A.7.1 Quantitative Fundamental Investing from Zero

Basic Prerequisites: Core Financial Ratios · 01 From Zero (what a ratio is). No prior factor-model knowledge needed.

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1. Intuition & Practical Objective

This page builds the why of quantitative fundamental investing with no prior knowledge needed. The objective is one idea: a fundamental factor is an accounting number that, when you sort the whole market on it and hold one side, has historically out-earned the other side - reliably, across many years. The entire folder is that idea, elaborated and then stress-tested.

Start with the absurd question a factor answers: why would one pile of accounting numbers predict the future returns of a whole market? It sounds like it shouldn’t - but it does, and it has for a century. Benjamin Graham’s whole tradition was “buy what’s cheap and solid,” but he did it by judgment. The quantitative revolution asked the mechanical version: can we write the rule as “sort every stock on book-to-market, buy the cheapest tenth, sell the dearest tenth, repeat every year” - and does that rule beat just owning the market? The answer from Fama–French 1992 is yes, and that is where this subject starts.

Three steps:

1. A factor is a sort, not a formula. You never invest “in the B/M ratio.” You rank the entire universe on B/M and hold the cheap side against the expensive side. The sort is the strategy; the accounting number is just the axis. This is why every factor in this folder is built the same way: rank → split into portfolios → compare realized returns. Learn that skeleton and every factor, from value to the F-score, is the same machine with a different axis.

2. Accounting predicts returns because prices are slow to digest accounting. Ball & Brown (1968) showed stock prices move in the direction of earnings news - accounting information moves markets. The factor literature’s deeper claim is that prices under-react: a firm that is cheap on book value and financially strong keeps earning a premium for years afterward (Piotroski’s under-reaction; Bernard & Thomas’s post-earnings-announcement drift). Fundamental data predicts returns because the market is systematically late to re-price it.

3. The premium is an average over a long horizon, not a guarantee for any single stock. Value out-earns growth over decades, but in any single year the expensive-and-wonderful can crush the cheap-and-ugly. A factor is a statistical edge - a positive expected spread - and that is why 05 · Failure Modes (crowding, data mining, drift) matters as much as the construction.

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2. Mathematical Ground Truth & Derivations

The value characteristic - book-to-market. Let BE be the book value of common equity and ME the market value of equity (price $\times$ shares). The value factor sorts on

$$\text{B/M}=\frac{\text{BE}}{\text{ME}}.$$

The intuition is direct: BE is the accounting capital the shareholders actually put in and retained; ME is what the market currently prices it at. A high B/M (cheap) means the market prices the firm at little more than its book capital - Graham’s bargain. A low B/M (dear) means the market is paying for future growth far above book. Fama–French 1992’s central finding was that high-B/M firms earned higher average returns than low-B/M firms, and that this ordering survived controlling for beta.

The sort-and-compare estimator. With $N$ firms, rank them on the characteristic $c_i$, split into $K$ portfolios by rank, and compare equal-weighted average returns:

$${\overline{r}}_k=\frac{1}{N_k}\sum _{i\in \text{portfolio }k}{r}_i,\text{factor spread}={\overline{r}}_K-{\overline{r}}_1.$$

If the characteristic is a priced factor, the spread ${\overline{r}}_K-{\overline{r}}_1$ is reliably positive over many re-balancing periods. This is the single estimator every construction in the folder reduces to - a fact worth remembering before any exotic factor design.

Why earnings yield is value in disguise. Book-to-market and earnings yield are two lenses on the same “cheapness” idea:

$$\text{E/P}=\frac{\text{NI}}{\text{ME}}=\frac{1}{\text{P/E}},$$

and Basu (1983) showed high-E/P (low P/E) firms earn more. Both ask “is the price cheap relative to a fundamental?” - the fundamental is book value in one case, earnings in the other.

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3. Computational Implementation - the value sort, stdlib only

The entire discipline in one script: rank twelve firms on book-to-market, split into three value portfolios, and read off the realized return spread. This is the machine every later page scales up.

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4. Failure Modes & First-Principles Breakdowns

1. Confusing “a factor” with “a formula.” The value edge lives in the sort across the whole market, not in any single firm’s B/M. One cheap stock can stay cheap forever (a value trap); the premium is the average over thousands of firms and many years. Reading any single stock’s B/M as a factor signal is the beginner error.
2. Believing the spread is a guarantee. The +4.00% here is a realized sample spread; in a given year the dear side can win. Factors are expected-value edges with long, painful drawdowns - which is exactly why 05 · Failure Modes exists.
3. Ignoring that profitability can swamp a naive value sort. This page’s sort pays because the sample was chosen so. Real markets confound - the profitable-but-expensive firm earns a lot yet looks “dear” on B/M alone. That is the Novy-Marx critique and the reason value must be combined with profitability (03 · Value & Profitability).

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5. References

• Ball, Ray & Brown, Philip: “An Empirical Evaluation of Accounting Income Numbers” (JAR, 1968)
• Basu, Sanjoy: “The Relationship Between Earnings Yield, Market Value and Return for NYSE Common Stocks” (JFE, 1983)
• Fama & French: “The Cross-Section of Expected Stock Returns” (JF, 1992)
• Bernard, Victor & Thomas, Jacob: “Post-Earnings-Announcement Drift” (JAR, 1989)
• Graham, Benjamin: The Intelligent Investor

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6. Connected Graph Bridges

• Back: Core Financial Ratios · 01 From Zero · Index Hub
• Forward: 02 · Fundamental Factors · Index Hub
• Base: Fundamental Analysis & Screening