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 essentially represents the expected value of the optionality embedded in, or stripped from, the position by rate volatility. A 30-year Treasury with 400 units of convexity, financed in repo at prevailing Overnight Reverse Repo rates, will show substantially different adjusted carry depending on whether the implied vol regime assumes 80bp or 120bp of rate volatility.

Why It Matters for Traders

Ignoring convexity when sizing carry trades is a classic source of crowded-position blowups. Mortgage-backed securities, for example, 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 vol is properly priced in.

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 yield to form composite return estimates over 3- to 12-month horizons.

How to Read and Interpret It

• Positive convexity-adjusted carry > +50bp annualised: Attractive, with limited hidden vol-tax risk.
• Raw carry positive but adjusted carry near zero or negative: A warning that implied volatility is pricing away the income — often seen in high-carry EM local bonds during stressed vol regimes.
• Large divergence between raw and adjusted carry: Signals a vol-sensitive position; monitor the volatility term structure for shifts that could flip the sign of adjusted carry overnight.
• Compare across instruments: a 10-year versus a 2-year position may have similar raw carry after financing, but the duration mismatch creates vastly different convexity profiles.

Historical Context

During the 2013 Taper Tantrum, 30-year Treasury carry looked attractive at roughly +150bp over 3-month T-bills when viewed on a raw basis. However, with rates implied vol (measured by the MOVE Index) spiking from approximately 60 to 110, convexity costs on long-duration positions ballooned, turning many carry-focused duration longs into effective losers on an adjusted basis within weeks. Funds that had incorporated the convexity adjustment reduced notional earlier and avoided the worst of the 100bp+ sell-off in long rates.

Similarly, in 2022, as the Fed began its most aggressive hiking cycle in four decades, negative-convexity agency MBS widened dramatically — holders who had underweighted convexity costs in their carry models saw unexpected mark-to-market losses well beyond carry income earned.

Limitations and Caveats

Convexity-Adjusted Carry is only as reliable as the implied volatility input used. In compressed-vol regimes (e.g., post-QE environments with suppressed volatility risk premium), the adjustment appears small and traders may underweight its future importance. The measure also assumes a static vol environment over the holding period — in practice, vol regimes shift, rendering the adjustment stale quickly. Finally, it does not capture basis risk, liquidity premium, or credit spread volatility that also affect total return.

What to Watch

• MOVE Index levels: sustained readings above 100 meaningfully increase convexity costs on long-duration positions.
• Fed balance sheet runoff (Quantitative Tightening) impacting MBS supply and convexity-hedging flows.
• Dealer convexity hedging activity in swaption markets, visible through skew and term structure in rate vol.
• Cross-market divergence between raw carry rankings and convexity-adjusted rankings as a signal of carry-trade crowding.