Investor Factors: Betermier, Calvet, Knupfer & Kvaerner (2025)

What this is. The paper’s core results, datasets, and theory: enough to know what it found without reading all 42 pages. For replication or extension, read the full source at the original (paywall).

TL;DR

Using complete administrative stockholdings of Norwegian individual investors (308,000 investors/month, Feb 1997 to Dec 2017, 535 OSE stocks), the paper derives theoretical conditions under which investor portfolio holdings reveal pricing factors for the cross section of equity returns. It then constructs Investor Pricing Factors (IPFs) by sorting investors into 90 groups by age, wealth, and other characteristics. A two-factor model consisting of the market (MKT) and a combined age-wealth portfolio (AW) prices both Norwegian equities and established firm-based factors, while IPFs outperform firm-factor models out-of-sample. Portfolio tilts toward the age-wealth factor are positively linked to financial sophistication and negatively linked to debt and macroeconomic income risk, consistent with joint hedging and sentiment channels.

Core results

Magnitudes and significance are as reported; **/*** = 5%/1%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Two PCs explain 80% of cross-sectional variation in group portfolio holdings; PC1 tracks the market (R2 = 0.62), PC2 tracks the combined age-wealth portfolio (R2 = 0.55)	Table I, p. 2807	PC1 alone: 72% of variance; PC1+PC2: 80%; market R2=0.62 on PC1, AW R2=0.55 on PC2
R2	The combined age-wealth factor (AW) earns a significant CAPM alpha of 32 bps/month (3.8%/yr) after controlling for the market	Table II col. (2), p. 2810	alpha = 0.32%, t = 3.16; CAPM beta on AW = -0.12, t = -6.96
R3	AW spans firm factors: its alpha remains 24 bps/month (sig. 5%) even after controlling for all five FF factors (size, value, momentum, profitability, investment)	Table III col. (5), p. 2813	alpha = 0.24, t = 2.55; adj. R2 rises from 0.16 to 0.29 but AW alpha never insignificant
R4	IPF* prices established firm factors: adding AW to the market renders momentum, profitability, and investment alphas statistically insignificant and reduces them by ~40%	Table IV, p. 2814	MOM alpha: 0.77% (CAPM) vs. 0.43% (IPF*); RMW: 0.73% vs. 0.46%; CMA: 0.52% vs. 0.32%; all three IPF* alphas statistically insignificant (MOM t=1.04, RMW t=1.42, CMA t=0.99)
R5	Out-of-sample Sharpe ratio of IPF* (0.45) exceeds all firm-factor models (0.19-0.40 range) and is 45% above the market (0.31)	Table V, p. 2817	IPF* OOS SR = 0.45; 3-factor age+wealth model = 0.51; best firm model (FIRM-6) = 0.40; market = 0.31; OS/IS ratio for IPF* = 0.67 vs. 0.43 for all-firm model
R6	Factor tilts increase monotonically with age and wealth: tilt rises from -0.3 (investors under 30) to +0.1 (70-75), equivalent to ~1.2%/yr average return difference	Figure 2 + p. 2821	Tilt range [-0.3, +0.1] over life cycle; 0.4 x 3% = 1.2%/yr gap; holds for new entrants mimicking experienced investors within cohort
R7	Debt and income beta reduce tilts (hedging channel) while finance occupation, stock market experience, and female gender raise tilts (sophistication/sentiment channel)	Table VII, p. 2823	Income beta coef = -0.051 (t = -6.40); debt = -0.047 (t = -5.55); finance occup. = 0.627 (t = 34.60); stock mkt. experience = 0.026 (t = 7.58); male dummy = -0.156 (t = -15.00)
R8	Stocks in the long leg of AW have higher market cap, book-to-market, and profitability than short-leg stocks; short-leg stocks have higher CAPM beta (1.02 vs. 0.73), volatility (0.18 vs. 0.08), and turnover	Table VIII, p. 2825	Long-leg median mkt cap 973M NOK vs. 483M NOK; BtM 0.90 vs. 0.66; profitability 0.06 vs. 0.05; CAPM beta 0.73 vs. 1.02; volatility 0.08 vs. 0.18

Overall (paper’s conclusion). Individual investor portfolios contain recoverable pricing information. The market and the combined age-wealth portfolio (long mature/wealthy, short young/less-wealthy investors) form a parsimonious two-factor model that prices the Norwegian cross section, absorbs firm factors, and outperforms firm-factor models out-of-sample. Hedging and sentiment jointly drive investor tilts toward the pricing factor.

Datasets used

Dataset	Role in paper	Wiki page
Titlon (Oslo Stock Exchange database)	Stock prices, returns, shares outstanding for 535 OSE stocks, 1997-2017	Titlon (OSE) (licensed)
VPS (Norwegian Central Securities Depository)	Complete individual investor stockholdings at monthly frequency, 300,000+ investors	no page yet
Statistics Norway (Statistisk sentralbyra)	Investor demographics, balance sheets, income, wealth from tax records; annual 1997-2017	no page yet
OSE market index (Norwegian market portfolio)	Benchmark factor; market-cap-weighted portfolio of OSE stocks	no page yet

Sample: 308,000 individual investors per month on average; 535 unique stocks; 251 months (Feb 1997 to Dec 2017).

Theory / model

The paper’s central theoretical object is the tangency portfolio, which prices the cross section of excess stock returns. For J stocks with excess return vector $R^e$, expected return vector $\mu$, and variance-covariance matrix $\Sigma$, the tangency portfolio has weights (eq. 1, p. 2795):

$$\tau = \frac{1}{\phi} \Sigma^{-1} (\mu - R_f \mathbf{1}), \qquad \phi = \mathbf{1}' \Sigma^{-1} (\mu - R_f \mathbf{1}) > 0$$

Every stock’s risk premium satisfies $\mu_j - R_f = \phi \, (\Sigma \tau)_j = b_{j,\tau} (\mu_\tau - R_f)$, so pricing the tangency portfolio is equivalent to pricing all stocks (eq. 2, p. 2795).

Spanning condition. The key insight is that the researcher can recover the tangency portfolio from investor portfolio holdings when Assumption 1 holds (p. 2796): there exist N long-short investor portfolios $\pi^1, \ldots, \pi^N$ extracted from the sample such that

$$\tau \in \operatorname{Span}[ m, \pi^1, \ldots, \pi^N ],$$

where $m$ is the market portfolio and $\operatorname{Span}[\cdot]$ denotes the set of all linear combinations. When this holds, the tangency portfolio is a linear combination (eq. 4, p. 2796):

$$\tau = m + \sum_{n=1}^{N} \eta_n \, \pi^n,$$

and every stock’s risk premium satisfies a multifactor pricing equation (Proposition 1, eq. 6, p. 2797):

$$\mu_j - R_f = \beta_{j,M} (\mu_M - R_f) + \sum_{n=1}^{N} \beta_{j,n} \, E(p_n),$$

where $p_n = (\pi^n)' R^e$ is the return on the n-th IPF and $(\beta_{j,M}, \beta_{j,1}, \ldots, \beta_{j,N})'$ is the vector of OLS regression coefficients of stock j’s return on the (N+1) factors.

Proposition 1 also implies that a stock’s CAPM alpha satisfies (eq. 7, p. 2798):

$$a_{j,M} = \phi \sum_{n=1}^{K} \eta_n (b_{j,n} - b_{j,M} \, b_{M,n}) \sigma_n^2,$$

where $b_{j,n} = \operatorname{cov}(R^e_j, p_n) / \sigma_n^2$ and $b_{M,n} = \operatorname{cov}(\text{MKT}, p_n) / \sigma_n^2$. Stocks in low demand (positive net exposure $b_{j,n} - b_{j,M} \, b_{M,n}$ with $\eta_n > 0$) are underpriced relative to CAPM and tend to have low market betas.

Theoretical foundations for age and wealth as IPF characteristics. The paper derives the spanning condition under two complementary models (Section I.D, pp. 2802-2804):

1. ICAPM (Merton 1973, Breeden 1979) with heterogeneous investors: each investor i has CRRA utility and holds a portfolio deviating from the tangency by hedging demands. Under a Taylor approximation, the portfolio factor structure is (eq. 17, p. 2803):

   $$\omega^i_t = \tau_t - (T - 1 - A^i_t) \, d^1_t - (L^i_t / W^i_t) \, d^2_t,$$

   where $A^i_t$ is investor age, $L^i_t / W^i_t$ is the income-to-wealth ratio, and $d^1_t, d^2_t$ are deviation portfolios. Mature and wealthy investors hold portfolios closer to $\tau$ and therefore earn higher CAPM alphas.

2. Sentiment model (Fedyk, Heyerdahl-Larsen, and Walden 2013): sentiment covaries with age and wealth, yielding a reduced-form factor structure (eq. 18, p. 2804):

   $$\omega^i_t = \tau_t - f_1(A^i_t) \, d^1_t - f_2(W^i_t) \, d^2_t.$$

   Both frameworks predict age and wealth as natural IPF sorting characteristics.

Method

The construction has two parts: grouping investors into a factor structure and extracting priced long-short portfolios. It builds on sdf-projection (the tangency-spanning condition) and portfolio-sort (investor sorting by socioeconomic characteristics).

Step 1: Factor structure of investor portfolios. The strong factor structure in individual investor portfolios documented by Balasubramaniam, Campbell, Ramadorai, and Ranish (2023) motivates the PCA grouping approach. $G = 90$ investor groups are formed annually by age (12 groups), wealth (12 groups), permanent real income (12 groups), gender (2), education (3), region (9), industry (17), and occupation (9). For group g with investor equity-wealth weights $w^g_i$, the group portfolio is (eq. 14, p. 2801):

$$\omega^g = \sum_{i \in I_g} w^g_i \, \omega^i, \qquad w^g_i = E^i \Big/ \sum_{i' \in I_g} E^{i'}.$$

PCA is applied to the $G \times G$ variance-covariance matrix of the $G = 90$ group portfolio holdings, $\Omega'_t \Omega_t / J_t$, to obtain principal components $PC_{k,t}$ (eq. 19-20, p. 2806). The first two PCs explain 80% of the cross-sectional variance in group holdings.

Step 2: Extracting IPFs as long-short portfolios. An IPF is a zero-investment long-short portfolio $\pi^n$ formed as a weighted average of group portfolios (eq. 15, p. 2802):

$$\pi^n = \sum_{g=1}^{G} z^g_n \, \omega^g, \qquad \sum_{g=1}^{G} z^g_n = 0.$$

The age portfolio $\pi_{\text{AGE},t}$ is long investors aged 70-75 and short investors aged 18-30 (equal weights -1/2 on groups 1 and 2). The wealth portfolio $\pi_{\text{WEALTH},t}$ is long the top 1% wealthiest investors and short the bottom 10%-30% of wealth (text, p. 2808). The combined age-wealth portfolio is:

$$\pi_{\text{AW},t} = \tfrac{1}{2} \left( \pi_{\text{AGE},t} + \pi_{\text{WEALTH},t} \right).$$

Returns on the IPFs are computed as $AW_t = (\pi_{\text{AW},t-1})' R^e_t$ (net of the 1-month Norwegian Interbank Offered Rate, NIBOR, as risk-free rate; p. 2810).

Out-of-sample Sharpe ratio evaluation. The bootstrap procedure (eq. 24, p. 2815) follows Fama and French (2018): 100,000 bootstrap draws of $T = 251$ months from the factor return panel are used. The in-sample covariance matrix is shrunk as $\hat{\Sigma}_p = \Sigma_p + \gamma I$ ($\gamma = \operatorname{tr}(\Sigma_p) / (T \, E[\text{SR}]^2)$, with $E[\text{SR}] = 0.5$ selected) following Kozak, Nagel, and Santosh (2020), and the tangency portfolio is $\hat{\tau} = \hat{\Sigma}_p^{-1} \mu_p / (\mathbf{1}' \hat{\Sigma}_p^{-1} \mu_p)$. Out-of-sample SR is computed on the hold-out months not drawn in each simulation.

Empirical specifications

PC factor-structure regression (R1; Table I, p. 2807). The stock weight in PC k is regressed monthly on the market, age, and wealth portfolio weights (OLS, eq. 22, p. 2809):

$$PC_{j,k,t} = a^k_t + \lambda^k_{\text{MKT},t} \, m_{j,t} + \lambda^k_{\text{AGE},t} \, \pi_{\text{AGE},j,t} + \lambda^k_{\text{WEALTH},t} \, \pi_{\text{WEALTH},j,t} + \epsilon^k_{j,t}, \qquad j = 1,\ldots,J_t.$$

Time-average $R^2$ reported over 2005-2017. Identifies PC1 with market ($R^2 = 0.62$) and PC2 with combined age-wealth factor ($R^2 = 0.55$).

IPF alpha and beta regressions (R2, R3; Tables II-III, pp. 2810-2813). Monthly OLS spanning regressions of IPF returns on the market and/or firm factors, February 1997 to December 2017 (T = 251):

$$AW_t = \alpha + \beta_{\text{MKT}} \, \text{MKT}_t + [\beta_{\text{SMB}} \, \text{SMB}_t + \beta_{\text{HML}} \, \text{HML}_t + \beta_{\text{MOM}} \, \text{MOM}_t + \beta_{\text{RMW}} \, \text{RMW}_t + \beta_{\text{CMA}} \, \text{CMA}_t] + v_t.$$

Five Fama-French firm factors (SMB, HML, RMW, CMA) and momentum (MOM) are constructed from Norwegian equities using standard accounting and price data (Internet Appendix Section III.B). Newey-West standard errors are not mentioned; heteroskedasticity-robust t-statistics are reported.

Firm-factor alpha regressions under IPF (R4; Table IV, p. 2814).* Each firm factor $F_t \in \{\text{SMB}, \text{HML}, \text{MOM}, \text{RMW}, \text{CMA}\}$ is regressed on the market and AW:

$$F_t = \alpha_F + \beta_{F,\text{MKT}} \, \text{MKT}_t + \beta_{F,\text{AW}} \, AW_t + v_t.$$

AW absorbs ~40% of momentum, profitability, and investment alphas, rendering them statistically insignificant at the 5% level (MOM t = 1.04, RMW t = 1.42, CMA t = 0.99; Table IV columns 2, 6, 8, 10).

IPF stock-level multifactor model (eq. 23, p. 2811).* The preferred two-factor model (labelled IPF*) for each stock j:

$$R^e_{j,t} = \alpha_j + \beta_{j,\text{MKT}} \, \text{MKT}_t + \beta_{j,\text{AW}} \, AW_t + v_{j,t},$$

where $\alpha_j = 0$ for all j if IPF* is correctly specified.

Portfolio tilt regression (R6, R7; Table VII, p. 2823). This extends the life-cycle links between demographics and value-factor tilts that Betermier, Calvet, and Sodini (2017) documented for Swedish households into a full IPF extraction framework. The panel regression of investor i’s tilt toward IPF AW is run at annual frequency, 2004-2017 (N = 911,432 investor-years):

$$\text{TILT}^i_{\text{AW},t} = \delta_t + \theta' \chi^i_t + \xi^i,$$

• $\text{TILT}^i_{\text{AW},t} = \sum_{j=1}^{J_i} \omega^i_{j,t} \, D_{j,\text{AW},t}$ with $D_{j,\text{AW},t} = +1 / -1$ if stock j is in the long / short leg of AW (eq. 25, p. 2819).
• $\chi^i_t$ is a vector of investor characteristics (income beta, debt indicator, stock market experience, finance occupation, gender, Oslo residence, top management dummy).
• $\delta_t$ are year fixed effects with additional age-group and wealth-group fixed effects.
• Standard errors clustered by calendar year x investor level.

When to read the full paper

Read the full source if you are: constructing IPFs for other markets or asset classes; extending the spanning-condition theory to institutional holdings; using the bootstrap out-of-sample Sharpe methodology (Section III.C) for factor evaluation; auditing specific coefficients in Tables III-VIII; or reviewing the Internet Appendix robustness tests (alternative age/wealth cutoffs, institutional portfolio pricing), where IPF* also prices the institutional investor portfolio held on the OSE, the pricing question studied by Koijen and Yogo (2019). The locators above point to the exact tables.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 80(5), October 2025. Copyright 2025 the American Finance Association. This distillation was extracted by an LLM on 2026-05-31 and is not human-verified or independently reproduced. The paper is paywalled; only extracts are reproduced here under fair use for scholarly commentary.

Betermier, Sebastien, Laurent E. Calvet, Samuli Knupfer, and Jens Soerlie Kvaerner. “Investor Factors.” The Journal of Finance 80, no. 5 (October 2025): 2789-2830. DOI: 10.1111/jofi.13474. Copyright 2025 the American Finance Association. All rights reserved. This page contains an extract-only distillation by the Institute for Automated Research; the verbatim article is available at the publisher site.