Fear Buys Variance, Not Return: Sentiment and the Shape of Forward Equity Returns

00Executive summary

“Sentiment” gets used as if it were one number. It is at least three different instruments — what households say (surveys), what option and credit markets charge (VIX, spreads), and what the news flow worries about (policy uncertainty) — and right now those instruments disagree with each other more than at any point in the sample. This piece builds a five-proxy fear composite the same way the macro-regime piece built its growth composite — expanding-window z-scores, so the reading at month $t$ uses only data available at $t$ — and asks the question in a form that can fail: does the level predict the forward 3-month S&P return, and if not, what exactly does it predict? This revision also turns the referee's guns on its own results: a vol-clustering control, four timing conventions, a beta hedge on the factor spreads, and a dummy for the Michigan survey's 2024 redesign. Two of the original headline numbers do not survive, and the text says so.

• 01The level predicts almost nothing, under any timing convention. The composite's correlation with the forward 3-month return is 0.04; the top-minus-bottom quintile spread is +1.3pp (bootstrap CI [-3.8, 6.4]) and ranges only -0.7 to +1.8pp across lagged-input, market-only and PCA variants. Out of sample the linear signal scores -1.5%.
• 02Fear prices variance — literally, and not as a vol-clustering artifact. A 1σ rise predicts +5.25 points of forward 3-month realized volatility (HAC t = 4.7), and the 90th-percentile return coefficient is +4.03pp raw and +4.67pp after controlling for trailing realized vol (CI [2.18, 6.16]). The composite knows something trailing vol does not.
• 03Six horses, one survivor: news-based policy uncertainty, at +1.54pp per σ (t = 3.6), Bonferroni-adjusted p = 0.002. It survives a one-month lag (t = 3.7) and both crisis exclusions; detrending is its weakest cut (t = 2). The variance risk premium — the canonical benchmark — does not place (t = 0.9).
• 04Two honest deaths. The Michigan “vibecession” gap shrinks from −4.16σ to −1.03σ once the survey's 2024 phone-to-web redesign is dummied out (shift = −27 points, t = -5.6). And the fear-tercile factor spreads mostly collapse under a beta hedge — cyclicals−defensives goes from +2.1% to 0.3% — so what fear buys in the cross-section is largely market beta itself.

01One word, five instruments

Table 1 is the current state of the five gauges, each standardized against its own history (expanding-window z) with a percentile since 2000. Read the extremes first. The Baa−Aaa credit spread, at 0.48pp, is at its tightest reading since 2000 — the 0th percentile; the credit market is pricing essentially no default-risk premium. The VIX sits at 17.9, its 51st percentile. Policy uncertainty is at its 91st percentile. And the Michigan survey is at 44.8 — a level associated in every prior instance with deep recession, printed against a 4-handle unemployment rate (§09 examines how much of that is the survey itself). The five signed z-scores net to a composite of -0.1 — the 41st percentile, i.e. neutral. That netting is the first result: when the instruments disagree this much, a single “sentiment” number is an average of contradictions, and anyone quoting one is choosing which contradiction to ignore.

Table 1. Sentiment dashboard as of 2026-06 (Michigan: 2026-05, publication lag). z is standardized on the expanding window; percentile vs 2000–2026. Sign convention: higher z = more fear, so the survey enters inverted; red = fear above its history. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

Why these five: they span the three ways “sentiment” is actually measured. The VIX is the option market's price of 30-day variance; Baa−Aaa is the bond market's price of quality (the series Moody's has published since 1919 — used here instead of the high-yield OAS because ICE licensing caps that series at a trailing three-year window, useless for a real-time z); the NFCI risk subindex aggregates ~50 financial-stress series; the Baker-Bloom-Davis EPU index counts newspaper coverage of policy uncertainty; Michigan asks roughly 600 households how they feel. One caveat belongs up front rather than in the appendix: the instruments are correlated — Baa−Aaa and the NFCI risk subindex at 0.79, VIX and NFCI at 0.69 (the subindex actually contains the VIX among its inputs) — so an equal-weight composite implicitly overweights the market-priced family. The full correlation matrix is in the appendix, and §06 re-runs the headline numbers on a market-only composite and a principal-component weighting.

02Construction: a fear composite and a disagreement index

Each proxy is standardized on an expanding window and signed so that higher always means more fear; the composite is the equal-weight mean, requiring at least four of five to be available. Alongside it I track the cross-sectional dispersion of the five z-scores — the “instruments disagree” observation from Table 1 turned into a monthly variable:

The z at month $t$ uses only data through $t$, so every sort and regression below is one an investor could have run in real time — with the honest qualifier that “real time” refers to the standardization, not to data vintages (revisions and publication lags are handled as explicit robustness checks in §06 rather than assumed away). Daily series are averaged within the month rather than sampled at month-end, which damps the noise in a series whose whole personality is spikes. Figure 1 plots the composite against the SPY drawdown; the spikes land where they should — 2001–02, 2008–09, the 2011 and 2015 growth scares, March 2020, 2022 — the eyeball check that the construction measures what it claims to.

03The level tells you almost nothing about the mean

Start where a contrarian wants the answer to be: does high fear predict high forward returns? Table 2 reports the correlation of each proxy (signed, fear-positive) with the forward 1-, 3- and 12-month SPY return, alongside the composite, the disagreement index, and — as the external benchmark — the Bollerslev-Tauchen-Zhou variance risk premium. The composite's 3-month correlation is 0.04. The honest correction makes it worse: forward 3-month returns sampled monthly overlap by two-thirds, so the 315 months carry roughly 105 independent observations, and the t-statistic is 0.4. The quintile sort (Fig. 2, Table 3) says the same thing in portfolio form: a Q5−Q1 spread of +1.3pp whose bootstrap interval, [-3.8, 6.4], contains zero with room to spare.

One detail in Table 3 deserves more attention than the means: the hit rate falls as fear rises — 73% of high-calm months are positive against 67% of high-fear months — while the mean rises. More losing months, bigger winning ones. That is not a mean effect at all; it is a variance effect wearing a mean's clothes, and §§04–05 make it explicit.

Table 2. Correlation of each fear-signed variable with forward SPY returns, 2000–2026 (n = 315 months). Effective n ≈ n/h corrects the overlap in h-month returns sampled monthly; t (eff.) is the corresponding t-statistic. VRP = VIX² − trailing 21-day realized variance. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

Table 3. Forward 3-month SPY return by fear quintile with circular block-bootstrap 95% intervals (block = 6 months, 3,000 resamples). Q5−Q1 = +1.3pp, CI [-3.8, 6.4]. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

04What fear prices: the shape — and the vol-clustering test

If fear changes the distribution of forward returns without changing its center, the right tool is quantile regression — the effect of the composite not on the conditional mean but on each conditional quantile:

Figure 3 is the article's central result. The OLS (mean) coefficient is 0.3pp per 1σ of fear with a t of 0.2 — nothing, as §03 promised. But the quantile coefficients fan out: at the 90th percentile a 1σ rise in fear adds +4.03pp (block-bootstrap CI [2.3, 4.93]), at the 75th +2.9pp (CI [1.44, 3.93]), while the median (1.38pp) and the lower quantiles (-2.18pp at the 10th) are statistically indistinguishable from zero. A rise in fear does not shift the forward-return distribution; it stretches it, materially in the right tail. Buying fear buys a bigger rebound if the rebound comes, and no reliable protection if it doesn't.

The obvious objection: volatility clusters, and two of the five composite legs are volatility measures, so “fear widens the quantiles” could be trailing vol wearing a costume. Table 4 runs the test — the same quantile regressions with trailing 63-day realized volatility as a control. The fan survives: the 90th-percentile coefficient is +4.67pp per σ of fear (CI [2.18, 6.16]) and the 75th is +3.18pp (CI [1.08, 5.24]), both holding trailing vol fixed. Whatever the composite carries about the width of the forward distribution, it is not simply a restatement of the vol the market already realized.

Table 4. Quantile-regression coefficients on fear, raw and controlling for trailing 63-trading-day realized volatility (standardized). Block-bootstrap CIs (1,200 / 800 resamples). Faint = CI includes zero. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

A model-free cross-check: a depth-two regression tree (exhaustive SSE search, minimum leaf 24 months) puts its root split at F = 0.61 — almost exactly the Q4/Q5 boundary — with 3.9% above versus 1.7% below. Inside the high-fear branch the moderately elevated band pays 5.9% (n = 30) while deep panic beyond 0.89σ pays 2.9% (n = 58) — both tails arriving together, as the quantile coefficients say. These are in-sample splits, read as description; §08 is the corrective.

05Fear predicts variance — literally

“Fear buys variance” should not rest on return quantiles alone. Table 5 tests it directly: forward 3-month realized volatility (from daily SPY returns), its downside and upside halves, regressed on the composite — raw, then controlling for trailing realized vol, plus the disagreement index. The headline: a 1σ rise in fear predicts +5.25 points of forward annualized volatility (t = 4.7). Some of that is vol clustering — the control cuts it to +3.74 (t = 1.7) — but the effect persists — and it leans the right way: the upside semivolatility loading (+2.92, t = 2) survives the control at least as well as the downside (+2.36, t = 1.4). Fear predicts a wider realized distribution with, if anything, the wider half on top — the realized-vol counterpart of the quantile fan.

The disagreement index earns its keep here too: it predicts forward realized vol (+4.31 to +4.79 points per σ across the semivols, t up to 2.9) but not returns (t = 1.1). Disagreement and the fear level are correlated (0.61), so I read them as two views of the same state rather than independent signals — but the pattern is consistent: when the instruments disagree, it is the width of what comes next that moves, not the direction.

Table 5. HAC regressions (lag 6), 2000–2026. Vol measures annualized % from daily SPY returns over the next 63 trading days; semivols from the signed halves. “RV ctrl” = fear coefficient holding trailing 63-day realized vol fixed. Disagreement = cross-sectional σ of the five z's (corr with fear: 0.61). Source: Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs), Federal Reserve Economic Data (FRED), St. Louis Fed; author's calculations.

06Does the timing convention matter?

A fair objection to any month-$t$ composite: could the investor actually have had every input at month-end? Michigan prints with a lag, EPU is compiled from the month's papers, CPI arrives mid-following-month. Table 6 re-runs the two headline numbers — the Q5−Q1 mean spread (the null) and the 90th-percentile quantile coefficient (the positive result) — under conservative conventions: every input lagged a full month; a market-priced-only composite (VIX, Baa−Aaa, NFCI risk — observable daily); market current with survey/news lagged; and a first-principal-component weighting. The null is robust: the spread ranges from -0.7 to +1.8pp and never approaches significance. And the tail coefficient is just as robust the other way: β(τ=0.90) stays between +3.2 and +4.03 across every variant. Neither result is an artifact of assuming same-month data.

Table 6. Headline statistics under alternative signal-timing and weighting conventions. β τ=0.90 is the point estimate (no bootstrap per variant). The PCA row uses full-sample weights (VIX 0.5, CREDIT 0.47, NFCIRISK 0.5, EPU 0.35, UMCSENT 0.39) and is a look-ahead robustness row only, exactly as in the macro-regime piece. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

07Horse race: six candidates, one survivor

Which instrument carries what little mean information exists? Table 7 runs each candidate alone and all six jointly against the forward 3-month return — the five proxies plus the Bollerslev-Tauchen-Zhou variance risk premium (VIX² − realized variance), the canonical sentiment-adjacent mean predictor at this horizon and therefore the benchmark to beat. Five of the six die: the VIX at β ≈ 0, the survey at t = 0.3, credit and financial conditions with the wrong sign, and the VRP itself at t = 0.9 — weaker in this sample than its literature reputation. The exception is the Baker-Bloom-Davis policy-uncertainty index: +1.26pp per σ alone (t = 3.6) and +1.54pp jointly (t = 3.6), the only coefficient that strengthens with controls. One aside for the econometrically suspicious: the joint R² of 13.8% against univariate R²s near zero is a suppressor effect — the correlated market-priced legs (appendix Table 12) hedge each other out and let the EPU component through — not an additivity error.

Table 7. Forward 3-month SPY return on fear-signed z-scores, 2000–2026 (n = 315); Newey-West HAC t (lag 6). Joint R² = 13.8%. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

A single survivor among six invites a multiple-testing discount, so Table 8 stress-tests it. The Bonferroni-adjusted p on the baseline is 0.002. Lagging EPU a month — so the signal uses only papers already printed — leaves it intact (t = 3.7). Excluding the GFC strengthens it; excluding COVID keeps it (t = 2.4). The weakest cut is the one that matters most: EPU has drifted secularly upward as coverage of policy expanded, an expanding-window z inherits that trend, and a detrended (rolling 10-year) z drops the t to 2 — still there, but marginal. The fair summary: an uncertainty premium consistent with the literature, robust to lags and crises, and partly — not wholly — a trend. I flag the follow-up test now, so it is pre-registered rather than fished for: the next piece should test EPU on rate-sensitive sector spreads, where a policy-uncertainty premium has a mechanism.

Table 8. The policy-uncertainty coefficient under stress. p from the HAC t (two-sided normal); Bonferroni ×6 for the six-way search. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

08Out of sample, nothing survives

Re-estimate everything on an expanding window and forecast truly out of sample, scoring against the expanding historical mean (Campbell-Thompson R²_OOS); training data at each month excludes any observation whose forward window hasn't closed. Over 2010-01 → 2026-03 (n = 195): the linear signal scores -1.5%, the +1σ tail rule -0.6% — both negative; the historical mean was the better forecast. Against an in-sample R² of 0.1%, there was little to lose. This is the closing argument on sentiment-based index timing, and it is why §04's tree thresholds stay descriptive. The result is not that sentiment contains nothing; it is that what it contains — the variance information of §05 — cannot be monetized by shifting the mean exposure of an index position.

Table 9. Campbell-Thompson out-of-sample R² vs the expanding historical mean, 2010-01 → 2026-03 (n = 195 monthly forecasts). Negative = the historical mean forecast was better. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

09The vibecession, re-measured

The loudest sentiment story of recent years is the divergence between what households report and what the economy prints. To measure it, regress the Michigan index on the things that are supposed to drive it — unemployment, CPI inflation, gas-price inflation, the trailing 12-month market return — re-estimated on an expanding window so the fitted value at $t$ is a real-time nowcast. The model explains 51% of the variance, with sensible coefficients (Table 10): a point of unemployment costs −4.8 index points, a point of CPI inflation −9. One folk belief does not survive controls: conditional on headline CPI, gas prices carry a small positive coefficient — pump prices matter through inflation, not on top of it.

Taken at face value, the residual is enormous: the survey prints 44.8 against a model-implied 92.1 — a gap of −47.3 points, −4.16σ against its own history. But face value is wrong, and this section exists to say so. The University of Michigan completed a phone-to-web transition in mid-2024, and survey methodologists associate the redesign with a level shift down. Adding a web-era dummy to the model attributes −27 points of the current shortfall to the instrument itself (t = -5.6); the residual gloom that survives is −17.2 points, or −1.03σ — unusual, not unprecedented. Roughly two-thirds of the headline “vibecession” number is the survey, not the vibes. What remains is still a puzzle worth watching — candidate explanations include inflation scarring (levels versus rates: the CPI enters as YoY, but households may anchor on three-year-ago price levels) and partisan response polarization — but the honest headline is the smaller number.

Does unexplained gloom mean anything for returns? Table 10 (right) sorts forward 3-month returns by the gap's real-time z. No contrast is significant: the gap's regression on the forward 12-month return has a t of 1, and — the sharper null — it does not predict the survey's own 12-month change either (t = 0.9). Unexplained gloom neither reverts on schedule nor drags equities with it. This extends the hard/soft result in the macro-regime piece with a stronger design — model residual rather than z-difference — and lands on a cleaner conclusion: the vibecession, whatever its true size, is a fact about the mood, not a signal about the market.

Table 10. Left: full-sample coefficient snapshot (2000–2026, HAC lag 12) including the web-redesign dummy; the gap series itself uses expanding-window re-estimation, and the redesign-adjusted gap z is measured against the baseline gap's history. Right: forward 3-month SPY return by gap-z quintile. Source: Federal Reserve Economic Data (FRED), St. Louis Fed, Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs); author's calculations.

10The cross-section: mostly beta, honestly

The first version of this piece called the cross-section “where fear pays.” Applying the same inferential standard used on the nulls, the claim mostly does not survive — and since it was the paper's most tradeable sentence, the correction matters more than the original. Table 11 conditions five long-short spreads on fear terciles, now with block-bootstrap CIs and, in the second panel, a beta hedge: each spread residualized on the market's forward return, because “cyclicals over defensives into a fear rebound” is close to a leveraged bet on the rebound itself. Raw, two spreads clear their intervals in the fear tercile — small−large at +1.6% [0.4, 3] and Nasdaq−S&P at +1.9% [0.5, 3.2] — while cyclicals−defensives, the most intuitive one, does not ([-0.3, 4.2]). Beta-hedged, nearly everything collapses: cyclicals−defensives to 0.3%, Nasdaq−S&P to +0.7%, both with intervals straddling zero. The lone residual candidate is small−large at +1.1% [-0.1, 2.4] — marginal. This sits adjacent to the Baker-Wurgler result that speculative, hard-to-value stocks earn low returns after high sentiment; what shows up here is the flip side — the high-beta end recovers hardest after fear — and the beta hedge says most of that is the recovery itself, not a separate sentiment premium.

Table 11. Forward 3-month relative return by fear tercile (cuts at F = -0.25 / 0.51, in-sample), 2000–2026, with circular block-bootstrap 95% CIs (2,000 resamples). β-adj = spread residualized on the market's forward 3m return (full-sample β shown). Cyclicals = XLY/XLF/XLI/XLB/XLE, defensives = XLP/XLU/XLV. Source: Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs), Federal Reserve Economic Data (FRED), St. Louis Fed; author's calculations.

11The overlay that shouldn't work, and doesn't

Close the loop by trying to monetize the level anyway — a deliberately simple, fully real-time overlay: the composite's state at month-end sets next month's SPY weight — 100% in the fear state, 70% neutral, 40% in the calm state, remainder in IEF. The first version used ±1σ cuts, which — on a right-skewed composite — fired the calm leg exactly 1 month in 281: a half-run experiment. The redesign here uses expanding-percentile states (≥80th percentile of the composite's own history → fear, ≤20th → calm), which is symmetric by construction; the σ-rule is kept as a robustness row. The verdict does not change (Fig. 5, Table 12): Sharpe 0.69 versus 0.77 for a static 70/30, a Sharpe difference of -0.08whose bootstrap interval is [-0.18, 0.03] — 92% of resamples have the overlay behind its benchmark. The mechanism is §04 exactly: the fear state's extra exposure captured the 2009 and 2020 rebounds and the full continuation of 2008. An index overweight cannot keep the right tail and shed the left one.

Table 12. Monthly, 2003-01 → 2026-06; risk-free ≈ 1.7% (avg 3m T-bill). Percentile design states: fear 86 / neutral 188 / calm 7 months; turnover 3.4%/mo. Sharpe difference vs 70/30: -0.08, block-bootstrap 95% CI [-0.18, 0.03]. Source: Yahoo Finance (SPY, ^GSPC, ^VIX, factor/sector ETFs), Federal Reserve Economic Data (FRED), St. Louis Fed; author's calculations.

12Conclusion

Sentiment is not one number, and right now the pretense costs more than usual: credit at its tightest since 2000, the survey at a record low, uncertainty at the 91st percentile — a composite that nets to a meaningless neutral. Measured with the discipline the question deserves, the level of fear carries no mean forward-return information under any timing convention tested, and none of it survives out of sample. What fear robustly prices is the width of what comes next — +5.25 points of forward realized volatility per σ, a +4.67pp effect on the 90th return percentile that survives the vol-clustering control — and width is not tradeable by re-weighting an index, as the overlay demonstrated at its own expense. The revision pass cut the paper's two most quotable numbers down to their honest size: the vibecession is −1.03σ once the survey redesign is dummied out, not −4.16σ; and the fear-tercile factor rotation is mostly market beta once hedged. What stands after the stress tests is narrower and more useful: fear is a state variable for dispersion and rebound convexity, not a directional signal — and the one mean effect left standing, the policy-uncertainty premium, has a pre-registered follow-up waiting in the rate-sensitive corners of the index.

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