CAPM vs Fama–French vs Carhart

This project reproduces the empirical design of Goncharov (2023), who compared the capital asset pricing model (CAPM), the Fama–French three-factor model (FF3), and the Carhart four-factor model on a GICS-balanced sample of 30 US equities over 2018–2021 — a period spanning trade tensions and the COVID-19 market shock.

For each stock we estimate three time-series regressions on daily log excess returns: CAPM uses market excess return only; FF3 adds SMB and HML; Carhart adds momentum (MOM). Model quality is judged by adjusted R² and residual standard error (RSE), with paired one-tailed t-tests on cross-sectional RSE vectors as in the thesis.

Consistent with the original findings, multifactor extensions raise average adjusted R² materially relative to CAPM, while momentum contributes only marginally beyond FF3. Formal RSE tests typically fail to reject equal precision at conventional significance levels.

Universe: Thirty US stocks from Goncharov’s Table 1, sampled across GICS sectors with large/small cap pairs where possible. Delisted tickers may be omitted if return history is unavailable.

Returns: Daily log returns $R_t=\ln (P_t/P_{t-1})$; excess return subtracts the Ken French daily risk-free rate.

Factors: Mkt-RF, SMB, HML, and momentum from the Dartmouth data library (same sources as the thesis).

Estimation: OLS with intercept for each model per stock. Adjusted R² penalizes extra factors; RSE uses $T-k$ degrees of freedom with $k$ = intercept plus factor count.

Inference: Paired one-tailed t-tests on RSE (CAPM vs FF3, FF3 vs Carhart, CAPM vs Carhart) after Shapiro–Wilk checks on the RSE vectors.

CAPM (one factor): Excess return on stock $i$ regressed on market excess return only. Tests whether a single beta explains daily variation during 2018–2021.

Fama–French three-factor (FF3): Adds SMB (size) and HML (value). Captures well-documented size and book-to-market effects in US equities.

Carhart four-factor: Adds momentum (MOM) to FF3. Momentum is often significant in US samples but may add little incremental adjusted R² once size and value are already included.

The results section reports cross-sectional means, medians, and dispersion of adjusted R² and RSE for each specification, with estimating equations shown below the tables.

Key insights (auto-generated from the sample) summarize mean R² gains, sector patterns, and RSE tests — read these before the tables.

The sector bar chart shows where FF3 adds the most explanatory power over CAPM; cyclical and consumer names often show larger lifts than utilities.

Per-stock grid sorting by FF3 adjusted R² highlights which names are well explained by factors vs dominated by idiosyncratic noise.

Contrast adjusted R² (variance explained) with RSE tests (residual precision): models can improve fit substantially even when formal RSE comparisons are borderline, as in Goncharov’s thesis.

Adjusted R² measures how much daily excess return variance is explained after penalizing additional factors. Goncharov reports large gains from CAPM to FF3 and only modest further gains from adding momentum — the bar chart on this page reproduces that pattern on the estimated sample.

Residual standard error (RSE) is the regression residual volatility; lower RSE implies tighter fit. Paired one-tailed t-tests on cross-sectional RSE vectors test whether a more complex model significantly reduces residual noise versus a simpler one (CAPM vs FF3, FF3 vs Carhart, CAPM vs Carhart).

When RSE differences are not statistically significant at conventional levels, a simpler model may be preferred on parsimony grounds even if adjusted R² rises slightly with extra factors.

The thesis window includes the 2018 trade-policy volatility, the sharp Q4 2018 equity drawdown, the 2020 COVID-19 crash and policy-driven rebound, and the 2021 reopening / inflation narrative. Factor models must fit both calm and crisis days — a stringent test for fixed linear betas.

A GICS-balanced panel reduces sector concentration: financials, technology, health care, and energy names enter with large/small pairs where possible so results are not driven by a single industry.

Stocks with incomplete return history are dropped; the dashboard reports how many of the requested thirty stocks were successfully estimated.

Fama–French Factor Lab — ETF-focused, multi-horizon factor dashboards and regime splits; this page is stock-level and fixed to Goncharov’s 2018–2021 design.

US IV Asset Pricing Lab — cross-sectional Fama–MacBeth with IV correction; here we only run time-series OLS per stock and compare models by fit statistics.

US Multi-Factor Model — custom value/quality/momentum composites; here factors are strictly Ken French long-short portfolios.

Summary cards report mean adjusted R² and percentage improvements (FF3 vs CAPM, Carhart vs FF3). The bar chart visualizes average fit by model; the RSE table documents paired test statistics; the per-stock grid shows individual α, β, and fit metrics.

Compare headline statistics against Goncharov (2023) thesis tables when validating the replication.

Public price data are not CRSP; corporate actions and delistings can differ from the thesis sample. Some 2018–2021 tickers are no longer listed.

The thesis used Excel OLS; this implementation uses statsmodels. Small numerical differences are expected.

Time-series fit on 2018–2021 does not prove that factors price the cross-section out of sample; it only measures explanatory power in-sample.

Research and education only — not investment advice.