Convexity-Adjusted Carry

What Is Convexity-Adjusted Carry?

In fixed income, carry is the income earned from holding a bond position net of financing costs, while convexity describes the non-linear relationship between price and yield, positive convexity adds value when yields move sharply in either direction, and negative convexity destroys it. Convexity-Adjusted Carry combines these two forces into a single measure of true expected holding-period return, recognising that raw carry overstates the profitability of negatively convex instruments and understates it for positively convex ones.

The adjustment is made by subtracting (or adding) the convexity cost, approximately ½ × Convexity × (Implied Volatility)², from the raw carry figure. This term represents the expected value of the optionality embedded in, or stripped from, the position by rate volatility. Consider a 30-year Treasury with roughly 400 units of convexity financed in the repo market at prevailing overnight rates: it will show substantially different adjusted carry depending on whether the implied vol regime assumes 80bp or 120bp of annualised rate volatility. At 80bp vol, the convexity drag is approximately 13bp annualised; at 120bp it balloons to nearly 29bp, a difference large enough to flip the sign of the net carry on a tightly structured trade. Crucially, this framework forces traders to price rate volatility as a real cost of carry, not an afterthought.

Why It Matters for Traders

Ignoring convexity when sizing carry trades is a classic source of crowded-position blowups. Mortgage-backed securities exhibit severe negative convexity because homeowners prepay when rates fall and extend duration when rates rise, the worst of both worlds. A trader seeing a +120bp raw carry pickup on agency MBS versus duration-matched Treasuries may actually be running a flat or negative convexity-adjusted carry trade once rate volatility is properly priced in. During periods of rate calm this mispricing is invisible; when vol reverts, losses can be sudden and large relative to accrued income.

Conversely, long-dated nominal Treasuries or long-gamma options strategies carry positive convexity that raw carry metrics systematically undervalue. Macro funds running duration overlays across sovereign markets routinely use convexity-adjusted carry to rank positions across the yield curve, blending it with roll-down return to form composite return estimates over 3- to 12-month horizons. Relative-value desks also use the measure to compare ostensibly similar instruments, for example, choosing between a 10-year on-the-run Treasury and a seasoned 12-year that has rolled down to a similar modified duration but carries a meaningfully different convexity profile and hence a different true carry after vol adjustment.

How to Read and Interpret It

• Positive convexity-adjusted carry > +50bp annualised: Generally attractive, with manageable hidden vol-tax risk under most vol regimes. Still subject to regime change, but offers a reasonable buffer.
• Raw carry positive but adjusted carry near zero or negative: A warning signal that implied volatility is pricing away the income. This is frequently seen in high-carry emerging-market local bonds during stressed vol regimes, where the MOVE Index or local rate vol surfaces have risen sharply.
• Large divergence between raw and adjusted carry (>40bp gap): Signals a highly vol-sensitive position. Monitor the volatility term structure for shifts that could flip the sign of adjusted carry. Positions with this profile require tighter stop-loss discipline or explicit vol hedges.
• Compressed divergence in suppressed-vol environments: When the MOVE Index trades below 70, the adjustment appears small and traders may underweight its importance, ironically the moment when complacency risk is highest.
• Compare across instruments rigorously: a 10-year versus a 2-year position may have similar raw carry after financing costs, but the duration mismatch creates vastly different convexity exposures and hence very different adjusted carry, particularly in a bear-steepener or bull-flattener scenario.

Historical Context

During the 2013 Taper Tantrum, 30-year Treasury carry appeared attractive at roughly +150bp over 3-month T-bills on a raw basis. However, with the MOVE Index spiking from approximately 60 to over 110 between May and July of that year, convexity costs on long-duration positions roughly doubled, turning many carry-focused duration longs into net losers on an adjusted basis within weeks. Funds that had incorporated the convexity adjustment systematically reduced notional earlier and avoided the worst of the 100bp+ sell-off in 30-year yields.

The 2022 Federal Reserve hiking cycle provided an even starker illustration. As the Fed embarked on its most aggressive tightening in four decades, agency MBS spreads widened dramatically, primary current coupon spreads moved from roughly 80bp over Treasuries in early 2022 to nearly 180bp by autumn. Holders who had underweighted convexity costs in their carry models suffered unexpected mark-to-market losses far exceeding the carry income earned over the prior year. The lesson was sharp: negative-convexity instruments can consume multiple years of raw carry in a single volatile quarter.

More recently, in late 2023 as 10-year Treasury yields briefly touched 5%, swaption-implied volatility on the 10-year point ran near 110bp normalised, pushing the convexity cost on long-duration positions to historically elevated levels and compressing convexity-adjusted carry even on bonds that looked superficially rich in income terms.

Limitations and Caveats

Convexity-Adjusted Carry is only as reliable as the implied volatility input used. In compressed-vol regimes, particularly post-QE environments where the volatility risk premium is suppressed by central bank asset purchases, the adjustment appears trivially small, and traders systematically underweight its future importance. The measure also assumes a static vol environment over the full holding period; in practice, vol regimes shift abruptly, rendering point-in-time adjustments stale. A position that looks attractively adjusted at 70 MOVE can flip to unattractive at 110 MOVE within a single FOMC meeting cycle.

The framework further assumes parallel or well-behaved yield curve shifts. In reality, basis risk from curve twists, changes in the term premium, liquidity premium fluctuations, and credit spread volatility all affect total return in ways convexity-adjusted carry does not capture. For MBS specifically, the convexity itself is model-dependent, prepayment model errors can materially mis-state convexity, making the adjustment circular in stressed environments when prepayment behaviour deviates from historical norms.

What to Watch

• MOVE Index levels: Sustained readings above 100 meaningfully increase convexity costs on long-duration positions; readings above 130, as seen in late 2022, can make even 30-year Treasury carry unattractive on an adjusted basis.
• Fed balance sheet policy: Quantitative Tightening directly affects MBS supply and the marginal buyer's need to convexity-hedge, feeding back into swaption pricing and shifting the adjustment in real time.
• Swaption market structure: Dealer convexity-hedging activity is visible through skew and term structure in rate volatility surfaces; a steepening of the vol surface or rising receiver skew signals elevated convexity demand and rising adjustment costs.
• Cross-market carry rankings: When raw carry rankings across G10 sovereign markets diverge significantly from convexity-adjusted rankings, it is often a signal of carry-trade crowding in low-convexity instruments, a setup that has historically preceded disorderly unwinds.
• Repo market conditions: Financing cost spikes, as seen during quarter-end window-dressing episodes, compress raw carry directly and can turn marginally positive adjusted carry negative without any change in yields or vol.