It's just beta

Glossary

The terms used throughout the primer. Each definition links to the chapter that introduces it. Notation is tabulated in the appendix.

# Factor

A driver of returns shared across many stocks: the market, an industry, a style like value or momentum. Each factor is one column of X. Chapter 3

# Factor model

The claim that r = Xf + ε: a stock’s return is its exposures times the factor returns, plus a leftover that belongs to the stock alone. Everything on this site unpacks that one equation. Chapter 2

# Factor exposure/Factor loading

How much of a factor one stock carries. A row of X holds one stock’s full set. Style exposures are standardized so zero means market-average. Industry exposures are just membership, 0 or 1. Chapter 3

# Descriptor

The raw measurement behind a style exposure, like book-to-price or trailing 12-month return. It gets cleaned, winsorized, and standardized before it is allowed into X. Chapter 3

# Factor return

What one unit of exposure earned this period. In a fundamental model nobody observes it. The cross-sectional regression estimates it, one regression per period. Chapter 6

# Specific return/Idiosyncratic return

ε. The part of a stock’s return the factors can’t explain, assumed uncorrelated across stocks. Earnings surprises live here. Chapter 2

# Specific risk

The volatility of a stock’s specific return. One number per stock, sitting on the diagonal of Δ. Chapter 8

# Factor covariance matrix

F: how the factors move together, K×K, estimated from the factor-return history. Most of the craft is deciding how fast the estimate should forget old data. Chapter 8

# Risk model

X, F, and Δ taken together. Σ = XFXᵀ + Δ turns the three into a risk forecast for any portfolio the model covers. Chapter 8

# Beta

Sensitivity to the market factor. By extension, any return that comes from factor exposure rather than skill. Hence the name of this site. Chapter 1

# Active weight

w_p − w_b: what you hold minus what the benchmark holds. Tracking error and active return are computed on these, not on total weights. Chapter 9

# Portfolio exposure

x = Xᵀw. Weight each stock’s exposures by its position and add them up, and you know how much value, momentum, or tech the whole book carries. Chapter 2

# Tracking error

The annualized volatility of active return, forecast by running active weights through the risk model. Chapter 9

# Cross-sectional regression

One regression per period where the stocks are the data points: this period’s returns against exposures known at its start. The fitted coefficients are the factor returns. Chapter 6

# Fundamental factor model

The Barra-style family, and what most commercial risk models are. Exposures are measured from company characteristics, and factor returns are estimated by the cross-sectional regression. Chapter 4

# Macroeconomic factor model

Here the factor returns are observable series: the market’s return, inflation surprises, yield-curve shifts. What needs estimating is each stock’s sensitivity to them, by time-series regression. Chapter 4

# Statistical factor model

Nothing is observed but returns. PCA pulls both the factors and the exposures out of the return history. Reacts fast. Good luck naming factor 7. Chapter 4

# Estimation universe

The stocks the model learns from. Curated, so the factor regression sees liquid, representative names rather than every listing with a price. Chapter 5

# Coverage universe

Everything the model must be able to describe, learned from or not. Often an order of magnitude bigger than the estimation universe, because a client portfolio can arrive holding anything. Chapter 5

# Pure factor portfolio

The long-short basket the regression implicitly holds: one unit of exposure to its factor, zero to every other. Estimating a factor return and running this portfolio are the same act. Chapter 7

# Risk attribution

Splitting predicted risk into factor and specific parts, then across factors and positions. It answers “where does my risk come from” before the loss happens. Chapter 9

# Performance attribution

The ex post twin of risk attribution: realized active return split into what each factor bet paid, plus a specific part. Where you learn that the momentum bet you never meant to take cost 72bp. Chapter 10

# Alpha

Whatever the model can’t explain. Decompose a candidate signal against X and only the orthogonal remainder is new information. The rest is factor exposure you could have bought cheaper. Chapter 14

# Hedge overlay

Futures, ETFs, swaps, or a basket layered on top of the book so the unwanted factor exposures cancel. The stock positions never move. The arithmetic happens in factor space. Chapter 13

# Bias statistic

Divide each period’s return by the volatility forecast for it, then take the standard deviation. A calibrated model prints 1. Above that, it under-forecast risk. Below, it cried wolf. Chapter 15