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# Forward Quotations from Forward Points

## Forward Quotations

The points on a forward rate quote are the differences between the spot exchange rate quote and the forward exchange rate quote. These points are scaled to relate to the last decimal in the spot quote. It is important to note that forward quotations are displayed as the number of forward points at each maturity. Swap points also express forward points.

When the forward rate is higher than the spot rate, the points are positive, and thus the base currency is said to be trading at a forward premium. Otherwise, the points are negative and said to be trading at a forward discount.

To get the gist of this argument, consider that at one point in 2017, the spot USD/CAD exchange rate was 1.3845, and then, the six-month forward rate was 1.38475. This implies that the forward rate was trading at a premium to the spot rate, and the six-month forward points were quoted as 2.5, which is from:

$$1.38475-1.3845=0.00025$$

We multiply by 10,000 to reach the desired result.

## Finding Forward Points

To convert forward quotations expressed on a point basis or in percentage terms into an outright forward quotation, we will use an example of RUB/CNY from the following table of maturity and forward or spot rate points.

$$\begin{array}{c|c} \text{Maturity} & \text{Spot rate or forward points} \\ \hline \text{Spot} & 1.6459 \\ \hline \text{One week} & -0.2 \\ \hline \text{One month} & -1.0 \\ \hline \text{Three months} & -5.6 \\ \hline \text{Six months} & -12.7 \\ \hline \text{Twelve months} & -25.3 \\ \end{array}$$

Therefore, the task is to divide the number of points by 10,000 to scale down the fourth decimal place that is in the spot rate.

We can take the case of the six-month forward rate. Here we have:

$$1.6459 +\frac{-12.7}{10,000} = 1.6459 – 0.00127 = 1.64463$$

Often, the forward rate is represented as a percentage of the spot and not as an absolute number of points. As such, the six-month forward rate for RUB/CNY can be shown as:

$$\frac{1.6459 – 0.00127}{1.6459}– 1 = -0.001\%$$

To convert this percentage into a forward rate, we simply need to multiply the spot rate by one plus the percentage forward premium or discount:

$$1.6459 × (1 + (-0.001)) = 1.6459 × (1 – 0.001) = 1.6459 × 0.999 = 1.6443$$

### Question

Refer to the following table of maturity and forward points or spot rate below.

$$\begin{array}{c|c} \text{Maturity} & \text{Spot rate or forward points} \\ \hline \text{Spot} & 1.6459 \\ \hline \text{One week} & -0.2 \\ \hline \text{One month} & -1.0 \\ \hline \text{Three months} & -5.6 \\ \hline \text{Six months} & -12.7 \\ \hline \text{Twelve months} & -25.3 \\ \end{array}$$

The three-month forward rate is closest to:

Solution

B. 1.45677

C. 1.63546

A. 1.64534

When we divide the forward points of -5.6 by 10,000, we get –0.00056. The next step is to subtract this from our spot rate of 1.6459 which will lead us to a result of 1.64534.

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