Do Higher Factor Loadings Mean Higher Expected Returns?

Run a small-cap value fund through a Fama-French regression and you get precise-looking numbers: a value loading of 0.55, a size loading of 0.89, t-statistics above 10. Multiply those loadings by the historical factor premiums and you get an expected return. Summitward’s dividend growth vs. small-cap value guide did exactly that and found AVUV’s loadings implied about 4.9 percentage points a year more than VTI’s at the full 1963–2026 premiums.

The two inputs to that multiplication are known with very different precision. Seven years of monthly returns pin AVUV’s value loading to within about 0.1. Sixty-three years of factor data leave the value premium anywhere from 0.4% to 6.7% a year at 95% confidence. Carry both errors through and AVUV’s implied edge over VTI runs from 1.5% to 8.1% a year, and that range still assumes the past six decades were one stable regime.¹

The short version

A higher loading means a higher expected return only if the factor carries a positive premium. The regression measures the loading; it says nothing about the premium.
Loadings converge fast. Premiums converge slowly: pinning the value premium to ±1 point at 95% confidence would take about 400 years of i.i.d. monthly data.
For three small-value funds, the uncertainty in the premiums contributed roughly four to seven times as much standard error to the implied edge over VTI as the uncertainty in the loadings.
Use loadings to compare funds and check what you own. Treat the return they imply as a scenario, and never add it to a retirement plan’s base case.

A loading measures sensitivity

The Fama-French five-factor model regresses a fund’s monthly return in excess of Treasury bills on five factor returns: the market ( $MKT$ ), size ( $SMB$ , small minus big), value ( $HML$ , high minus low book-to-market), profitability ( $RMW$ , robust minus weak) and investment ( $CMA$ , conservative minus aggressive).²³

R_{p,t}-R_{f,t}=\alpha_p+\beta_M\,MKT_t+\beta_S\,SMB_t+\beta_H\,HML_t+\beta_R\,RMW_t+\beta_C\,CMA_t+\varepsilon_{p,t}

Each $\beta$ is a loading. A value loading of $\beta_H = 0.55$ means that, holding the other four factors fixed, the fund’s return moved 0.55 points for every 1-point move in HML over the sample. The intercept $\alpha_p$ is the average return the five factors leave unexplained, and $\varepsilon_{p,t}$ is the month-to-month residual.

A loading is a sensitivity to a long-short research portfolio, so it does not translate into a percentage of your money. A portfolio’s loading is the weighted average of its funds’ loadings, with weights $w_i$ :

\boldsymbol\beta_{\text{port}}=\sum_i w_i\,\boldsymbol\beta_i

A 30% sleeve of AVUV adds $0.30\times0.545\approx0.16$ to the portfolio’s value loading. Owning three differently named small-value funds averages three similar loadings. The Fama-French factor analysis guide covers how to read t-statistics, alpha and R².

Expected return needs a premium

Write $\lambda_j = E[F_j]$ for the expected return of factor $j$ , its premium. Take expectations of the regression and the residual drops out:

E[R_p]-R_f=\alpha_p+\boldsymbol\beta_p^{\top}\boldsymbol\lambda

If the model prices the fund correctly, expected alpha is zero and the expected excess return is the loadings times the premiums, $E[R_p]-R_f\approx\boldsymbol\beta_p^{\top}\boldsymbol\lambda$ . For two funds $A$ and $B$ under the same model, the expected gap depends only on the difference in loadings:

E[R_A-R_B]=(\boldsymbol\beta_A-\boldsymbol\beta_B)^{\top}\boldsymbol\lambda

If the funds differ only in their value loading, this reduces to

\Delta E[R]=\Delta\beta_{H}\,\lambda_{H}.

The answer to the title question sits in that product. A larger value loading raises expected return if and only if $\lambda_H > 0$ . If the value premium is zero from here, an extra 0.5 of value loading buys nothing but tracking error. A regression estimates $\Delta\beta$ from the fund’s own history; $\lambda$ has to come from somewhere else, usually the long-run average of the factor itself.

How precisely each piece is known

Loadings: tight after a few years

The ordinary least squares standard error of a loading depends on how much residual noise is left and how much the factors moved:

\mathrm{SE}(\hat\beta_j)=\sqrt{\hat\sigma_\varepsilon^2\,\big[(X^{\top}X)^{-1}\big]_{jj}}

Here $\hat\sigma_\varepsilon^2$ is the residual variance and $X$ the matrix of factor returns. For VTI and the three small-value funds below, the five factors explained 97% to 99.9% of monthly variance, so $\hat\sigma_\varepsilon$ is small and the loadings settle quickly. Over the 83 months from October 2019 to August 2026, AVUV’s value loading came out at 0.55 with a Newey-West standard error of 0.05.⁴ Its 95% interval of roughly 0.45 to 0.64 is ±18% of the estimate.

Premiums: wide after six decades

A premium estimate is the average of a noisy factor return. With $T$ monthly observations and monthly standard deviation $\sigma_{\text{mo}}$ , the standard error of the annualized mean is approximately

\mathrm{SE}(\hat\lambda_{\text{ann}})\approx\frac{12\,\sigma_{\text{mo}}}{\sqrt{T}}.

For HML from July 1963 to August 2026, $\sigma_{\text{mo}} = 2.97\%$ and $T = 758$ :

\mathrm{SE}\approx\frac{12\times2.97\%}{\sqrt{758}}\approx1.29\%\text{ a year.}

Factor returns are mildly autocorrelated, so the table below uses Newey-West standard errors, which widen HML’s to 1.60%. A 95% interval is $\hat\lambda\pm1.96\,\mathrm{SE}$ . The same arithmetic run backwards gives the number of years an estimate needs to reach a margin of $\pm h$ , with annual volatility $\sigma_{\text{ann}}$ :

T_{\text{years}}\approx\left(\frac{1.96\,\sigma_{\text{ann}}}{h}\right)^{2}

HML’s annual volatility is 10.3%, so a ±1-point interval takes $(1.96\times10.3/1)^2\approx407$ years. The U.S. five-factor data start in July 1963.⁵

Factor	Mean, %/yr	NW std. error	95% interval	10-yr windows below 0	Years for ±1 pt
Market (Mkt-RF)	7.22	2.00	3.3 to 11.1	13%	916
Size (SMB)	2.24	1.46	−0.6 to 5.1	33%	420
Value (HML)	3.53	1.60	0.4 to 6.7	22%	407
Profitability (RMW)	3.02	1.16	0.8 to 5.3	10%	241
Investment (CMA)	2.92	1.08	0.8 to 5.0	10%	198

Summitward calculation from Ken French’s monthly five-factor data, July 1963 to August 2026 (758 months). Newey-West standard errors with 12 lags. Rolling windows overlap, so the share below zero describes history and does not count independent trials. “Years for ±1 pt” assumes i.i.d. returns.

Of the four style premiums, only size has an interval that includes zero, from −0.6% to 5.1%. Every interval is wider than its own point estimate. The value premium’s lower bound is 0.4%, about one-ninth of its point estimate.

What the uncertainty does to a fund’s implied edge

To get the error in an implied edge, regress the fund’s return minus VTI’s on the five factors. That gives the loading gap $\Delta\boldsymbol\beta$ and its covariance $\Sigma_{\Delta\beta}$ directly. The premium estimates are correlated with each other (HML and CMA at 0.71 over 1963–2026), so the errors cannot be added factor by factor. The standard error from the premiums is

\mathrm{SE}_{\lambda}\big(\Delta\boldsymbol\beta^{\top}\hat{\boldsymbol\lambda}\big)=\sqrt{\Delta\boldsymbol\beta^{\top}\,\widehat\Sigma_{\lambda}\,\Delta\boldsymbol\beta},\qquad \widehat\Sigma_{\lambda}=\frac{\widehat S_{NW}}{T},

where $\widehat S_{NW}$ is the Newey-West long-run covariance of the monthly factor returns, annualized. The loading error adds $\boldsymbol\lambda^{\top}\Sigma_{\Delta\beta}\,\boldsymbol\lambda$ to the variance. For the three small-value funds over their common window:

Fund	Size gap	Value gap	Profitability gap	Implied edge, %/yr	95% band
VBR	0.61 ±0.04	0.36 ±0.04	0.11 ±0.04	2.85	0.6 to 5.1
DFSVX	0.82 ±0.05	0.47 ±0.04	0.21 ±0.04	4.08	1.1 to 7.1
AVUV	0.90 ±0.06	0.52 ±0.05	0.21 ±0.07	4.81	1.5 to 8.1

Summitward calculation. Loading gaps are fund minus VTI, October 2019 to August 2026 (83 months), ± one Newey-West (6 lag) standard error. Implied edge uses the 1963–2026 premiums on all five factors; the band combines premium and loading error. Gross of fees and taxes.

For VBR the premium error contributes a standard error of 1.12 points against 0.19 from the loadings. For AVUV, with the shortest history, it is 1.63 against 0.44. Even with only seven years of fund data, the loading side is the smaller problem. The point estimates match the blender guide’s: AVUV’s 4.8 points here against its 4.9, computed over a slightly different window.

Two settings are worth trying. At the McLean-Pontiff setting (42% of the historical style premiums), AVUV’s implied edge falls to 2.3 points with a band of 0.8 to 3.8. At zero, the edge is 0.5 points, almost entirely from AVUV’s market beta of 1.06, a reminder that a higher market loading is also a bet on a premium.

The last 20 years gave a different answer

The table above uses every month since 1963. An investor estimating the value premium from the 20 years ending August 2026 would have found −1.2% a year, with a 95% interval from about −6.2% to +3.8%. The same exercise at the end of 2006 gave 5.1%, and at the end of 1989, 6.9%. Neither window was wrong about its own history. Both are samples of a quantity that moves far more than the loadings do.

Fama and French made the same point in “Volatility Lessons”: even if expected premiums equal their historical averages, volatility makes negative realized market, value and size premiums likely over three- and five-year periods, and less likely but not trivial over 10 and 20 years.⁶ In our data, 22% of rolling 10-year windows had a negative value premium and 12% of rolling 20-year windows did.

AVUV, 2019 to 2026: what the loadings implied and what happened

At the full 1963–2026 premiums, AVUV’s loadings implied an arithmetic edge over VTI of 4.8 points a year. From October 2019 to August 2026 the realized factor returns were far from those averages: the market returned 13.9% a year over bills, size returned −1.3%, value 1.7%, profitability 2.5% and investment 0.3%. AVUV’s loading gap times those realized factor returns comes to 1.1 points. Its actual arithmetic average beat VTI’s by 1.9 points; the remaining 0.8 points sit in the regression’s alpha.

Compounded, the 1.9 points nearly vanished. AVUV’s annualized return was 15.94% against VTI’s 15.85%. Compound growth $g$ sits below the arithmetic mean $\mu$ by about half the variance:

g\approx\mu-\tfrac{1}{2}\sigma^{2}

AVUV’s annualized volatility was 25.5% against VTI’s 17.1%, so its extra variance drag was $\tfrac{1}{2}(0.255^2-0.171^2)\approx1.8$ points. Subtract that from the 1.9-point arithmetic gap and about 0.1 point of compound edge remains, which is what happened. A premium estimated as an arithmetic mean overstates the compound growth of the higher-volatility portfolio that earns it.

VBR shows the other limit of the method. Over the same window it compounded 3.8 points a year behind VTI, and its loading gap times the realized factor returns explains almost none of that (−0.1 point). The five-factor regression still had an R² of 0.90 on the return difference, yet left a −2.5-point alpha. A high R² means the factors track the fund month to month; the average return can still sit in the alpha. Lewellen, Nagel and Shanken made the same warning about cross-sectional R² in asset-pricing tests.⁷ Our Beyond Fama-French guide found that VBR’s five-factor alpha over 2014–2025 mostly disappeared under the q5 model, so part of this gap is model choice.

The band understates the uncertainty

The 95% bands above treat 1963–2026 as one regime with a fixed premium. Several things the sampling error does not capture push the other way:

Publication. McLean and Pontiff found that 97 published return predictors earned 26% less out of sample and 58% less after publication.⁸ Ilmanen and coauthors, studying value, momentum, carry and defensive factors across six asset classes over about a century, found a 30% drop in estimated premiums out of sample and attributed it mostly to overfitting.⁹
Valuation spreads. Arnott, Harvey, Kalesnik and Linnainmaa found that HML’s 55% drawdown from 2007 to mid-2020 was more than explained by value stocks becoming cheaper relative to growth stocks.¹⁰ Realized premiums depend on how valuation spreads move, which a full-sample average folds into one number.
Research factors are not funds. HML and the other factors are long-short portfolios rebalanced without costs, and nobody holds them. A long-only fund captures part of the long side, after fees and trading costs.
Which story explains the premium. If value pays for bearing risk that hurts in bad times, the premium should persist. Under the stochastic discount factor $m$ , an asset’s expected excess return depends on its covariance with bad times: $E[R^e_i]=-\mathrm{Cov}(m,R^e_i)/E[m]$ . If value pays because investors extrapolate past growth, as Lakonishok, Shleifer and Vishny argued, competition can shrink it.¹¹ Daniel and Titman found that firm characteristics, rather than factor loadings, explained returns in their sample, which weakens the idea that the loading itself earns the premium.¹² The ABCs of factor investing covers these explanations in more detail.

Dimensional, which runs factor funds, reports that in almost half of rolling 10-year U.S. periods from July 1963 to December 2022, one of the market, size, value and profitability premiums was negative, and that there were no periods with three or four negative at once.¹³ Diversifying across premiums helps; it does not shrink the uncertainty in any single one.

What loadings are good for

The asymmetry in precision points to where loadings earn their place in a DIY investor’s process.

Comparing funds. Two funds labeled small-cap value can carry very different exposures. Over the common window, AVUV’s value loading was 0.55 and VBR’s 0.39; their size loadings were 0.89 and 0.60. Regressing AVUV’s return minus VBR’s on the factors puts the size gap at 4.7 standard errors and the value gap at 2.4. The VBR vs. AVUV guide covers what drives them.
Checking what you own. Weighted loadings show whether a portfolio of several funds adds up to the tilt you intended, or to a market fund with extra fees.
Sizing a tilt. Because $\Delta E[R]=\Delta\boldsymbol\beta^{\top}\boldsymbol\lambda$ is linear, the loading tells you how much of any assumed premium a sleeve would capture. A 20% AVUV sleeve captures about a fifth of AVUV’s implied edge, whatever premium you assume.
Testing a plan. Run the plan at a zero style premium and treat any premium as upside. The retirement simulator lets you change the expected return. A tilt that only works if you raise the base-case return by a point is a plan that depends on the least precise number in the chain, and the arithmetic premium would overstate compound growth anyway.

When a bigger loading is not worth paying for

Net of costs, the comparison between two funds is approximately

\Delta E[R_{\text{net}}]\approx\Delta\boldsymbol\beta^{\top}\boldsymbol\lambda-\Delta c_{\text{fee}}-\Delta c_{\text{tax}},

where $\Delta c_{\text{fee}}$ is the difference in expense ratios and $\Delta c_{\text{tax}}$ the difference in annual tax drag. If you start from a fund’s actual returns instead of research factors, its expense ratio is already in them, so do not subtract it twice. The Is Factor Investing Dead? guide has a calculator for this hurdle. Three situations make a larger loading a poor trade:

Switching in a taxable account. Selling an appreciated VTI position to buy AVUV realizes gains now in exchange for an edge whose 95% band at the McLean-Pontiff setting runs from 0.8 to 3.8 points a year, before AVUV’s higher fee. Directing new contributions to the higher-loading fund gets the exposure without the tax bill.
Tracking error you will not hold through. About one in five 10-year windows since 1963 had a negative value premium. An investor who sells after a lost decade turns a positive expected premium into a realized loss.
Near-term withdrawals. If you will spend the money within a few years, the premium has little time to show up, and the extra volatility of a deep small-value fund adds to sequence risk.

What I recommend

I use factor loadings to choose between funds and to check what my portfolio holds, and I treat the return they imply as a scenario. If you tilt, buy the fund with the most loading per dollar of fees and taxes, size the tilt so that a zero premium for 20 years would not change your plan, and fund it with new money in taxable accounts. A higher loading is a higher exposure to a premium whose size, even after 60 years of data, is known only to within several points.

How Summitward helps

The Portfolio page runs Fama-French regressions on your holdings and shows each fund’s loadings with t-statistics, so you can see the exposure your allocation carries before deciding what premium, if any, to assume for it.

Key Takeaways

Loading times premium. A higher loading raises expected return only when the factor’s premium is positive. The regression estimates only the loading.
Loadings are precise. AVUV’s value loading, October 2019 to August 2026, was 0.55 with a standard error of 0.05.
Premiums are not. Over July 1963 to August 2026 the value premium averaged 3.5% a year with a 95% interval of 0.4% to 6.7%; a ±1-point interval would need about 400 years of data.
The band is wide even before decay. At full 1963–2026 premiums, AVUV’s implied edge over VTI was 4.8 points with a 95% band of 1.5 to 8.1, assuming one stable regime.
Arithmetic premiums overstate compound growth. From October 2019 to August 2026, AVUV beat VTI by 1.9 points a year on average and by 0.1 point compounded.
Use loadings for decisions you can verify. Compare funds, check overlap and size tilts; run plans at a zero style premium.

Frequently Asked Questions

What is a factor loading?

A regression coefficient that measures how much a fund’s return moved with a factor’s return, holding the other factors fixed. A value loading of 0.5 means the fund rose about 0.5 points for each 1-point rise in the Fama-French value factor over the sample.

Does a higher value loading mean higher returns?

A higher expected return, if the value premium is positive. The expected gap between two funds is their loading difference times the premium. Realized returns can differ for a decade or more: 22% of rolling 10-year windows since 1963 had a negative value premium.

How accurate are factor premium estimates?

Not very. Over July 1963 to August 2026, the 95% interval for the value premium ran from 0.4% to 6.7% a year and for the size premium from −0.6% to 5.1%. Shorter samples are wider, and the intervals ignore post-publication decay.

Is a loading of 0.5 the same as 50% in value stocks?

No. A loading is a sensitivity to a long-short research portfolio. A portfolio’s loading is the weighted average of its funds’ loadings, so a 30% sleeve of a fund with a 0.55 value loading adds about 0.16 to the portfolio.

Should I add a factor premium to my retirement projections?

Run the base case without one and treat the premium as a sensitivity case. The premium is the least precise input in the calculation, it is an arithmetic mean that overstates compound growth for a more volatile portfolio, and a premium shortfall arriving early in retirement is the case that hurts.

Why did AVUV only match VTI from 2019 to 2026?

The factor returns in that window were far below their long-run averages, with the size premium negative. AVUV’s arithmetic average beat VTI’s by 1.9 points a year, but its higher volatility cut the compound gap to 0.1 point.

Related Guides

Dividend Growth vs. Small-Cap Value Loadings times premiums, with the Factor Exposure Blender.
Fama-French Factor Analysis How to read loadings, t-statistics and alpha.
Is Factor Investing Dead? Replication, decay and costs, with a tilt hurdle calculator.
Beyond Fama-French Why a fund’s alpha depends on the model.
The R² Trap Why a high R² can coexist with weak evidence.
VBR vs. AVUV Fees, screens and the tax cost of switching.

Sources

Summitward calculations: factor premiums, standard errors and rolling windows from Ken French monthly data, July 1963 to August 2026 (758 months); fund regressions October 2019 to August 2026 (83 months) and over each fund’s own history; numpy OLS with Newey-West standard errors (6 lags for loadings, 12 for premiums). Data: Ken French data library (August 2026 cut), Yahoo Finance adjusted closes. Script and output: summitward-research
Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics 33(1), 1993, 3–56. doi.org
Eugene F. Fama and Kenneth R. French, “A Five-Factor Asset Pricing Model,” Journal of Financial Economics 116(1), 2015, 1–22. doi.org
Whitney K. Newey and Kenneth D. West, “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica 55(3), 1987, 703–708. doi.org
Kenneth R. French, Data Library, and the description of the Fama/French five factors (2x3). Since the January 2025 release, U.S. returns are built from CRSP’s CIZ files, with dividends reinvested on ex-dates. tuck.dartmouth.edu
Eugene F. Fama and Kenneth R. French, “Volatility Lessons,” Financial Analysts Journal 74(3), 2018, 42–53. doi.org
Jonathan Lewellen, Stefan Nagel and Jay Shanken, “A Skeptical Appraisal of Asset Pricing Tests,” Journal of Financial Economics 96(2), 2010, 175–194. doi.org
R. David McLean and Jeffrey Pontiff, “Does Academic Research Destroy Stock Return Predictability?” Journal of Finance 71(1), 2016, 5–32. doi.org
Antti Ilmanen, Ronen Israel, Rachel Lee, Tobias J. Moskowitz and Ashwin Thapar, “How Do Factor Premia Vary Over Time? A Century of Evidence,” Journal of Investment Management 19(4), 2021. aqr.com
Robert D. Arnott, Campbell R. Harvey, Vitali Kalesnik and Juhani T. Linnainmaa, “Reports of Value’s Death May Be Greatly Exaggerated,” Financial Analysts Journal 77(1), 2021, 44–67. doi.org
Josef Lakonishok, Andrei Shleifer and Robert W. Vishny, “Contrarian Investment, Extrapolation, and Risk,” Journal of Finance 49(5), 1994, 1541–1578. doi.org
Kent Daniel and Sheridan Titman, “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns,” Journal of Finance 52(1), 1997, 1–33. doi.org
Dimensional Fund Advisors, “Perspective on Premiums,” September 2023. Dimensional manages factor funds. dimensional.com

Author disclosure

Summitward has no business relationship with Avantis, Dimensional, Vanguard or any firm mentioned here and receives no compensation from them. Figures labeled as Summitward calculations are historical measurements over the stated window, not forecasts. Nothing here is investment advice.