###### Fundamental Determinants of Residual I ...

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A **forward contract** is an agreement between two parties to trade one currency for another on a specified future date and at a pre-determined rate. In other words, it is an exchange rate transaction whose settlement timeline exceeds T+2.

The **mark-to-market value** of a contract is a value that a party is willing to pay if they decide to close out a position before the scheduled settlement date. In other words, it indicates the profit or loss resulting from dissolving a forward contract sometime before the settlement date.

**Closing out a contract position** means offsetting it with a similar and opposite forward position. This process involves the utilization of the current spot exchange rate and forwards points available in the market at the time the offsetting position is created. Essentially, a forward contract has a long and short position. For instance, we offset a long position by taking a short position, thereby either making a profit or suffering a loss.

The mark-to-market value of a forward contract is zero at the time the contract is initiated (time 0). It, however, changes during the life of the contract to reflect changes in spot exchange rates and/or interest rates in either of the currencies involved.

An investor purchases USD 100 million, which is to be delivered in one year against the CAD at an “all-in” forward rate of 1.8045 CAD/USD. Six months later, the investor decides to close out the forward contract.

The bid-offer quotes for spot and forward points six months prior to the settlement date are as follows:

$$\small{\begin{array}{l|c}\\ \hline\text{Spot rate (CAD/USD)} & 1.8245/1.8250 \\ \hline \text{Six-month points} & 140/150 & \\ \hline \end{array}}$$

Assuming that the annual CAD Libor is 5%, calculate the mark-to-market value of this forward contract.

**Note**: The all-in forward rate is equal to the sum of the spot rate and the scaled forward points.

**Solution**

The base currency (USD) is sold to offset the investor’s position. In other words, we are computing the bid part of the market. Therefore, the applicable forward rate is:

$$ 1.8245+\frac{140}{10,000}=1.8385 $$

The investor bought 100 million USD at the initial rate of 1.8045 and is now selling the same at a new rate (1.8385). As such, the cash flow at the settlement date is:

$$ (1.8385-1.8045)100 = +\text{CAD } 3.4 \text{ million} $$

This is a cash inflow since the USD appreciated (CAD/USD increased).

To find the mark-to-market value, we need to discount the cash inflow using the USD Libor rate:

$$ \text{Mark-to-market value} =\frac{3.4}{1+0.05\times\frac{180}{360}}=\text{CAD }3.317 \text{ million} $$

This is the mark-to-market value of the extended forward contract of USD 100 million if it is closed out six months before the settlement date.

From the example above, the process of computing the mark-to-market value comprises the following steps:

**Construct an offsetting forward position that is equal but opposite to the original position**: In the example above, the investor had initially been long USD 100 million, and thus the offsetting forward contract is short USD 100 million.**Determine the applicable all-in forward rate for the new contract position**: If the base currency was sold, then we calculate the bid rate. Otherwise, we calculate the offer rate.**Calculate the cash flow that results from the transaction on the settlement date**: The size of the cash flow will be a product of the original contract size and the difference between the initial forward rate and the new forward rate in step II. It will either be a cash inflow (positive) or a cash outflow (negative). In our example above, the cash flow was positive; hence it is a cash inflow.**Finally**,**calculate the present value of this cash flow on the future settlement date**: While at it, the discount rate used must match the currency of the cash flow. In the example above, the cash flow was in CAD, so we must use the CAD Libor.

## Question

An investment manager at CMY Inc. decides to take a long position in CAD 5 million forward against AUD at an “all-in” of 1.1300 (AUD/CAD). Six months before the settlement date, the manager decides to close out the forward contract. At this time, the following are listed in the market:

$$ \begin{array}{l|c} \text{Spot rate (AUD/CAD)} & 1.2525/1.2530 \\ \hline \text{6-month pips (points)} & -10.1/-8.1 \\ \hline \text{6-month AUD Libor} & 4.5\% \\ \hline \text{6-month CAD Libor} & 0.5\% \\ \end{array} $$

The mark-to-market value of the position is

closest to:

- -AUD 506,088.
- +CAD 507,197.
- -AUD 597,506.

Solution

The correct answer is C.Since the manager bought CAD 5 million, he will sell CAD 5 million to offset the original position, six months forward to the settlement date. Since CAD is the base currency, purchasing it implies that the manager pays the offer. Therefore, the “all-in” forward rate is:

$$ 1.2530-\frac{8.1}{10,000}=1.25219 $$

Therefore, the net cash flow at the settlement date is:

$$ 5,000,000 \times (1.1300 -1.25219)= -\text{AUD } 610,950 $$

To get the mark-to-market value, we need to discount using the AUD Libor. So,

$$ \text{Mark-to-market value}=\frac{-610,950}{1+0.045\times\frac{180}{360}}=-\text{AUD } 597,506.11 $$

Reading 8: Currency Exchange Rates: Understanding Equilibrium Value

*LOS 8 (d) Calculate the Mark-to-Market Value of a forward contract.*