A.5.2 The Accrual Anomaly

Basic Prerequisites: 01 · From Zero.

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1. Intuition & Practical Objective

Page 01 established the identity $\text{NI}=\text{CFO}+\text{Accruals}$ and argued the accrual term is the fragile part. This page is the empirical case: Sloan (1996) proved that the fragility is both real and mispriced. It is the founding paper of the entire earnings-quality literature and the reason “accruals” is a factor in every serious quantamental screen.

The argument has two independent legs, and you should keep them separate because they fall separately:

1. A statistical claim (not about markets at all): the earnings generated by accruals are less persistent than the earnings generated by cash flows. If this year’s profit is $1 and it arrived as cash, about 85 cents of it recurs next year; if it arrived as an accrual, only about 76 cents recurs. Accruals are, on average, lower-quality earnings - that is a property of accounting, not of investors.
2. A market claim (about mispricing): investors do not fully discount for that difference. They behave as if a dollar of accrual earnings equals a dollar of cash earnings - Sloan calls this “earnings fixation.” The consequence is a trading strategy: buy the firms whose earnings are all cash, short the firms whose earnings are all accruals, and you earn a large abnormal return while the mistake unwinds.

The practical objective: understand that accruals are not merely a forensic tool, they are a return predictor - and understand the three competing explanations for why, because they imply different things about whether the effect should still be there.

Three candidate explanations (Chan, Jegadeesh & Lakonishok 2006 sharpen exactly this):

• Manipulation hypothesis - managers deliberately inflate accruals; the market is fooled. If true, only the discretionary part of accruals should predict returns.
• Extrapolative-bias hypothesis - investors over-extrapolate the sales/earnings growth that mechanically drives working-capital accruals. If true, the nondiscretionary part predicts returns too.
• Delayed-reaction hypothesis - the information in accruals is public but absorbed slowly, exactly like post-earnings-announcement drift. If true, the anomaly is a drift phenomenon and should decay as arbitrage capital and data availability improve.

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2. Mathematical Ground Truth & Derivations

Setup (Sloan’s variables, all scaled by average total assets). Let $E_t$ be earnings performance (income from continuing operations / avg TA), $AC{C}_t$ the accrual component, $C{F}_t$ the cash-flow component, with $E_t=AC{C}_t+C{F}_t$.

Hypothesis 1 - differential persistence. The naive model constrains both components to revert at the same rate:

$$E_{t+1}=c_0+{\alpha }_1{E}_t+v_{t+1}.\text{\hspace{1em}(4)}$$

The correctly specified model frees them:

$$E_{t+1}={\gamma }_0+{\gamma }_{1}AC{C}_t+{\gamma }_{2}C{F}_t+v_{t+1},\boxed{{\gamma }_1<{\gamma }_2}.\text{\hspace{1em}(5)}$$

Sloan’s pooled estimates: ${\alpha }_1=0.841$ (earnings are mean-reverting but slow, far from a random walk), and

$${\gamma }_1=0.765(\text{accruals}),{\gamma }_2=0.855(\text{cash flow}).$$

An $F$-test rejects ${\gamma }_1={\gamma }_2$ at $F=614$. Industry-by-industry, ${\gamma }_1<{\gamma }_2$ in 86% of industries. Using decile ranks instead of raw values (to kill outlier influence) the gap widens: $0.565$ vs $0.838$.

Hypothesis 2 - market inefficiency. The returns test writes abnormal returns as the market’s mis-reaction to the components. Under the rational-expectations benchmark abnormal returns are zero in expectation; the misspecification is that the market uses a single combined coefficient instead of ${\gamma }_1,{\gamma }_2$. The prediction is directional and clean:

Firms with relatively high (low) accruals experience negative (positive) future abnormal returns.

The trading strategy. Rank all firms annually on the magnitude of the accrual component, form deciles, hold one year (return cumulation starts four months after fiscal year-end, by which time almost all statements are public). Size-adjusted abnormal returns (Sloan Table 6):

Portfolio	Year +1	Year +2	Year +3
Lowest-accrual decile (long)	+4.9% ($t=2.65$)	+1.6% ($t=1.17$)	+0.7% ($t=0.55$)
Highest-accrual decile (short)	−5.5% ($t=-3.98$)	−3.2% ($t=-2.25$)	−2.2% ($t=-1.61$)
Hedge (long low, short high)	+10.4% ($t=4.71$)	+4.8% ($t=3.15$)	+2.9% ($t=1.64$, n.s.)

Jensen-alpha returns (Ibbotson technique) are “generally consistent.” The effect concentrates in the first year and decays - and Sloan finds roughly a quarter of the abnormal return is clustered around subsequent earnings announcements, i.e. it is a drift, not a one-time repricing.

Sample scale. 40,679 firm-years, 1962–1991, NYSE/AMEX - a 30-year panel, which is why the result is treated as sturdy rather than a single-decade artifact.

Sign convention warning (the most common error on this page). Sloan sorts on the magnitude of the accrual component, and the accrual component is positively related to earnings but negatively related to cash flow (rank correlation of accruals with cash flows is −0.53). So “high accrual” means “high reported earnings, low cash behind them.” Do not confuse it with “high accrual ratio” sorting - Sloan notes the rank correlation between the accrual component and the accruals/earnings ratio is 0.94, so the variants are near-identical, which is why several implementations are all defensible.

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3. Computational Implementation - reconstructing the anomaly

Stdlib only. The script builds a panel from Sloan’s own data-generating process, runs both regressions via a hand-rolled OLS (normal equations + Gaussian elimination - no numpy), sorts into accrual deciles, and reports the hedge returns. It should recover ${\gamma }_1\approx 0.765$, ${\gamma }_2\approx 0.855$.

The recovered coefficients ($0.765$, $0.857$) match Sloan’s pooled estimates (0.765, 0.855) to the second decimal (0.857 vs 0.855, within sampling noise) - the estimator and the DGP agree, which is the point of the exercise.

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4. Failure Modes & First-Principles Breakdowns

1. The anomaly decays, and may not pay after costs. The hedge return falls from 10.4% (year 1) to 4.8% (year 2) to 2.9% (year 3, insignificant). Accrual-based strategies are high-turnover and load on small, illiquid, high-idiosyncratic-risk stocks - Sloan himself checks portfolio betas and finds the high-accrual decile is riskier, so part of the raw spread may be compensation, not free money. A paper’s 10.4% is not a strategy’s 10.4%.
2. Correlated measurement error and look-ahead. Accruals computed from restated Compustat data leak the future; the paper’s own point-in-time discipline (4-month lag, as-reported data) is what makes the 10.4% a tradable number. Any backtest that ignores this will overstate it. See Data Sources & Corporate Data.
3. The components are not independent. Accruals and cash flows are strongly negatively correlated (rank corr $-0.53$), so “long low-accrual, short high-accrual” is close to “long high-cash-flow, short low-cash-flow.” Before claiming an accrual effect, residualise one component on the other - otherwise you may be measuring a cash-flow anomaly wearing an accrual costume.
4. Trend, not level. Accruals revert, so the strongest signal is a rise in accruals (a deterioration), not a level. A firm with structurally high accruals (a fast-growing lender-like business model) is not a manipulation candidate - Chan et al. show the nondiscretionary component predicts returns too, which is inconsistent with the pure-manipulation reading.

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5. References

• Sloan, Richard G.: “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows About Future Earnings?” (TAR, 71(3), 289–315, 1996) - every equation, coefficient and table figure on this page is taken from and cross-checked against the corpus paper.
• Chan, Louis K. C., Jegadeesh, Narasimhan & Lakonishok, Josef: “Earnings Quality and Stock Returns” (JF, 61(2), 769–806, 2006)
• Bernard, Victor L. & Thomas, Jacob K.: “Post-Earnings-Announcement Drift: Delayed Price Response or Risk Premium?” (JAR, 27(Supplement), 1–36, 1989)
• Ball, Ray & Brown, Philip: “An Empirical Evaluation of Accounting Income Numbers” (JAR, 6(2), 159–178, 1968)
• Dechow, Ge & Schrand: “Understanding Earnings Quality…” (JAE, 2010)

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6. Connected Graph Bridges

• Back: 01 · From Zero · Index Hub
• Forward: 03 · Detecting Earnings Management (isolating the discretionary component of accruals) · 04 · Red Flags & Shenanigans
• Factor layer: Fundamental Multi-Factor Models · Quantitative Fundamental Investing
• Valuation: Equity Valuation (why low-persistence earnings deserve a lower multiple)