A hedge that shows a loss against spot has not failed. It has been measured against the one thing it never set out to predict.
Twelve months after the forward was dealt the mark is a loss of 8,130,844.04, and the audit committee wants it explained. It is explicable in one line: the company fixed 109,516,214.78 on 120,000,000.00 of dollars, twelve months in advance, on 66.1376 per cent of EBITDA — and it received 109,516,214.78. The 8,130,844.04 is the value of an outcome the company chose not to have.
Worked in full in Treasury Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A twelve-month forward is spot adjusted for two interest rates, because the bank on the other side has to borrow one currency and lend the other for the year. At a spot of 1.0800, a dollar rate of 4.50 per cent and a home rate of 3.00 per cent, the forward is 1.0957 and the forward points are 0.0157.
At spot, 120,000,000.00 of dollars is 111,111,111.11. At the forward it is 109,516,214.78. The gap, 1,594,896.33, is 1.4354 per cent of the spot value and it is the carry of the hedge: the interest differential showing up in the price. No bank charges it as a fee. A company with dollar receipts pays it; a company with dollar payables is paid it. Same forward, same day, opposite sign.
| Spot in twelve months | Unhedged proceeds | Hedged proceeds | Hedge gain (loss) |
|---|---|---|---|
| 1.0200 | 117,647,058.82 | 109,516,214.78 | -8,130,844.04 |
| 1.0800 | 111,111,111.11 | 109,516,214.78 | -1,594,896.33 |
| 1.1600 | 103,448,275.86 | 109,516,214.78 | 6,067,938.92 |
The row missing from that table is the break-even, and it is not the spot the forward was dealt at. It is the forward itself, 1.0957. Only if the dollar weakens by the full forward points does the hedge break even against doing nothing. At an unchanged spot the hedge still shows a loss, of exactly the carry, 1,594,896.33. A committee that expects a hedge to break even at an unchanged rate has been given the wrong break-even.
On the day the forward was dealt nobody knew whether the rate would be 1.0200 or 1.1600. One cent on the rate is worth 1,019,367.99, which is 0.6068 per cent of EBITDA; ten cents is 9,416,195.86, or 5.6049 per cent. A rate that can move ten cents in a year puts 5.6049 per cent of EBITDA at the mercy of a market the board never discusses. The forward removed that, and its price was the carry, known on the day.
A hedge is a position on variance, not on direction. The company that hedges is saying it would rather have 109,516,214.78 for certain than a draw from a distribution centred somewhere near it. If the draw comes out at 117,647,058.82, the company was still right to prefer the certainty, for the same reason a building was still worth insuring in a year it did not burn.
What would have been wrong is a hedge put on as a view — because the treasurer thought the dollar would weaken — and then defended as insurance when it did not. The distinction is visible in the paperwork. A hedge put on for the exposure is dealt at the ratio the policy sets, on the calendar the policy sets, whatever the treasurer thinks of the rate. A hedge put on as a view is dealt when the rate looks attractive.
The dollars are not sold on one day. The policy hedges the next four quarters at falling ratios, so that the rate achieved on any quarter is an average of four forwards dealt three months apart.
| Quarter ahead | Exposure (USD) | Hedge ratio | Hedged (USD) |
|---|---|---|---|
| First | 30,000,000.00 | 100 per cent | 30,000,000.00 |
| Second | 30,000,000.00 | 75 per cent | 22,500,000.00 |
| Third | 30,000,000.00 | 50 per cent | 15,000,000.00 |
| Fourth | 30,000,000.00 | 25 per cent | 7,500,000.00 |
| Total | 120,000,000.00 | 62.50 per cent | 75,000,000.00 |
The cost is in the same table. At any moment 45,000,000.00 of dollars is unhedged and the fourth quarter out is three-quarters open. Layering trades the risk of one bad dealing day for a permanent partial exposure. The ratios are a policy choice, and a steeper or flatter ladder moves the 62.50 per cent with it.
The annual plan carries a rate, and the divisions were given it to convert their dollar forecasts. If the budget was set at 1.0800 and the forward is 1.0957, no forward will achieve budget; the carry sees to that. A treasurer told to protect the budget rate will wait for spot to move in her favour, which is to take a view. A budget set at spot builds 1,594,896.33 of guaranteed shortfall into the year before anything has happened, and then blames the treasurer for it. Set the budget at the forward, or at the achieved rate of the hedges already in place.
Discard the mark-to-market as a measure of the programme: it measures the distance between the forward and where spot went, which is the one thing the hedge was never trying to predict. Read the rate the hedges fixed and the amount that fixes, 109,516,214.78 on 120,000,000.00. Read the ratio actually in place against the policy ratio, 62.50 per cent on average. And read the value of one cent on what is still open: 1,019,367.99 on the full exposure, 382,263.00 on the 45,000,000.00 left unhedged.
Judge a hedge by whether it fixed what it was meant to fix, never by whether it beat the spot.
No. A forward fixes a rate; it does not predict one. The hedge in this book showed a loss of 8,130,844.04 against spot and delivered exactly what it promised, 109,516,214.78 on 120,000,000.00 of dollars. The loss is the value of an outcome the company chose not to have.
The forward rate itself, not the spot on the day it was dealt. Here spot was 1.0800 and the forward 1.0957; at any spot stronger than the forward the hedge shows a loss against doing nothing, including at an unchanged rate, where the loss is exactly the carry of 1,594,896.33.
The interest differential between the two currencies, showing up in the forward price. On 120,000,000.00 of dollars at a spot of 1.0800 it is 1,594,896.33 a year, 1.4354 per cent of the spot value. It is not a fee, and a company with payables in the same currency is paid it rather than paying it.
This article is one calculation from Treasury Management. 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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