US equities have a stable same-day exposure of 11.16bp per basis point of the 10-year breakeven. A trader can measure that part of the paper.
For 2000 to 2021, Chaudhary and Marrow regress daily CRSP value-weighted returns on daily changes in the 10-year TIPS breakeven. Their estimate is 11.16 (t=13.03, N=5,021). Breakeven changes have a daily standard deviation of 3.6bp, so a one-sigma day brings an equity move of about a third of the 123.5bp daily return standard deviation. Scaled as the paper presents it, a 10bp breakeven move accompanies a 1.1% index gain. These figures all describe contemporaneous moves.
On CPI days, 11.88 versus 11.16 overall
Higher expected inflation raises nominal discount rates and hurts stocks in the naive account. The textbook response is that dividends inflate as well, cancelling the effect. The authors argue that, since 2000, higher long-run inflation expectations have signalled good news about the real economy. Investors assign less weight to bad states and accept a lower expected excess return. Prices rise today as a result. In this account, a falling risk premium supplies the return; cash flows and the real rate contribute little.
The authors try to get closer to causation by limiting the regression to the 274 CPI release days between January 2000 and December 2021. Their case rests on two assumptions: the print is the day's only news, and it changes other beliefs, including growth and the Fed, solely through inflation expectations. On CPI days the coefficient is 11.88 (t=4.43), close to the unconditional estimate. Before November 2010 it is 11.13; afterward it is 12.96, with 137 days in each subsample. All 30 Fama-French industries have positive loadings. Cumulative returns show no reversal through ten days.
In a monthly VAR, a 10bp CPI-day breakeven shock raises industrial production by 0.7% over a year. It also lowers VIX by more than 2 percentage points for nearly 18 months.
What inflation risk is being hedged?
The CPI-surprise table deserves a second reading. A surprise is the print minus the Bloomberg survey, and surprises send stocks down: the core month-on-month estimate is -1.902 (p<0.05). They send the 10-year breakeven up, with an estimate of 10.31 for core MoM (p<0.001). A hot print thus hurts equities directly while raising the breakeven that equities usually welcome.
The authors use a covariance identity to reconcile those signs. They divide the breakeven change into a surprise-driven component and an orthogonal component. The positive sign on the latter, in the paper's words, "follows by requirement". The hedge therefore covers revisions to long-run expectations unexplained by the print.
The picture changes in 2021 to 2023. Using S&P 500 total returns over November 2021 to October 2023, the 10-year beta drops to 2.06 (t=1.60), and the 2-year beta to 0.23 (t=0.23). The 2-to-10-year forward retains a coefficient of 2.36 (t=1.98). Across 25 CPI days, its point estimate is 14.69 (t=1.44).
The authors take the forward result as evidence that the relation persists at the long end. They argue that the short end of the breakeven curve is highly correlated with realized inflation. Because realized inflation hurts stocks, it offsets the positive expectations effect in the spot betas. This defence predicts precisely the 2.06 versus 2.36 pattern. It also accepts that the 10-year beta no longer gives a clean reading of long-run expectations.
Our reading of the table puts the 10-year beta of 2.06 against the full-sample 11.16, roughly four fifths smaller. Those estimates use different indexes and periods. The 2.06 comes from S&P 500 total return over November 2021 to October 2023; the 11.16 comes from the CRSP value-weighted index over 2000 to 2021.
The residual behind the 81.8% excess-return share
Expected excess returns are never observed here.
The mediation regressions assign to excess returns whatever the rate and strip controls fail to explain. The VAR forecasts excess returns directly and leaves dividends as the residual.
The Bernanke-Kuttner style monthly VAR uses six variables and six lags, with estimation beginning in 1990. Its total response is 14.11. Future excess returns account for 14.27 (t=2.80), real rates for 0.16 and dividends for -0.32. The authors fix ρ at 0.9962. The text calls the 14bp a response to a 1pp breakeven change; every other table reports bp per bp. Anyone replicating the result must resolve that unit before comparing 14.11 with 11.88.
For the mediation regressions, the controls are the 10-year TIPS real yield and 24-month S&P 500 dividend strips. Adding them takes the CPI-day coefficient from 11.98 to 9.80. The authors attribute 2.6% to rates, 15.6% to cash flow and 81.8% to expected excess returns. Using swaps gives shares of 3.5%, 0.6% and 95.7%.
The authors identify the weaknesses themselves. The strip measures risk-neutral expectations, and the real yield includes a term premium. Both controls therefore absorb some risk premia. A two-year strip also misses news about cash flows further out. The authors' response is that longer-term growth rates are notoriously difficult to forecast, so long-run dividend expectations should move little. The paper asserts this about investors without testing it. Using the strip also reduces the sample from 274 to 217 days.
The paper acknowledges that "all three methods have shortcomings" and says they "jointly provide heuristic evidence" for the excess-return channel. That joint evidence is less persuasive than the wording suggests. Of the four methods, only the mediation regression calculates the excess-return share as a remainder. The VAR leaves the dividend share as a remainder, so its -0.32 supplies no independent evidence against cash flows. For the 15.6% cash-flow share, the authors report that they cannot reject a zero effect for either the cash-flow or interest-rate channel. An insignificant 15.6% remains far from the abstract's "almost entirely".
Daily windows, term premium, and an undated median
The CPI-day design measures daily moves. A footnote argues that intraday data would leave the result unchanged, but we did not find an intraday test. The term premium matters across all days: adding the Kim-Wright 10-year term premium lowers the all-days beta from 11.16 to 7.69. The premium itself loads at 9.15 (t=6.89). On CPI days, the beta instead edges up to 12.60, while the premium coefficient is -2.19 (t=-0.55). The days you care about determine which number you should monitor.
The most interesting single estimate is the asymmetry result: 24.27 (t=3.03, N=74) when expectations fall and expected inflation is below median. The text did not let us determine whether that median uses the full sample or trails through time. A full-sample split would condition on information unavailable in real time. The table has five columns beneath four labels. Its first column reports N=277, the sum of the four cells, exceeding the 274 CPI days.
We left the breakeven beta unbacktested
We did not backtest this. Trading the inflation leg would require futures-type markets for which we have no price data. Our equity history permits only a post-2010 start and uses SPY in place of the CRSP value-weighted index. The published betas therefore cannot transfer automatically. We had sketched an overlay with a lagged risk adjustment. That would test something different from the paper's contemporaneous causal estimates or its decomposition.
The usable result is a risk number. Over 5,021 trading days, including 274 CPI release days, the CRSP value-weighted index has about 11bp of same-day exposure per basis point of 10-year breakeven. When expectations fall from below-median levels, the beta is 24.27. SPY should track this closely, though it holds a different portfolio.
In 2021 to 2023, the all-days 10-year beta fell to 2.06. The 25 CPI days produce 14.69 on the 2-10y forward, too few observations to settle the question. A CPI-day estimate reaching significance in post-2023 data would restore our confidence in it as a standing exposure. Until then, we size it as an exposure that can fade.