On an instantaneous fall of 10 per cent in sterling, a hedge locked five years out calls 52,378,487 of variation margin against 11,696,910 for a twelve-month programme rolled each year — 4.48 times, on the same 135,000,000 dollars, the same hedge ratio and the same counterparty. The only difference is how many tenors are open when the currency moves. Five open tenors call more cash than one, on any path, and the call arrives on the morning of the move.
Two policies, one difference
Kilmartin Industrial invoices 180,000,000 dollars a year and policy sells 75 per cent of it forward, which is 135,000,000 dollars. That exposure can be covered two ways. A twelve-month programme rolled each year holds one open tenor at any moment. Locking all five years at the outset holds five. Same currency, same amount, same direction, same counterparty, same hedge ratio. Everything a hedging policy is normally written to specify is identical across the two columns.
Suppose sterling falls in a single morning, at the outset, before anything has settled and while every tenor dealt is still open. Each policy owes variation margin that day on the mark against it.
Fall in sterling
Spot
Rolling call
Locked call
Ratio
5.0 per cent
1.1875
5,610,228
24,880,449
4.43
8.0 per cent
1.1500
9,182,846
41,020,602
4.47
10.0 per cent
1.1250
11,696,910
52,378,487
4.48
15.0 per cent
1.0625
18,499,672
83,111,588
4.49
20.0 per cent
1.0000
26,152,780
117,686,327
4.50
Instantaneous shock at the outset on 135,000,000 dollars, from a spot of 1.2500, against 36,000,000 of available liquidity.
The rolling call is not the undiscounted loss. At 1.1250 the loss is 0.088889 of sterling per dollar, which on 135,000,000 dollars is 12,000,000; the table prints 11,696,910, because the loss settles at the tenor's maturity and not on the day the rate moves.
Why the ratio is not five
Five open tenors against one suggests a factor of five. The table says between 4.43 and 4.50, and two corrections explain the gap. The first is discounting. The locked policy's tenors mature out to four years and nine months, and a loss that will be settled that far out is worth less today, so the collateral posted against it is smaller.
The second is that a currency loss is not linear in the exchange rate. A company selling dollars owns the reciprocal of the rate, and the reciprocal of a sum is not the sum of the reciprocals. A fall of 10 per cent costs 0.088889 of sterling per dollar; a fall of 20 per cent costs 0.200000. Twice the fall costs 2.25 times the money. So the ratio drifts, monotonically, from 4.43 at a fall of 5 per cent to 4.50 at a fall of 20 per cent, and neither it nor any single stress result can be scaled. Doubling the locked call at 10 per cent gives 104,756,974 against the 117,686,327 the model prints at 20 per cent, an understatement of 12,929,353.
The policy that looks prudent is the one that runs out of money first. Locking five years removes uncertainty from the income statement by moving it into the cash account, where nothing displays it. Against 36,000,000 of available liquidity the locked policy is exhausted at a spot of 1.1614 and the rolling policy at 0.9296.
What the call is measured against
Policy
Open tenors
Spot at exhaustion
Fall in sterling
Roll twelve months
1
0.9296
25.63 per cent
Lock five years
5
1.1614
7.09 per cent
Each derivation is one division against a spot of 1.2500.
The 36,000,000 is 11,000,000 of cash and 25,000,000 of committed undrawn facility, treated throughout as drawable overnight to post variation margin. If it is not — a notice period, a drawdown certificate, a representation that has to be given afresh — the honest denominator is 11,000,000, and the locked policy is through it before the first row of the table.
The commercial gain that arrives with a weaker pound is real and small. 45,000,000 dollars of annual sales go unhedged, 11,250,000 a quarter. At 1.1250 that quarter fetches 1,000,000 more sterling than at 1.2500. The locked call at the same level is 52.4 times the gain and the rolling call 11.7 times, and the two arrive by different post: the gain accumulates across ninety days of invoicing and collection, the call is wired the next morning.
What to do with it
Reverse the running order. The usual sequence settles what to hedge, then how much, then how long, and reaches liquidity last if it reaches it at all. The sequence these tables support is the opposite:
Establish what each candidate tenor calls in cash on an instantaneous fall of 10 per cent.
Set that figure beside the committed facility, and discard the tenors that do not fit.
Run at least two shock sizes, because one point says nothing about the curvature between it and the next.
Only then argue about the hedge ratio and the result.
One lever inside the cash column costs nothing to pull. On the declared path the locked policy's worst call is 43,749,502, and that assumes the swap and the currency book sit under a single collateral agreement, so that the swap's positive mark of 2,653,387 is set against the currency loss. Under two agreements with two counterparties they do not net, and the call is 46,402,888. How many banks a company deals with is a liquidity decision, normally taken on relationship and pricing grounds and minuted nowhere as one.
A hedge ratio is argued in committee and reported monthly. Tenor is settled in a term sheet by whoever is arranging the trade, on the reasonable ground that the exposure runs five years. That reasoning is sound about the profit and loss account and silent about the balance sheet. A proposal that claims to have removed uncertainty has moved it — the useful question is where.
The workbooks behind this article
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