A rolling programme buys an average of forward rates, not a better rate. The worked case shows what that average costs and what it smooths.
A layered programme hedges each future quarter in slices as it approaches, so the rate a quarter finally gets is an average of forward rates struck over a year. A euro company selling 30,000,000 dollars a quarter that covers 25 per cent four quarters ahead, then 50, 65 and 80 per cent, cut the standard deviation of its quarterly euro receipts by 55 per cent over twelve illustrative quarters. It paid for that with 1.4 per cent less euros than leaving the dollars unhedged, mostly in forward points.
Worked in full in Treasury Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Layered, rolling or staggered hedging is the default design in corporate FX policies because it answers the question boards actually ask: not "will we beat the market?" but "how much can next year's euro revenue move?". The worked case shows how the slices combine, what they smooth and what they cost.
| Input | Value |
|---|---|
| Dollar sales converted each quarter | 30,000,000 |
| Dollar interest rate; euro interest rate | 4.00%; 2.00% |
| Cover four quarters ahead | 25% |
| Cover three quarters ahead | 50% |
| Cover two quarters ahead | 65% |
| Cover one quarter ahead, final | 80% |
| EUR/USD spot, first five quarters | 1.0800, 1.1000, 1.1300, 1.1600, 1.1800 |
Because dollar rates are higher, the dollar trades at a forward discount: from a spot of 1.0800 the one-year forward is 1.1012, 212 points or 1.96 per cent worse for a company selling dollars. That carry is the running cost of every layer.
Take the quarter that settles when spot is 1.1800. Its first slice was sold forward a year earlier, its last a quarter earlier, and 20 per cent is converted at spot on the day.
| Slice placed | Added | Spot then | Forward rate | Dollars | Euros |
|---|---|---|---|---|---|
| Four quarters ahead | 25% | 1.0800 | 1.1012 | 7,500,000 | 6,810,897 |
| Three quarters ahead | 25% | 1.1000 | 1.1163 | 7,500,000 | 6,718,888 |
| Two quarters ahead | 15% | 1.1300 | 1.1412 | 4,500,000 | 3,943,259 |
| One quarter ahead | 15% | 1.1600 | 1.1658 | 4,500,000 | 3,860,106 |
| Open, at spot | 20% | 1.1800 | 1.1800 | 6,000,000 | 5,084,746 |
| Quarter | 100% | 1.1356 | 30,000,000 | 26,417,896 |
Effective rate = dollars ÷ Σ euros = 30,000,000 ÷ 26,417,896 = 1.1356
Unhedged, at 1.1800: 25,423,729 euros; the layers added 994,167
In Excel, with slice sizes in B2:B6 and rates in C2:C6: =SUM(B2:B6)/SUMPRODUCT(B2:B6,1/C2:C6)
This quarter the layers won because the dollar weakened all year. The point of the programme is that the next quarters, when the dollar recovers, give some of it back gently rather than all at once.
| Quarter | Spot | Layered rate | Layered, m EUR | Unhedged, m EUR | 100% a year ahead, m EUR |
|---|---|---|---|---|---|
| 1 | 1.1800 | 1.1356 | 26.42 | 25.42 | 27.24 |
| 2 | 1.1500 | 1.1503 | 26.08 | 26.09 | 26.75 |
| 3 | 1.1200 | 1.1579 | 25.91 | 26.79 | 26.04 |
| 4 | 1.0900 | 1.1547 | 25.98 | 27.52 | 25.36 |
| 5 | 1.0700 | 1.1383 | 26.35 | 28.04 | 24.93 |
| 6 | 1.0900 | 1.1205 | 26.77 | 27.52 | 25.59 |
| 7 | 1.1200 | 1.1120 | 26.98 | 26.79 | 26.27 |
| 8 | 1.1400 | 1.1109 | 27.00 | 26.32 | 26.99 |
| 9 | 1.1600 | 1.1222 | 26.73 | 25.86 | 27.50 |
| 10 | 1.1300 | 1.1353 | 26.43 | 26.55 | 26.99 |
| 11 | 1.1000 | 1.1403 | 26.31 | 27.27 | 26.27 |
| 12 | 1.0800 | 1.1367 | 26.39 | 27.78 | 25.81 |
| Strategy | Average, m EUR | Standard deviation | Lowest to highest | Twelve quarters |
|---|---|---|---|---|
| Unhedged | 26.83 | 0.78 | 2.61 | 321.94 |
| 100% hedged a year ahead | 26.31 | 0.77 | 2.56 | 315.75 |
| Layered 25/50/65/80% | 26.45 | 0.35 | 1.10 | 317.36 |
Two results stand out. The layered programme cuts the standard deviation from 0.78 to 0.35 million, and no quarter moves more than 0.42 million from the one before, against 0.74 unhedged. And hedging everything a year ahead smooths almost nothing: it simply replays last year's spot, plus the carry, a year late.
| Layers, four to one quarter ahead | Average, m EUR | Standard deviation | Lowest to highest |
|---|---|---|---|
| Light: 10 / 25 / 40 / 60% | 26.56 | 0.41 | 1.26 |
| Base: 25 / 50 / 65 / 80% | 26.45 | 0.35 | 1.10 |
| Heavy: 50 / 75 / 90 / 100% | 26.33 | 0.55 | 1.67 |
More cover is not more stability. The heavy profile fixes half of every quarter at the oldest forward and leaves nothing to spot, so it drifts towards the year-ahead hedge and inherits its lag. The smoothing comes from spreading the strike dates, not from the hedge ratio. Each step towards more cover also pays more forward points, which is why the average falls from light to heavy.
Judging the programme on whether it beat spot. Over these twelve quarters it received 4.58 million euros less than doing nothing, 1.4 per cent, and a board reading that as a loss will ask for the hedges to stop at exactly the wrong moment. Of that, 3.42 million was forward points, known on each trade date and the price of halving the volatility; the other 1.16 million was the spot path, which could as easily have gone the other way. That is the argument set out in did my currency hedge fail if it lost money. The right test is whether the volatility the policy targeted, for example a limit on cash flow at risk, was achieved.
A layered hedge is an averaging machine: each quarter's rate is a weighted average of four forwards and a spot, struck a quarter apart. On the illustrative dollar sales, layers of 25, 50, 65 and 80 per cent cut the standard deviation of euro receipts by 55 per cent for a carry cost of 1.4 per cent, while a single year-ahead hedge cut it by almost nothing. Choose the layers for the smoothing you need, then budget the points. The book's own hedging workbook, with the spot in twelve months as an input, is among the free workbooks for this case.
A layered or rolling hedge covers each future period in several slices placed at different dates, so the final rate is an average of forward rates struck over a year rather than one rate struck on one day. In the illustrative programme a quarter is 25 per cent hedged four quarters ahead and 80 per cent by the quarter before it settles; the worked quarter lands at 1.1356 against a spot of 1.1800.
Not necessarily over a rolling horizon. In the illustrative case, raising the layers to 50, 75, 90 and 100 per cent increases the standard deviation of quarterly euro receipts from 0.35 to 0.55 million, because more of each quarter is fixed by the oldest forward rates. Hedging 100 per cent a year ahead leaves it at 0.77, barely below the 0.78 unhedged.
Mainly the forward points. When dollar rates are 4.00 per cent and euro rates 2.00 per cent, a euro company selling dollars forward one year gets a rate about 1.96 per cent worse than spot. Over twelve illustrative quarters the layered programme received 4.58 million euros less than leaving the dollars unhedged, 1.4 per cent, of which 3.42 million was forward points, in exchange for halving the volatility.
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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