Volatility Timing or Factor Momentum? A Real-Time Horse Race on a Century of U.S. Factor Returns

Abstract

Volatility management and time-series factor momentum both time a factor using nothing but its own past returns. We race them on the Fama–French market, size and value factors, 1,189 months from July 1927 to July 2026. Volatility management earns a spanning alpha only for the market, 3.35% per year (t = 2.34); adding a momentum-managed leg cuts it to 2.04% (t = 1.52). The mirror specification is not symmetric — momentum-managed alphas of 5.56%, 2.59% and 3.37% per year survive — but those alphas come with lower Sharpe ratios, so neither leg is a better portfolio. Real-time volatility-managed Sharpe ratios fall for every factor, and the market effect is entirely pre-1963.

I. Introduction

Two literatures claim that a factor portfolio can be improved using only the factor's own history. Moreira and Muir (2017) scale each factor by the inverse of its lagged realized variance and report large alphas, higher Sharpe ratios and utility gains, extended to long horizons in Moreira and Muir (2019); Barroso and Santa-Clara (2015) apply the device to momentum. The economics is that conditional variance moves far more than the conditional risk premium, weakening the trade-off of French, Schwert and Stambaugh (1987) at monthly horizons. Separately, Gupta and Kelly (2019), Ehsani and Linnainmaa (2022) and Arnott, Kalesnik and Linnainmaa (2023) show most factors are positively autocorrelated, so a factor's trailing twelve-month return is itself a timing signal; Haddad, Kozak and Santosh (2020) find dominant equity factors predictable more generally.

The two signals are functions of the same object — one the squared magnitude of the last year of returns, the other their level — so if they carry the same information, part of one literature is redundant. No study we know of races them on the same factors under one real-time discipline; Grobys, Kolari and Rutanen (2022) combine them as complements, on option-implied volatility over a short sample.

We run that race twice: in sample, in the spanning framework that literature uses, and in strict real time, every scaling constant estimated on an expanding window ending in the prior month, in the out-of-sample spirit of Goyal and Welch (2008). Real-time discipline is the crux of the critical literature. Cederburg, O'Doherty, Wang and Yan (2020) show across 103 strategies that positive spanning alphas coexist with no real-time outperformance, because the scaling constant and the loading are full-sample objects; Liu, Tang and Zhou (2019) make the same look-ahead point for the market; DeMiguel, Martín-Utrera and Uppal (2024) show conditional multifactor portfolios do survive out of sample, leaving the single-factor verdict open.

Four results follow. The Moreira and Muir (2017) benchmark replicates only for the market and only weakly, 3.35% per year (t = 2.34), falling to 2.04% (t = 1.52) once the momentum-managed market enters the regression. The mirror specification is not symmetric — momentum-managed alphas of 5.56%, 2.59% and 3.37% survive — but these are spanning alphas without portfolio gains: the momentum-managed market earns a Sharpe ratio of 0.412 against 0.448 unmanaged. In real time the volatility-managed Sharpe ratio is below the unmanaged one for every factor. And the inverse-variance signal does not forecast the conditional mean, so its in-sample gain rests on a full-sample normalization the real-time constant destroys. We thus supply the missing head-to-head test and extend the Cederburg et al. (2020) critique to a century of data and to size and value. Sections II to VI cover hypotheses, data, results, robustness and conclusions.

II. Hypothesis Development

Let $f_t$ be a factor's excess or long–short return. Volatility management multiplies $f_t$ by a weight inversely proportional to a variance estimate formed at $t-1$: if conditional variance is persistent while the conditional mean is not proportional to it, the managed portfolio has a higher unconditional mean-to-variance ratio, and a spanning regression of managed on unmanaged returns yields a positive intercept. Factor momentum instead multiplies $f_t$ by the sign of the trailing return; positive autocorrelation again yields a positive intercept, but here the conditional mean, not the variance, is timed. Both weights are functions of $\{f_{t-1},\dots,f_{t-12}\}$, so the strategies can be correlated by construction.

H1 (distinctness), tested factor by factor. For any factor whose volatility-managed portfolio earns a benchmark alpha significant at the 5% level, that alpha remains positive with a Newey–West t-statistic above 1.96 once the momentum-managed factor enters the spanning regression. H1 is informative only where there is an alpha to absorb; Table II shows this is the market factor alone.

H2 (implementability). Under expanding-window real-time implementation, the volatility-managed portfolio's annualized Sharpe ratio exceeds the unmanaged factor's.

The joint hypothesis requires both. Our code recorded a pre-committed rule requiring at least two of three factors on each condition; we report it alongside the factor-by-factor verdicts, which are the informative test.

III. Data and Methodology

A. Data

We use the file "Fama–French three factors, monthly" from the Kenneth R. French Data Library, Tuck School of Business, Dartmouth College (Fama and French 1993), retrieved on 8 September 2026. It holds 1,201 monthly observations from July 1926 to July 2026 in five columns: Date (first day of the month), Mkt-RF (the value-weighted CRSP market return less the one-month Treasury bill rate), SMB (small minus big), HML (high minus low book-to-market) and RF (the bill rate). All series are in percent per month and are divided by 100 before use; there are no missing values. One filter applies: an observation enters only if the factor has a complete twelve-month lagged history, which drops the first twelve months and leaves 1,189 monthly observations from July 1927 to July 2026 for each factor. The provider notes that pre-1963 coverage rests on thinner data; Section V treats that period separately.

B. Variable construction

For each factor $f \in \{\text{Mkt-RF}, \text{SMB}, \text{HML}\}$, both signals use only information available at the close of month $t-1$:

The two managed portfolios are

where $c_v$ and $c_m$ set each managed series to the unconditional standard deviation of the unmanaged factor, following Moreira and Muir (2017). The momentum-managed portfolio goes short the factor after a losing year, the time-series construction of Gupta and Kelly (2019) and Ehsani and Linnainmaa (2022). Because the file is monthly, $RV_{t-1}$ is a trailing monthly-return variance rather than the within-month realized variance built from daily data; it is the only variance measure available across the century, and it bounds what we can conclude (Section VI).

C. Specifications

The benchmark and horse-race spanning regressions are

The predictive horse race regresses the factor on standardized signals, so each slope is a one-standard-deviation effect in percentage points per month:

All regressions use Newey and West (1987) standard errors with six lags; *, **, *** denote 10%, 5% and 1% significance. Alphas are annualized by multiplying the monthly intercept by twelve, and the appraisal ratio is the annualized alpha over the annualized residual standard deviation. Both $c_v$ and $c_m$ in equations (3) and (4) use the whole sample, so those alphas are not attainable by any investor; Table V is their implementable counterpart. It re-estimates $c_v$ and $c_m$ on the expanding window through $t-1$ after a 120-month burn-in, giving 1,069 out-of-sample months from July 1937 to July 2026. Sharpe differences are tested by the Ledoit and Wolf (2008) studentized circular block bootstrap (block six, 999 replications, seed 20260908), and certainty equivalents are $\mu - \tfrac{1}{2}\gamma\sigma^{2}$ at $\gamma = 5$.

IV. Results

Table I. Summary statistics for the Fama–French factors.

Notes. Monthly returns from the Kenneth R. French Data Library, re-annualized from percent per month; July 1927 to July 2026, all months with a complete twelve-month lagged history. Sharpe ratios are $\sqrt{12}$ times the monthly mean-to-standard-deviation ratio; the last column correlates the two signals of equation (1).

Table II. Volatility-managed spanning regressions (benchmark) and managed-portfolio Sharpe ratios.

Notes. Equation (3), July 1927 to July 2026, both scaling constants set on the full sample. Newey–West(6) standard errors, t-statistics in parentheses; *, **, *** denote 10%, 5% and 1%. Alphas and Sharpe ratios are annualized over the same 1,189 months.

The benchmark survives at the 5% level only for the market, at roughly two-thirds the magnitude reported with daily realized variance: 3.35% per year on 13.12% residual volatility, an appraisal ratio of 0.26 — real, but modest. For size and value the volatility-managed Sharpe ratio is below the unmanaged one. The last row shows the two managed legs are near-orthogonal, so the horse race is a genuine contest rather than a collinearity problem.

Table III. Horse-race spanning regressions.

Notes. Equation (4), July 1927 to July 2026, again with full-sample scaling constants, so neither panel's alpha is attainable in real time. Panel A adds the momentum-managed factor to the benchmark; Panel B is the mirror image. Newey–West(6) t-statistics in parentheses.

Table III refutes H1 where it is informative. The market is the only factor with a benchmark alpha to absorb, and the momentum-managed leg cuts it by 39%, from 3.35% to 2.04%, and the appraisal ratio from 0.26 to 0.16, leaving t = 1.52. For SMB and HML the horse race cannot discriminate, because Table II leaves nothing to absorb; the pre-committed count returns 0 of 3, but only the market entry is informative.

Panel B is the mirror-image specification and the result is not symmetric: all three momentum-managed alphas are positive, with t-statistics of 2.99, 2.55 and 2.89, significant at the 1%, 5% and 1% levels. This is not evidence of a better portfolio, and the Cederburg et al. (2020) diagnosis applies to it as forcefully as to the volatility-managed leg. The momentum-managed market's Sharpe ratio is 0.412 against 0.448 unmanaged in sample and 0.397 against 0.524 out of sample (Table V), and its Panel B alpha owes much to the loading of −0.170 on the factor itself, which turns a lower-Sharpe portfolio into a positive intercept against a benchmark it partly shorts. The claim is one of relative spanning only: factor momentum spans volatility management, not the reverse, while neither leg beats holding the factor.

Table IV. Predictive regressions of factor returns on standardized signals.

Notes. Equation (5), N = 1,189 months in every column; the dependent variable is the factor return in percent per month, so each coefficient is a one-standard-deviation effect in percentage points per month. Newey–West(6) t-statistics in parentheses; the Wald statistic tests both slopes jointly.

Table IV explains the asymmetry. The inverse-variance signal never forecasts the conditional mean: a one-standard-deviation increase in $RV^{-1}_{t-1}$ is associated with 8 to 15 basis points lower return next month for every factor, never with a t-statistic beyond −1.59. Factor momentum has the right sign everywhere and is significant at the 5% level for SMB, where a one-standard-deviation move is worth 24 basis points per month alone and 22 jointly; the joint Wald test rejects at the 5% level only for SMB. The volatility-managed market's gain thus comes not from return prediction but from normalizing a portfolio whose variance is predictable.

Table V. Real-time out-of-sample performance, July 1937 to July 2026.

Notes. Scaling constants re-estimated each month on an expanding window ending at $t-1$ after a 120-month burn-in; 1,069 out-of-sample months. $\Delta$Sharpe is managed minus unmanaged; LW p is the two-sided Ledoit and Wolf (2008) bootstrap p-value of Section III.C. CE is the certainty equivalent at risk aversion five; Max DD compounds monthly returns.

Table V refutes H2 for every factor. The volatility-managed Sharpe ratio is lower than the unmanaged one in all three cases, though no shortfall is distinguishable from zero at the 10% level: a real-time investor gained nothing, rather than demonstrably losing. The Sharpe comparison is the clean test of timing value, and it returns nothing. The certainty-equivalent column is not: because the real-time constant cannot equalize volatility ex post, the managed market realizes 26.49% annualized volatility against 15.79%, so the fall from +2.04% to −4.11% per year measures a leverage mismatch — an estimation failure in $c_v$ — not the absence of timing information, and that mismatch also deepens maximum drawdown from −55.7% to −82.8%. Momentum management raises the real-time Sharpe ratio for one factor only, SMB (0.241 against 0.171, p = 0.612).

V. Robustness

Table VI. Real-time leverage and a capped-leverage variant.

Notes. Leverage is the real-time weight $c_v/RV_{t-1}$ over the 1,069 out-of-sample months of Table V; the final column caps that weight at three before returns are computed. Sharpe ratios are annualized.

The strategy is genuinely levered — a third of months above twice the unmanaged position for the market, with a maximum of eleven times — yet capping the weight at three barely moves performance, 0.520 against 0.507. The verdict is neither a leverage artifact nor rescued by a realistic constraint.

Table VII. Subsample split at July 1963.

Notes. Equations (3) and (4) on July 1927–June 1963 ("pre") and July 1963–July 2026 ("post"), scaling constants recomputed within each subsample. Newey–West(6) t-statistics in parentheses.

Table VII is the most damaging single result for volatility timing. The market's benchmark alpha is 9.53% per year before July 1963 and 0.54% after; in the horse race, 7.51% and −0.22%. The whole monthly-data effect lives in the period the provider flags for thinner coverage, and neither SMB nor HML is significant at the 10% level in either subsample.

Table VIII. Sensitivity of the benchmark alpha to the variance window.

Notes. Annualized alphas from equation (3), percent per year, Newey–West(6) t-statistics in parentheses, re-estimating $RV_{t-1}$ over the stated window. N varies because a longer window drops more initial months. The one positive in-sample result is fragile: the market alpha is insignificant at the 10% level at three and six months and reaches the 5% level only at twelve and twenty-four.

Three limitations bear on the reading. The variance proxy uses twelve trailing monthly returns, not within-month daily data as in Moreira and Muir (2017), so our nulls bound the informativeness of monthly-frequency variance, not of volatility timing in general. All returns are gross: no transaction, financing or margin costs are imposed on a strategy levered above two in a third of months, so Table V is an upper bound. And the momentum-managed leg uses a sign-based weight; no long-only or continuously scaled variant was estimated. We test three factors from one country.

VI. Conclusion

On a century of monthly U.S. factor returns, and with a variance signal built from monthly data alone, volatility management is neither distinct from time-series factor momentum nor implementable in real time. Its only trace is a market alpha of 3.35% per year that falls to 2.04% and loses significance at the 5% level once a momentum-managed leg is present, is confined to the pre-1963 sample, and yields no out-of-sample Sharpe improvement. The mirror specification survives for all three factors, but with lower Sharpe ratios than the unmanaged factors, so the Cederburg et al. (2020) and Liu, Tang and Zhou (2019) diagnosis — spanning alphas without portfolio gains — applies to both legs alike.

The qualifier matters. Table VIII shows the in-sample estimate depends on the variance window, so our evidence bounds the timing content of monthly-frequency variance; we cannot reject that a within-month realized variance from daily returns would deliver a different answer, and testing that is the natural next step, since Barroso and Detzel (2021) and DeMiguel, Martín-Utrera and Uppal (2024) both find structure a single-factor monthly design cannot see. Whether the pre-1963 concentration reflects time variation in the risk–return trade-off or the thinner data of that era is unresolved.

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