the following diagram, which is essentially Diagram 3-2 because the exporter transferred the exposure to the bank:

###### Diagram 3-4

In practice, the exposure will be immediately taken off by selling the USD in the FX spot market, subject to available exposure limit and risk appetite of the trader. We assume the following for our subsequent discussion:

1. The bank purchases USD 2 million and sells MYR to the exporter at the rate of 4.2075 for a month forward fx contract.
2. The bank sold USD 2 million for MYR the rate of 4.2000 for value spot.
The exposure of the bank after the above transactions is depicted below.

###### Diagram 3-5

The forward transaction from the exporter and the spot transaction to eliminate the FX imitate a swap transaction. Although the FX risk has been eliminated, there are cashflows mismatches in both currencies.

The cash flows in Diagram 3-5 suggest that USD was lent and MYR was borrowed. In return, on maturity USD2,000,000 will be received implying a lending rate of 0.00% and MYR8,415,000 will be paid reflecting a borrowing rate of 2.03683% assuming 32 days in the one month period.

\begin{align} r_{MYR} &= \left(\dfrac{\textrm{8,415,000}} {\textrm{8,400,000}} -1\right)\dfrac{365}{32} \\ &=2.03683\textrm{%} \end{align}

The bank’s original exposure in Diagram 3-4 can be managed using the money market borrowing and lending. Assuming USD rate of 0.30% for the 32-day period, the present value of USD2,000,000 will be:

\begin{align} P_{USD} &= \dfrac{\textrm{2,000,000}} {\left(1 + \frac{0.03\textrm{ x }32}{360}\right)} \\ &=1,999,466.81 \end{align}

The bank will borrow USD 1,999,466.81 for 32 days and sell the USD for MYR at USD/MYR exchange rate of 4.2000 for value spot and the MYR received will be lent for 32 days through the interbank money market. On maturity of USD borrowing, the principal and interest will be paid from the USD received under the FX forward contract with the exporter. The following diagram illustrates the time frame of the cash flow:

###### Diagram 3-6

For the time being, the calculation of MYR interest has been omitted. If the forward contract and the spot FX are omitted from Diagram 3-6, it will be similar to Diagram 3-3 implying that the borrowing and lending activities can replicate a swap transaction.

Diagram 3-6 can also be summarised as a formula and the process is described in steps below.

1. The USD borrowing and its maturity amount is represented by Equation 1-2. $$FV_{USD} = P_{USD}\left(1+\frac{r_{USD}t}{360} \right)$$
2. The borrowed amount is then sold to obtain MYR and can be represented by: $$P_{MYR} = P_{MYR}\textrm{ x FX Rate}$$
3. The MYR amount is then invested and the future value is as per Equation 1-2. $$FV_{MYR} = P_{MYR}\left(1+\frac{r_{MYR}t}{365} \right)$$

If $$P_{MYR} = P_{USD}\textrm{ x FX Rate}$$ then $$\textrm{FX Rate } = \frac{P_{MYR}}{P_{USD}}$$.

By the same token, the forward FX rate is simply the ratio of MYR future value to USD future value i.e.

\begin{align} \textrm{FX forward rate} &= \dfrac{FV_{MYR}}{FV_{USD}} \\ &= \frac{P_{MYR}\left(1+\frac{r_{MYR}t}{365} \right)} {P_{USD}\left(1+\frac{r_{USD}t}{360} \right)} \\ &= \dfrac{P_{USD}\textrm{ x FX Rate} \left(1+\frac{r_{MYR}t}{365} \right) }{P_{USD}\left(1+\frac{r_{USD}t}{360} \right)} \\ &= \dfrac{\textrm{FX Rate} \left(1+\frac{r_{MYR}t}{365} \right) }{\left(1+\frac{r_{USD}t}{360} \right)} \end{align}

The general equation for the formula is;

\begin{align} \textrm{FX forward rate} &= \dfrac{\textrm{FX Rate} \left(1+ r_{c1}d_{c1} \right) }{\left(1+r_{c2}d_{c2} \right)} \\ \textrm{where } r_{c1} &= \textrm{ rate for the monetary currency, MYR in our example} \\ d_{c1} &= \textrm{ day count factor for the monetary currency, MYR in our example} \\ r_{c2} &= \textrm{ rate for the base currency, USD in our example} \\ d_{c2} &= \textrm{ day count factor for the base currency, USD in our example} \\ \end{align}
###### Equation 3-1

Equation 3-1 is a no-arbitrage equation in which deviation from the calculated FX forward rate will lead to arbitraging The following assumptions were previously made:

1. $$r_{USD} = 0.30 \textrm{%}$$
2. $$t = 32$$ days
3. FX forward rate = 4.2075

The information are also tabulated in Table 3-1. User can change any value in the cell and see the impact on each and net cash flows in Table 3-2

$$r_{MYR}$$ can now be calculated and is the breakeven MYR rate. The above equation can be rearranged to solve for $$r_{MYR}$$. Day count factor was described in Chapter 1.

$$r_{MYR} = \left( \dfrac{\textrm{FX Forward}\left(1 + r_{USD}d_{USD} \right)}{\textrm{FX Rate}} \right)\dfrac{1}{d_{MYR}}$$

###### Equation 3-2

Hence;

\begin{align} r_{MYR} &= \left( \dfrac{4.2075\left(1 + \frac{0.003 \textrm{ x } 32}{360} \right)}{4.2000} \right)\dfrac{365}{32} \\ &= 2.34154 \textrm{%} \end{align}

###### Table 3-1

Ceteris paribus, if the cost of lending MYR is higher than 2.34154%, there will be a profit for the activities in Diagram 3-6 and a loss will be recorded if the cost of lending is lower. The cost of lending MYR and the net cash flow from Diagram 3-6 is tabulated in Table 3-2. Similarly, if the cost of borrowing USD is lower than 0.30%, there will be a profit for the activities in Diagram 3-6 and a loss will be recorded if the cost of borrowing is higher.

In general the following will be beneficial to the bank.

1. a lower cost of purchasing the USD
2. a higher lending rate
3. a lower borrowing rate

###### Table 3-2

Other factors affecting the profitability of the transactions can be seen by changing the values in Table 3-1. Refresh the page to restore the default values.

### Swap Point

FX swap is quoted in the market in terms of point. For USD/MYR a point is equivalent to 0.0001. The swap point is the difference between the FX forward rate and the FX spot rate. It is actively traded in the market and crucial for cash flow management of foreign currencies.

Table 3-4 list the standard terms for FX swap market. Although the table listed the standard tenors, non-standard tenors can still be transacted directly with an interbank counterparty or negotiated through the brokers. By comparison a forward foreign exchange, itself is not a standard product dealt in the interbank market due to, among other things, the volatility of the spot FX market. The FX swap market is important to create as it enable creation of forward foreign exchange exposure to manage forward-dated foreign currency cash flows.

###### Table 3-3

A swap point can be either at a premium or discount. A premium swap point indicates that the forward rate is higher than the spot FX rate and the local currency interest rate is higher than interest rate of the commodity currency. On the other hand, a discount swap point indicates that the forward rate is lower that the spot FX rate and the local currency interest rate is lower than interest rate of the commodity currency. When the interest rate of the local and commodity currencies are the same, the swap point will be at par or zero, assuming the day count convention is the same.

Table 3-4 is a simple calculator to calculate the swap point. Yellow cells are user editable.