## Sunday, October 02, 2011

### Forward Market Calculations

CFA Level 1 - Global Economic Analysis

The spread on a forward currency quotation is calculated in the same manner as the spread for a spot currency quotation.

The reasons that spreads vary with forward foreign currency quotations are similar to the reasons for the variability of spreads with spot foreign currency quotations. The unique factor associated with spreads for forward foreign currency quotations is that spreads will widen as the length of time until settlement increases. Currency exchange rates would be expected to have a higher range of fluctuations over longer periods of time, which increases dealer risk. Also, as time increases, fewer dealers are willing to provide quotes, which will also tend to increase the spread.

Calculating a Forward Discount or Premium, Expressed as an Annualized Rate.

Forward currency exchange rates often differ from the spot exchange rate. If the forward exchange rate for a currency is higher than the spot rate, there is a premium on that currency. A discount exists when the forward exchange rate is lower than the spot rate. A negative premium is equivalent to a discount.

If the ninety day ¥ / \$ forward exchange rate is 109.50 and the spot rate is ¥ / \$ = 109.38, then the dollar is considered to be "strong" relative to the yen, as the dollar's forward value exceeds the spot value. The dollar has a premium of 0.12 yen per dollar. The yen would trade at a discount because its forward value in terms of dollars is less than its spot rate.

The annualized rate can be calculated by using the following formula:

Formula 5.3

Annualized    =        Forward Price - Spot Price  x        12           x 100%

Spot Price                   # of months
forward

So in the case listed above, the premium would be calculated as:

((0.0091324 - 0.0091424) ÷ 0.0091424) × (12 ÷ 3) × 100% = -0.44%

Similarly, to calculate the discount for the Japanese yen, we first want to calculate the forward and spot rates for the Japanese yen in terms of dollars per yen. Those numbers would be (1/109.50 = 0.0091324) and (1/109.38 = 0.0091424), respectively.

So the annualized forward discount for the Japanese yen, in terms of U.S. dollars, would be:
((109.50 - 109.38 ÷ 109.38) × (12 ÷ 3) × 100% = 0.44%
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