A forward sale of USD 20,000,000 against a hypothetical derivative, three quarters of period and cumulative ratios, and the lower-of test that sets the P&L charge.
The dollar offset method divides the change in fair value of the hedging instrument by the change in value of the hedged item, usually measured with a hypothetical derivative, and, under US GAAP practice and the old IAS 39, calls the hedge highly effective when the ratio sits between 80 and 125 per cent. On an illustrative forward selling USD 20,000,000, the cumulative ratio is 100.3 per cent after two quarters, but the second quarter on its own reads 167.8 per cent because spot moved only 12 pips. The ratio fails on small numbers, not on a bad hedge, which is why the cumulative test is the one to document.
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Under US GAAP a hedge must be expected to be, and must prove to be, highly effective, and the dollar offset ratio with an 80 to 125 per cent band is the most common way of showing it, alongside regression. IAS 39 used the same band. IFRS 9 removed the bright line: qualification rests on an economic relationship, credit risk not dominating and a sound hedge ratio. But ineffectiveness still has to be measured every period and recognised in profit or loss, and the arithmetic below is the same arithmetic.
A company with sterling as its functional currency expects to receive USD 20,000,000 from a customer in twelve months and designates a forward sale of the dollars as a cash flow hedge. The bank's standard date gives a forward maturing in eleven months, a month before the cash arrives. The hedged item is measured with a hypothetical derivative: a perfect forward to the receipt date, struck at market at inception so that it is worth nothing on day one. Rates are illustrative and held constant.
| Input | Value |
|---|---|
| Forecast receipt, sold forward | USD 20,000,000 |
| GBP/USD spot at inception | 1.2700 |
| USD and GBP interest rates | 4.5% / 4.0% |
| Actual forward: maturity and rate | 11 months, 1.2756 |
| Hypothetical derivative: maturity and rate | 12 months, 1.2761 |
| Spot at the three quarter ends | 1.3050, 1.3062, 1.2900 |
Forward rate = spot × (1 + rUSD × t) / (1 + rGBP × t)
Value of the forward in GBP = USD 20,000,000 × (1 / contract rate − 1 / current forward) / (1 + rGBP × t)
Period ratio = change in the hedge's value in the quarter / change in the hypothetical's value in the quarter
Cumulative ratio = change since inception in the hedge / change since inception in the hypothetical
Excel: =ABS(D5-D4)/ABS(E5-E4) for the period test and =ABS(D5)/ABS(E5) for the cumulative one, with values from inception at zero.
| Quarter | Spot | Hedge value | Hypothetical value | Hedge change | Hypothetical change | Period ratio | Cumulative ratio |
|---|---|---|---|---|---|---|---|
| Q1 | 1.3050 | 392,181 | 390,880 | 392,181 | 390,880 | 100.3% | 100.3% |
| Q2 | 1.3062 | 391,902 | 390,714 | −279 | −167 | 167.8% | 100.3% |
| Q3 | 1.2900 | 186,417 | 186,109 | −205,485 | −204,604 | 100.4% | 100.2% |
The dollar weakened in Q1, so the forward gained 392,181 and the hypothetical 390,880: a ratio of 100.3 per cent. The one-month mismatch makes almost no difference, because the forward points to eleven and twelve months, 56 and 61 pips, are close.
In Q2 spot moved 12 pips. With spot unchanged, the run-down of the forward points over the quarter would have cost the hedge 14,100 and the hypothetical 13,936; the small spot gain almost exactly offset that decay, leaving changes of a few hundred pounds. The ratio of two numbers close to zero is 167.8 per cent, outside the band, for a hedge that has not changed in any way that matters. Q3 brings a real move and the ratio is back at 100.4 per cent.
Hold Q1 as it was and run Q2 with different spot moves:
| Q2 spot | Move (pips) | Hedge change | Hypothetical change | Period ratio | Cumulative ratio |
|---|---|---|---|---|---|
| 1.2850 | −200 | −248,242 | −247,219 | 100.4% | 100.2% |
| 1.3050 | 0 | −14,100 | −13,936 | 101.2% | 100.3% |
| 1.3062 | 12 | −279 | −167 | 167.8% | 100.3% |
| 1.3100 | 50 | 43,318 | 43,271 | 100.1% | 100.3% |
| 1.3250 | 200 | 212,973 | 212,304 | 100.3% | 100.3% |
The failure is confined to the narrow range of spot where the two effects cancel. The cumulative ratio never leaves 100.2 to 100.3 per cent. Documenting the cumulative dollar offset at designation, or a regression test, avoids failing a sound hedge on a quiet quarter; switching method after a failure is not allowed.
Under IFRS 9, as under IAS 39, the amount in the cash flow hedging reserve is the lower, in absolute terms, of the cumulative change in the hedge and the cumulative change in the hypothetical. Any excess on the hedge is ineffectiveness and goes to profit or loss. US GAAP no longer splits it out: since ASU 2017-12, the whole change in a highly effective cash flow hedge goes to other comprehensive income, so the test below is the IFRS entry.
| Quarter | Hedge | Hypothetical | Hedging reserve | Cumulative ineffectiveness in P&L |
|---|---|---|---|---|
| Q1 | 392,181 | 390,880 | 390,880 | 1,301 |
| Q2 | 391,902 | 390,714 | 390,714 | 1,188 |
| Q3 | 186,417 | 186,109 | 186,109 | 308 |
Ineffectiveness is 0.33 per cent of the hedge's value in Q1, a gain of 1,301 in profit or loss because the hedge has moved more than the hedged item, reversing by 113 in Q2 and 880 in Q3. The quarter that failed the period ratio produced the smallest profit or loss entry of the three.
The frequent error is to read a ratio outside the band as evidence that the hedge has stopped working and to de-designate it, which sends every later movement of the forward straight to profit or loss. The second is to measure the hedged item with spot rather than with a hypothetical derivative on the hedged item's own terms, which builds the forward points into the ineffectiveness every quarter. Before acting on a ratio, look at the denominator: if it is a few hundred pounds on a hedge worth hundreds of thousands, the ratio is noise. Whether a hedge that lost money has failed is a different question, answered in did my currency hedge fail if it lost money.
The accounting memo and the derivative note for a hedging programme are laid out with the free workbook for this case, and the forward rate formula used above is worked in how to calculate an FX forward rate.
No. IFRS 9 replaced the bright line with an economic relationship, credit risk not dominating and a consistent hedge ratio. Ineffectiveness must still be measured and recognised: in the example the forward's cumulative gain of 392,181 exceeds the hypothetical's 390,880, so 1,301 goes to profit or loss. US GAAP still requires a highly effective hedge and practice commonly uses the 80 to 125 per cent band, but since ASU 2017-12 it books no separate ineffectiveness on a cash flow hedge.
Cumulative, in most cases, because period ratios are unstable when both changes are small. In the worked case a quarter with a 12-pip spot move gives 167.8 per cent, outside the band, while the cumulative ratio stays at 100.3 per cent. The method has to be chosen and documented at designation, not after a failure.
A derivative with the exact terms of the hedged item, struck at market at inception so it is worth zero, used to measure changes in the hedged item. Here it is a forward to the 12-month receipt date at 1.2761, against the actual 11-month forward at 1.2756.
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