- The question
- From yields to CHF-hedged returns
- A one-year, maturity-matched example
- Building a fair comparison
- From carry to scenarios
- Why the better carry is not automatically the better investment
- A practical decision framework
The question
A USD bond yields 5.00%. A comparable CHF bond yields 1.50%. Both figures are hypothetical, chosen only to frame the problem; neither is a market quote for any specific issue, date or market. Which is the better investment for a CHF-based institution?
The two headline yields alone cannot answer that. They sit in different currencies over different risk-free bases, and a CHF-based insurer or pension fund pays claims and benefits in CHF. A yield that exists only in USD is not a return until it is converted, and conversion, whether hedged or left open, changes the return and adds risk of its own.
The argument of this article: compare the two bonds on expected CHF returns and on the risks that matter to the institution (duration, credit, liquidity, collateral), on a consistent basis, before deciding which is "better."
From yields to CHF-hedged returns
A CHF-based investor who wants USD-bond exposure without open currency risk converts CHF to USD at spot, buys the bond, and sells USD forward, typically rolling shorter-dated forwards rather than one long-dated contract, so USD cash flows convert back to CHF at a rate agreed today.
Why forward points track the rate differential
Under covered interest parity (CIP), the forward rate is set by the two currencies' interest rates, not by a view on where spot is headed. Quoting S and F as CHF per USD:
F = S × (1 + r(CHF)) / (1 + r(USD))
If the CHF rate sits below the USD rate, F is below S: the USD trades at a forward discount against CHF. This is the no-arbitrage condition that stops anyone borrowing CHF, buying USD, investing at the USD rate, and selling the proceeds forward for a riskless profit (Corporate Finance Institute, "Covered Interest Rate Parity (CIRP)").
Two points follow. The forward discount is not an exchange-rate forecast: it reflects only the rate gap between the two money markets. The literature on uncovered interest parity has long found forward rates to be poor, even perversely biased, predictors of the subsequent spot rate, with higher-rate currencies tending to depreciate less than the forward discount implies, not more (Fama, 1984). Reading hedge cost as a view on where USD/CHF is going confuses a financing identity with a forecast.
CIP does not hold exactly. Since 2008, a persistent cross-currency basis has sat between the rate differential money markets imply and the rate actually available in the forward market, reflecting bank balance sheet costs and, at times, lopsided hedging demand (Borio, McCauley, McGuire and Sushko, "Covered interest parity lost: understanding the cross-currency basis," BIS Quarterly Review, September 2016). For a CHF-based investor hedging USD assets, this basis typically adds to the cost; bid-ask spreads and rolling transaction costs add a further, separate drag.
One more point: today's short-dated hedge cost is a snapshot, not a multi-year constant. A bond held five years but hedged with three-month forwards is rehedged roughly twenty times, each at whatever the differential and basis happen to be that day. Assuming today's cost holds for the bond's life is an assumption, not a fact.
A useful approximation, with limits
Approximate CHF-hedged carry ≈ USD bond carry + signed FX hedge contribution − implementation costs
Sign convention: a negative hedge contribution reduces the CHF return. The hedge contribution bundles the CIP-implied rate differential and the cross-currency basis; implementation cost is a separate line for bid-ask and transaction costs, so the basis is not counted twice.
This is a carry approximation, not a return forecast. Yield to maturity is the return promised if held to maturity with coupons reinvested at that yield and no default; carry is the income earned over the actual, shorter holding period; realized total return additionally reflects what happens to rates, spreads, and the actual rolled hedge cost. Subtracting hedge cost from yield approximates carry; it is not a reliable estimate of total return.
A one-year, maturity-matched example
Before the multi-year bonds, isolate the hedge mechanics on the simplest instrument: a one-year zero-coupon bond with a matching one-year hedge. All inputs are hypothetical.
Assume spot S = 0.9000 CHF per USD, a one-year USD risk-free rate of 4.50%, and a one-year CHF risk-free rate of 1.00%. Under pure CIP:
F = 0.9000 × 1.0100 / 1.0450 = 0.8699 (forward points −0.0301; USD at a one-year forward discount of about 3.0 CHF cents)
For an investor who buys the bond and sells the known USD proceeds forward at F, the fully hedged CHF return is:
CHF return = (1 + USD return) × F/S − 1
This assumes the terminal USD proceeds are known and fully hedged, true for a single-cash-flow zero-coupon bond. A coupon bond generates several USD cash flows at different dates and must hedge each at its own maturity-matched rate, or accept residual timing risk; it does not reduce to one forward.
(1.0450) × (0.8699 / 0.9000) − 1 = 1.00%, exactly the CHF risk-free rate. That is the point of CIP: with no basis and no default risk, the hedged CHF return collapses to the CHF risk-free rate, whatever the USD yield looked like in isolation, extinguished by the forward discount almost by construction.
In practice the basis and transaction costs are the wedge that remains. A hypothetical 15bp/year basis moves the realistic forward to F' = 0.8686, dropping the pre-cost CHF return to 0.85%; a further hypothetical 10bp/year implementation cost brings it to 0.75%, about 25bp below the pure-CIP outcome, the entire gap between the textbook hedge and the one actually available.
Building a fair comparison
Return to the multi-year bonds, built so currency is the only major variable left standing: two hypothetical five-year, senior unsecured bullet bonds from the same issuer, same seniority, same A rating, one in USD and one in CHF. Real pairs rarely match this cleanly on index membership, covenants or liquidity; treat any such gap as a residual still needing explanation, not as currency risk.
Both bonds carry the same hypothetical 0.50% credit spread over their own risk-free rate, so the entire 350bp pre-hedge yield gap is interest rates alone: the USD bond's 5.00% is 4.50% risk-free plus 0.50% spread; the CHF bond's 1.50% is 1.00% risk-free plus the same spread. Modified and spread duration are computed from each bond's own yield on a five-year bullet schedule (spread duration assumed equal to modified duration, no embedded optionality).
Capital base: CHF 1,000,000 equivalent, one-year horizon. Hedge policy: a rolling three-month forward, notional reset quarterly to the bond's then-current market value (clean price plus accrued coupon) at the prevailing spot. Between resets, price moves and coupon accrual create a small, temporary mismatch between hedge notional and the bond's CHF-equivalent value; that residual FX exposure closes out at the next reset and is treated as de minimis over the one-year window modeled here.
| USD bond | CHF bond | |
|---|---|---|
| Instrument | Senior unsecured corporate, bullet | Senior unsecured corporate, bullet |
| Credit quality | A (hypothetical)* | A (hypothetical)* |
| Remaining maturity | 5 years | 5 years |
| Yield to maturity | 5.00% | 1.50% |
| Carry assumption | 5.00% | 1.50% |
| Modified duration | 4.38 years | 4.80 years |
| Spread duration | 4.38 years | 4.80 years |
| Signed FX hedge contribution | −3.65% | n/v |
| Implementation cost | 0.10% | n/v |
| Approx. CHF-hedged carry | 1.25% | 1.50% |
*Same hypothetical issuer, seniority and rating assumed for both bonds, to isolate the currency effect from credit risk.
Because the risk-free differential and spread are identical by construction, the entire 25bp gap between the USD bond's hedged carry (1.25%) and the CHF bond's carry (1.50%) is explained exactly by the 15bp basis and 10bp implementation cost, nothing else. On carry alone, the CHF bond screens better here, though carry is only the first input to the decision.
The CHF bond's 4.80-year modified duration against the USD bond's 4.38 is not an artifact: a lower discount rate on the same cash flow schedule mechanically produces longer duration. That gap matters more to the final decision than the 25bp carry gap, as the next section shows.
The 25bp gap is also not fixed; it is a function of the hedge-cost assumption. Holding the USD bond's carry and implementation cost fixed and letting only the signed hedge contribution vary shows how sensitive the conclusion is, and where it flips:
At the assumed −3.65% hedge contribution, the USD bond's hedged carry (1.25%) sits 25bp below the CHF bond's. Break-even, where the two carries are equal, sits at a hedge contribution of −3.40%: a hedge 25bp cheaper than assumed here, all else equal, would make the two carries identical. A narrow margin for an assumption reset at every rollover.
From carry to scenarios
Carry describes what happens if nothing changes. A one-year return also depends on what happens to rates and spreads, and, for the hedged leg, on what the hedge actually costs as it rolls. A transparent, simplified approximation:
Return ≈ carry + roll-down − modified duration × Δrisk-free yield − spread duration × Δcredit spread + FX hedge contribution − implementation costs
Two simplifications are stated rather than hidden: roll-down (the price gain from aging down an upward-sloping curve) is excluded entirely, and convexity is omitted. At the ±100bp shocks used below, with these moderate durations, the resulting error is second-order but not zero. The scenarios are illustrative, parallel shocks to each currency's own curve, not forecasts, and not a claim that USD and CHF rates move in lockstep.
| Scenario | Assumption, both currencies | Return, USD (hedged) | Return, CHF | P&L, USD (hedged) | P&L, CHF |
|---|---|---|---|---|---|
| 1. Unchanged | Risk-free & spread unchanged | 1.25% | 1.50% | +CHF 12,500 | +CHF 15,000 |
| 2. Rates +100bp | Risk-free +100bp in each currency | −3.13% | −3.30% | −CHF 31,260 | −CHF 32,998 |
| 3. Rates −100bp | Risk-free −100bp in each currency | +5.63% | +6.30% | +CHF 56,260 | +CHF 62,998 |
| 4. Spreads +50bp | Credit spread +50bp in each currency | −0.94% | −0.90% | −CHF 9,380 | −CHF 8,999 |
| 5. Hedge cost +100bp at rollover | USD forward re-struck +100bp at month 6 (remaining 6 months only); CHF unaffected, no hedge | 0.75% | 1.50% | +CHF 7,500 | +CHF 15,000 |
Scenario 5's timing matters: the 100bp increase does not apply to the full year, only from the rollover date. A month-6 rollover means the annualized hedge contribution runs at −3.65% for the first half and −4.65% for the second, a weighted average of −4.15% for the year, a 50bp full-year-equivalent drag from a 100bp mid-year jump, because only half the year was exposed. Treating the full 100bp as a full-year cost would overstate the damage by half.
Two things stand out. Duration dominates: a 100bp parallel move swings each bond's return by several percentage points, dwarfing the 25 to 40bp carry and hedge-cost differences. The CHF bond's longer duration also makes it outperform in a rally and underperform in a sell-off by slightly more than the hedged USD bond; the currency hedge does not change that, since it was never meant to. The one scenario purely about hedging risk, the rollover shock, costs the USD position about 50bp relative to its base case while leaving the CHF bond untouched: the risk taken on by choosing to hedge rather than by choosing the currency.
Why the better carry is not automatically the better investment
A 25bp carry edge, or a few scenario basis points, is a thin basis for a portfolio decision alone. Several considerations sit above the math:
CHF liabilities and cash-flow matching. A Swiss pension fund or insurer pays benefits in CHF. A hedged USD bond still requires running a USD-to-CHF conversion program for the life of the holding; a CHF bond does not. Structural, not cosmetic.
Duration relative to liabilities. The 4.80-versus-4.38-year gap is real interest-rate sensitivity, not a currency artifact. If liabilities are long-duration, the shorter USD position leaves more of that gap open; hedging currency does nothing to close it.
Credit concentration and diversification. This example used one issuer in both currencies to isolate the currency effect. A real portfolio should not: USD and CHF credit markets offer different issuers and sectors, and spreading credit risk across both is a diversification benefit a single-currency carry comparison never shows.
Collateral and liquidity from derivatives. A rolling forward program is not costless beyond basis and transaction costs. Under an ISDA/CSA or through a CCP, the hedge generates variation margin calls as spot and rates move, funded in eligible collateral, typically CHF or high-quality liquid assets, a draw the CHF bond carries none of.
Repeated rollover and uncertain future hedge costs. Scenario 5 showed the mechanism in miniature. Over five years hedged with three-month forwards, that rollover happens roughly twenty times, each priced at whatever the differential and basis happen to be that day, an uncertainty the CHF bond holder never faces.
Accounting, regulatory and jurisdictional differences. A Swiss insurer sits under FINMA's Swiss Solvency Test (SST), whose standard model capitalizes interest rate, spread and currency risk directly from the balance sheet (FINMA SST fact sheet). An EU insurer sits under Solvency II's standard formula instead, where the currency risk sub-module applies a prescribed shock, generally 25%, to each foreign-currency position against the reporting currency (Delegated Regulation (EU) 2015/35, Article 188). These are distinct regimes, never interchangeable; a Swiss institution answers to the SST, not Solvency II. In both, hedging reduces only the currency-risk capital charge, leaving interest rate, spread and liquidity charges untouched.
Hedging currency risk removes currency risk. It does not remove interest rate, credit or liquidity risk, and it introduces a risk of its own: an uncertain future hedging cost.
A practical decision framework
A short checklist for comparing a foreign bond against a domestic alternative, once the currency question is on the table:
- Put both bonds on the same currency basis first, using hedge cost and basis, not the headline yield gap, as the starting point.
- Decompose the expected difference into carry, rate, credit and FX-hedge-roll components, sized against the institution's own risk tolerance, not one blended number.
- Check modified and spread duration against the liability profile, not only against the other bond's duration.
- Confirm the hedge program's collateral and liquidity draw is financeable within the portfolio's actual cash and repo capacity, under stress as well as calm markets.
- Weigh issuer, sector and currency-market diversification, not just the standalone carry pickup; a matched-issuer comparison like this one hides that benefit entirely.
- Treat today's hedge-cost assumption as a policy input to revisit at every rollover, not a feature of the bond.
On the hypothetical numbers used here, the CHF bond's own carry (1.50%) is about 25bp better than the CHF-hedged USD bond's approximate carry (1.25%), because basis and implementation costs outweigh what is otherwise an identical risk-free and credit setup. The USD-hedged bond carries less duration, useful to an institution short of duration against its liabilities, and the USD market may offer issuer and sector diversification the CHF bond cannot. Neither instrument is categorically better; which one fits depends on the specific gap, in duration, credit or liquidity, the institution is trying to close, a portfolio-construction question, not a currency one.
Verification note. Every figure in this article comes from one calculation module (app/data/chf-hedged-bonds.ts), mirrored by a standalone, independently runnable script (scripts/chf-hedged-bonds-calc.py) for reproduction outside the website. All rate, yield, spread, basis and cost inputs are hypothetical and labeled as such; none are live market quotes. Modified and spread duration are computed from first principles for a five-year bullet bond priced at par, with spread duration assumed equal to modified duration (no embedded optionality). Roll-down is excluded from the scenario formula; convexity is omitted. Hedge notional resets quarterly to the bond's then-current market value; the resulting intra-period residual FX exposure is treated as de minimis over the one-year window modeled. Scenario shocks are parallel and illustrative, not forecasts, and are not assumed to co-move between currencies in reality. Displayed figures are rounded (two decimals for percentages, nearest CHF for P&L); underlying calculations use full floating-point precision. The full dataset behind every table and chart is available as a CSV download.
Sources
- Borio, C., McCauley, R., McGuire, P. and Sushko, V. (2016). "Covered interest parity lost: understanding the cross-currency basis." BIS Quarterly Review, September 2016.
- Fama, E. F. (1984). "Forward and Spot Exchange Rates." Journal of Monetary Economics, 14, 319-338.
- Corporate Finance Institute. "Covered Interest Rate Parity (CIRP)."
- FINMA. "Swiss Solvency Test (SST)" fact sheet.
- Commission Delegated Regulation (EU) 2015/35, Article 188 (currency risk sub-module). EUR-Lex.