The 25 per cent currency shock, the aggregation with the insurer's other market risks and the hedge cost that breaks even, worked on one illustrative dollar share class.
Under the Solvency II standard formula a euro insurer holding a fund in another currency is charged the loss from a 25 per cent fall in that currency against the euro, on top of the charges on the fund's assets. On an illustrative €150.0 million dollar share class of a BB credit fund, the standalone charge rises from 18.90 to 43.90 per cent, €65.85 million. At the margin, inside an insurer that already carries currency risk, the 25 per cent costs €13.68 million, and a hedge is worth paying for up to 3.02 per cent of the fund a year.
Worked in full in Insurance Capital for Asset Managers by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The currency sub-module (Article 188 of the Delegated Regulation) shocks every foreign currency by 25 per cent up and down against the insurer's reporting currency. The charge for each currency is the larger of the two losses on own funds, and the currency charges are added together. With look-through, the fund's own assets carry their usual charges, here the spread charge on the loans, and the currency charge is applied to the euro value of the holding as well. The two do not replace each other: the dollar fund carries both.
The case is the dollar share class, one of the three cases in the companion files of Insurance Capital for Asset Managers, priced against the book's fictional insurer, Calder Life. All amounts are illustrative, in euro millions.
| Input | Value |
|---|---|
| Allocation, private credit fund, dollar class | 150.0 |
| Spread charge, BB at 4.2 years duration | 18.90% |
| Currency shock | 25.00% |
| Expected return, net of fees | 8.90% |
| Calder Life, existing charges: interest / equity / property | 180 / 240 / 95 |
| Spread / currency / concentration | 520 / 60 / 40 |
Calder Life's existing 60 of currency charge is on dollar assets, so the new exposure adds to it.
Step 1: the standalone charges.
Spread: 150.0 × 18.90% = 28.35
Currency: 150.0 × 25.00% = 37.5
Standalone, unhedged: 65.85, or 43.90% of the holding
Step 2: aggregate. Market risk is not the sum of its sub-modules; it is the square root of Σ Corrij × SCRi × SCRj with the Annex IV correlations. Currency correlates at 0.25 with interest, equity, property and spread, and at zero with concentration. Before the fund, Calder Life's market risk aggregates to 911.25.
Hedged, or in a euro class: spread 548.35, currency 60; aggregate 937.8
Unhedged: spread 548.35, currency 97.5; aggregate 951.5
Excel: =SQRT(MMULT(MMULT(TRANSPOSE(v),Corr),v)) on the vector v of six charges
Step 3: the marginal cost, after less before.
Hedged: 937.8 − 911.25 = 26.58
Unhedged: 951.5 − 911.25 = 40.25, of which the currency 13.68, 36.5% of its standalone 37.5
| Measure | Hedged or euro class | Dollar class, unhedged |
|---|---|---|
| Standalone charge | 28.35 | 65.85 |
| Marginal capital at Calder Life | 26.58 | 40.25 |
| Expected income | 13.35 | 13.35 |
| Return on marginal capital | 50.23% | 33.16% |
The currency is large standalone and moderate at the margin, because it is only weakly correlated with the rest of the book. Even so, it takes the return on marginal capital from 50.23 to 33.16 per cent. The hedge cost at which the two tie is the income lost that brings the hedged return down to the unhedged one:
Break-even hedge cost = 13.35 × (1 − 26.58 / 40.25) / 150.0 = 3.02% of the fund a year
A forward hedge has a second cost the break-even must cover. If the dollar instead rises 25 per cent, the hedge loses what the fund gains and calls 37.5 of cash margin. Carrying that cash at an assumed 2.00 per cent of yield given up costs 0.75 a year, 0.50 per cent of the fund, which leaves 2.52 per cent for the hedge's own cost, the interest differential and the dealing spread.
| Hedge ratio | Currency exposure added | Marginal capital | Of which currency | Return on marginal capital |
|---|---|---|---|---|
| 0% | 37.50 | 40.25 | 13.68 | 33.16% |
| 50% | 18.75 | 33.25 | 6.68 | 40.15% |
| 75% | 9.38 | 29.87 | 3.30 | 44.69% |
| 90% | 3.75 | 27.89 | 1.31 | 47.87% |
| 100% | 0.00 | 26.58 | 0.00 | 50.23% |
The insurer's existing currency charge also matters, and it is the reason the same dollar class costs two insurers different amounts. Because the charges for each currency are added, what counts is the total currency charge already on the book, not only the dollar part. With no currency charge at all the dollar class adds 11.54 at the margin; with 120 already on the book it adds 15.67. An insurer with dollar liabilities is the exception: the new assets offset them in the dollar shock and can reduce the charge.
The common mistake is to quote only the asset charge. A manager who markets the dollar class as an 18.90 per cent spread charge leaves out a 25 per cent currency charge that is bigger than the whole spread charge of an investment-grade fund: a BBB fund at 4.2 years is charged 10.50 per cent, and the BBB charge only reaches 25 per cent at a duration of 15 years. The opposite mistake is to price the currency at its standalone 37.5 when diversification brings it to 13.68 here. Price it at the margin, with the insurer's own sub-module charges, as in how to calculate the marginal SCR of an investment, and remember that the correlations used are the ones in Solvency II market risk aggregation. The case, with its hedge break-even and margin call, is in the free companion files.
A 25 per cent rise and a 25 per cent fall of each foreign currency against the insurer's reporting currency, under Article 188 of the Delegated Regulation, with the larger loss taken for each currency and the results added. Lower shocks apply to currencies pegged to the euro. On a EUR 150.0 million dollar holding the charge is 37.5 million before diversification.
A hedge that offsets the holding's currency exposure removes the corresponding currency charge, because the shocked loss on the fund is offset by the gain on the hedge. On the illustrative dollar class, hedging cuts the marginal capital from 40.25 to 26.58 million and lifts the return on marginal capital from 33.16 to 50.23 per cent. The hedge calls cash margin instead, 37.5 million if the dollar rises 25 per cent.
Because currency risk is aggregated with the other market risks at a correlation of only 0.25, so it adds less to the total than its standalone size. At Calder Life the 37.5 million standalone currency charge adds 13.68 million, 36.5 per cent of it. At an insurer with no currency charge at all it adds 11.54 million; with 120 million of existing currency charge, 15.67 million.
This article is one calculation from Insurance Capital for Asset Managers. 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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