The mark-to-market of an outstanding currency forward, step by step: the new forward, the sterling difference, the discounting, and the spot shortcut that overstates it.
An outstanding FX forward is valued by asking what it would cost to close it today: price the remaining term at today's forward rate, take the difference in the reporting currency, and discount it to today. A UK company that sold USD 10,000,000 forward at 1.2761, revalued with six months left and spot at 1.2400, holds a contract worth minus 204,426 sterling. The common shortcut, valuing at spot without discounting, reports minus 228,140, 11.6 per cent too much.
Worked in full in Derivatives by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A forward costs nothing on the day it is dealt, so it sits off the balance sheet until rates move. From then on it has a fair value that goes into the accounts at every reporting date, drives the collateral called under a credit support annex, and is the figure the hedge effectiveness test compares with the hedged item. Treasury systems and bank confirmations print it, but a treasurer who cannot reproduce it cannot challenge a bank's number or explain a movement to the audit committee.
The contract is the one built in how to calculate an FX forward rate: one year, spot at 1.2700, dollar rate 4.5 per cent, sterling rate 4.0 per cent, forward 1.2761. Six months later the market has moved.
| Input | Value |
|---|---|
| Dollars sold forward | 10,000,000 |
| Contract rate, dollars per pound | 1.2761 |
| Spot today | 1.2400 |
| Six-month USD rate, simple | 4.40% |
| Six-month GBP rate, simple | 3.90% |
| Time to settlement | 0.5 years |
Rates are illustrative money market rates on a simple-interest basis, which is the market convention for terms under a year. Credit and funding adjustments are left out; they are a separate line.
Current forward F = spot × (1 + rUSD × t) / (1 + rGBP × t)
Value in GBP = (USD / K − USD / F) / (1 + rGBP × t)
In Excel, with notional in B1, K in B2, spot B3, USD rate B4, GBP rate B5, t B6:
=(B1/B2-B1/(B3*(1+B4*B6)/(1+B5*B6)))/(1+B5*B6)
Step 1, today's forward for the remaining six months. The interest factors are 1 + 4.40% × 0.5 = 1.0220 for dollars and 1 + 3.90% × 0.5 = 1.0195 for sterling. The forward is 1.2400 × 1.0220 / 1.0195 = 1.2430. Dollar rates are higher than sterling rates, so the pound stands at a premium in the forward market, exactly as it did at inception.
Step 2, the two sterling amounts. The contract delivers 10,000,000 / 1.2761 = 7,836,376 pounds at settlement. A new forward dealt today for the same date would deliver 10,000,000 / 1.2430 = 8,044,789 pounds. The company is locked into 208,412 fewer pounds than the market now offers for the same dollars.
Step 3, discount to today. That shortfall is a sterling amount payable in six months, so it is discounted at the sterling rate: minus 208,412 / 1.0195 = minus 204,426. For the bank on the other side the same contract is an asset of 204,426.
A cross-check. Value each leg on its own curve and convert at spot. The sterling leg is worth 7,836,376 / 1.0195 = 7,686,490. The dollar leg is worth 10,000,000 / 1.0220 = 9,784,736 dollars, or 7,890,916 pounds at 1.2400. The difference, 7,686,490 less 7,890,916, is again minus 204,426. The two methods are the same identity written twice, and agreeing them is the simplest control on a spreadsheet.
| Line | Amount |
|---|---|
| Pounds receivable under the contract | 7,836,376 |
| Pounds a new forward would deliver | 8,044,789 |
| Difference at settlement | -208,412 |
| Fair value today, discounted | -204,426 |
The negative value is not a loss on the hedging programme. The company sold dollars it expects to receive. With sterling down from 1.2700 to 1.2400, those dollars are worth more in pounds, and the receivable has gained roughly what the forward has lost. That offset is what the dollar offset test of hedge effectiveness measures.
| Spot | Forward | Value, GBP |
|---|---|---|
| 1.20 | 1.2029 | -467,457 |
| 1.22 | 1.2230 | -333,785 |
| 1.24 | 1.2430 | -204,426 |
| 1.26 | 1.2631 | -79,173 |
| 1.28 | 1.2831 | 42,165 |
| 1.30 | 1.3032 | 159,770 |
The forward is worth zero when today's forward equals the contract rate, at a spot of 1.2761 × 1.0195 / 1.0220 = 1.2730, not at 1.2761. The value is not symmetric either: a fall of four cents in spot costs more than a rise of four cents earns, because the dollar amount is fixed and the pound amount is its reciprocal.
Rates matter less than spot but are not nothing. With spot held at 1.2400, a six-month dollar rate of 3.40 per cent instead of 4.40 lowers the forward to 1.2370 and the value to minus 243,221; at 5.40 per cent the forward is 1.2491 and the value minus 166,009. A one-point move in the rate gap moves the value by about 38,606, more than a half-cent move in spot, which is worth 31,690.
Valuing the contract at spot: 10,000,000 / 1.2761 less 10,000,000 / 1.2400 = minus 228,140. Two errors are hiding in that figure. Spot is the wrong price for a contract that settles in six months, and the result is a future amount reported as a present one. Of the 23,714 overstatement, 3,986 is the missing discounting and the rest is the forward points that the shortcut ignores. On a single contract that looks small; across a programme of rolling hedges it shifts the reported fair value by more than a tenth and creates hedge ineffectiveness that does not exist.
The reverse mistake is also common: discounting the sterling difference at the dollar rate, or converting the dollar leg at the forward and then discounting it again. Each leg is discounted on its own curve, once, and converted at spot.
Derivatives treats the forward points as an interest differential rather than a cost and reconciles the treasury report's figures line by line; the forward revaluation, the rolling programme and the collateral it calls are all in the free workbooks for the book. For the credit charge on the same kind of contract, see how to calculate CVA on a swap.
Because the contract settles at maturity, and the market price today for the same maturity is the forward, not spot. With spot at 1.2400 and dollar rates 0.50 points above sterling for six months, the forward is 1.2430. Valuing the 10,000,000 dollar contract at spot instead gives minus 228,140 against a correct minus 204,426.
The rate of the currency in which the value is reported, for the time left to settlement. The sterling difference of minus 208,412 is payable in six months, so it is discounted at the 3.90 per cent sterling rate, by a factor of 1.0195, to minus 204,426. Discounting the dollar leg at the dollar rate and converting at spot gives the same answer.
No. The company sold dollars it expects to receive. Sterling has fallen to 1.2400, so those dollars are worth more in sterling and the forward has lost about the same amount. At spot 1.2730 the forward would be worth zero; at 1.2800 it would be worth 42,165. The hedge fixed the sterling outcome, which is what it was for.
This article is one calculation from Derivatives. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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