US IV Asset Pricing Lab

Standard two-stage asset pricing tests (Fama–MacBeth) estimate factor betas in a first-stage time-series regression, then use those noisy estimates as regressors in a second-stage cross-section. This errors-in-variables (EIV) problem biases OLS risk-premium estimates even when the time series is long.

Researchers historically formed portfolios to diversify away estimation error, but grouping sacrifices cross-sectional information and can mask stock-level effects. Instrumental variables (IV) methods retain individual stocks as test assets while delivering N-consistent premium estimates as the number of stocks grows (Jegadeesh et al., 2019).

A Turkish-market study (1990–2022) applied this framework and found that classic and modern factors (CAPM, Fama–French, liquidity-adjusted LCAPM) often fail to price risk once firm characteristics are controlled — highlighting time-varying dynamics in emerging markets. This project asks whether similar patterns appear in US equities under the same econometric discipline.

Definition: EIV bias arises when independent variables (factor betas) are measured with error. In Fama–MacBeth, first-stage β̂ᵢ are treated as known in the monthly cross-section, distorting γ̂ₖ (risk premia) and standard errors.

Portfolio grouping averages away idiosyncratic beta noise but reduces power, hides variation visible only at the stock level, and limits how many characteristics can be studied simultaneously.

IV innovation: Use β̂ estimated from even calendar months as regressors and β̂ from odd months as instruments (roles swap in odd months). Measurement errors in the two samples are plausibly independent, mitigating EIV without abandoning individual stocks.

Universe: Sector-balanced sample of US large caps. Full academic replication would use CRSP returns and Compustat characteristics; this lab uses Ken French factors with standard econometric adjustments.

Factors: Daily Ken French MKT, SMB, HML, RMW, CMA, and momentum. Models tested: CAPM, FF3, FF4 (+Mom), FF5.

Stage 1 — Split-sample betas: Rolling 36-month window of daily excess returns. Separate time-series regressions on even-month vs. odd-month days. Dimson (1979): include contemporaneous, one-day lagged, and one-day led factor returns; sum loadings to total β per factor.

Stage 2 — Cross-section: Each month $t$, regress stock excess returns on lagged β̂ and optional controls: $r_{i,t}={\gamma }_{0,t}+{\sum }_k{\gamma }_{k,t}{\hat{\beta }}_{i,k,t-1}+{\sum }_l{\lambda }_{l,t}{\bar{C}}_{i,l,t-1}+{\xi }_{i,t}$. Even months: β̂_EV explanatory, β̂_IV instrument; odd months: roles reverse. Compare OLS and IV (2SLS).

Characteristics: Twelve-month rolling averages of size (log market cap), book-to-market proxy, profitability (ROE), and investment proxy — cross-sectionally z-scored. Many published “factor premia” weaken once these enter as direct controls.

IV validity requires sufficiently correlated instruments. Report ρ(β̂_EV, β̂_IV) each month; the Nelson–Startz (1990) rule of thumb requires ρ ≫ 1/√N (N = cross-section size) to avoid weak-instrument bias.

While true betas are unobserved, √(ρ(β̂_EV, β̂_IV)) proxies the correlation between estimated and true betas under independent measurement errors across splits.

Risk premia are time-averaged monthly γ̂ₖ with Fama–MacBeth t-statistics (mean over standard error of the monthly series). Compare IV vs. OLS and specifications with vs. without characteristics.

Factor vs. characteristic: If SMB or HML premia are significant in OLS but not after characteristics or under IV, the “priced factor” may reflect size or value characteristics rather than incremental risk compensation.

Persistent alpha: A positive, significant intercept under IV with characteristic controls suggests residual pricing not captured by linear factor models — consistent with both US anomaly literature and emerging-market findings.

OLS vs. IV: With long daily windows OLS and IV may look similar; IV is theoretically preferred when EIV bias is material or samples are shorter. Large shifts under IV indicate beta measurement error mattered for inference.

US vs. Turkey: Developed US markets are more liquid; nonsynchronous trading adjustments matter less but remain standard. Divergence from Turkish results would support market-specific drivers; convergence would suggest universal limits of classical factor models at the stock level.

The split-sample IV approach follows Jegadeesh, Noh, Gao, and Ravi (2019), who show that Fama–MacBeth OLS can misstate risk premia when betas are estimated with error, and that IV using independent beta estimates from alternating subsamples yields consistent inference as the cross-section grows.

The motivating emerging-market application (Borsa Istanbul, 1990–2022) documents that textbook factor premia often lose significance once firm characteristics enter the second stage — a pattern this US lab tests on a liquid large-cap panel with the same econometric steps.

Dimson (1979) lag-lead adjustments remain standard when daily returns are used: nonsynchronous trading between stocks and factors can otherwise deflate measured betas and bias premium estimates.

Compare OLS vs IV premia factor by factor: large gaps for the market leg suggest beta measurement error materially affects inference; stability across both estimators supports robust pricing.

The characteristic-control tables show whether SMB/HML-style premia survive once size, book-to-market, profitability, and investment enter directly — if premia collapse, the factor may be proxying for characteristics rather than incremental risk.

Instrument diagnostics validate whether split-sample betas are strong enough for IV; factors that fail Nelson–Startz should be interpreted cautiously.

The monthly IV premium path reveals time variation (crisis spikes vs calm periods) that a single full-sample average would hide.

Premium tables compare OLS and IV average γ̂ₖ (annualized where noted) for CAPM through FF5, with and without characteristic controls. Large gaps between OLS and IV for the same factor suggest EIV bias mattered; gaps between specs with vs. without characteristics suggest the factor may proxy for size, value, or profitability rather than incremental risk.

Monthly paths plot time series of estimated market (and other) premia — useful for spotting crisis spikes (e.g. March 2020) versus calm periods.

Instrument diagnostics report ρ(β̂_EV, β̂_IV) by month; values below the Nelson–Startz threshold warn that IV inference may be unreliable for that date.

Research notes below summarize headline findings for drafting and interpretation.

The Fama–French Factor Lab studies ETF time-series fit and regime conditioning with classical OLS — complementary, not redundant: this page focuses on stock-level cross-sections and IV correction for beta measurement error.

The US Multi-Factor Model builds composite value/quality/momentum scores and pooled panel regressions; here, factors are the official Ken French series and premia are Fama–MacBeth style.

The CAPM vs FF vs Carhart project compares time-series explanatory power (adjusted R²) on a fixed 2018–2021 stock sample; this lab compares cross-sectional pricing of risk and characteristics over a longer US history.

Public market prices and issuer metadata are not CRSP/Compustat. Investment and book-to-market proxies are simplified.

LCAPM (liquidity-adjusted CAPM) and q-factor models are noted for extension but not fully estimated here.

Overlapping monthly windows and large cross-sections make t-statistics indicative; bootstrap or Shanken corrections are not applied here.

Research and education only — not investment advice.

Interactive tables and charts below report OLS vs. IV premia by model, specifications with and without characteristics, monthly market-premium paths, instrument diagnostics, and structured notes suitable for drafting a research paper.