V5 Module 12 Errata: CAPM, the Market Model, and Factor-Based Equity Models

1. The Santevie Solution and Equation 8 Omit Beta's Sign Condition

Curriculum location: Use of the Market Model and CAPM to Estimate Cost of Equity, Santevie beta solution and Equation 8, p. 483.

"B is incorrect because a levered beta will never be less than its associated unlevered beta."

The same sign-blind rule is then printed as Equation 8:

$${\beta }_{L,Comps}\ge {\beta }_u\le {\beta }_{L,firm}.\text{\hspace{1em}(8)}$$

The displayed levering relation is ${\beta }_L=K{\beta }_u$, where $K=1+(1-t)D/\mathrm{MVE}$. Under its stated assumptions, $K\ge 1$. Multiplication by $K$ therefore cannot reduce absolute beta: it makes a positive beta greater or equal and a negative beta less or equal. The Santevie calculation remains correct because its unlevered beta is positive and its leverage factor exceeds one; the general sign-blind inequality does not.

Correct reading: The levering factor does not decrease $|\beta |$. If ${\beta }_u>0$, then ${\beta }_L\ge {\beta }_u$; if ${\beta }_u<0$, then ${\beta }_L\le {\beta }_u$; and if ${\beta }_u=0$, beta remains zero. The first two inequalities are strict only when $K>1$.

Candidates should check beta's sign before using a greater-than inequality to validate a relevering calculation.

2. The Historical-MRP Discussion Says Geometric MRP Is Always Smaller

Curriculum location: Use of the Market Model and CAPM to Estimate Cost of Equity, Historical Approach to MRP Estimation, p. 486.

"An MRP estimated using the geometric average (i.e., compound returns) will always be smaller than an MRP using the arithmetic average of the same data. This occurs specifically because volatility reduces the compounding effect of returns on riskier assets."

The passage defines historical MRP as a stock-return average minus a government-security return average. If $A_s,G_s$ are the stock arithmetic and geometric means and $A_g,G_g$ are the government-security means, then

$${\mathrm{MRP}}_A-{\mathrm{MRP}}_G=(A_s-G_s)-(A_g-G_g).$$

Each arithmetic mean is at least its own geometric mean, but that fact alone does not determine which series has the larger gap. The NYU Stern data family cited by the curriculum even reports a 1981–1990 Stocks–T.Bonds premium of $0.13\%$ arithmetic versus $0.19\%$ geometric. Exhibit 8 has the usual lower-geometric ordering; it is not a universal rule.

Correct reading: A geometric-average MRP is lower only when the stock series' arithmetic–geometric gap exceeds the corresponding gap for the selected government-security series.

This condition prevents candidates from rejecting a correctly calculated premium merely because its ordering differs from the exhibit.

3. APT Says Systematic Factor Risk Can Be Reduced Through Diversification

Curriculum location: Arbitrage Pricing Theory, p. 491.

"Rather, each factor reflects a theoretical risk to equity investing that can be reduced through portfolio diversification."

The same paragraph says a fully diversified portfolio retains systematic risk and that APT has multiple systematic factors. That is the key distinction: diversification makes independent, asset-specific noise negligible, but common factor exposure remains and is precisely what the model prices through factor betas and risk premiums.

Correct reading: Each APT factor represents a source of systematic, non-diversifiable risk. Diversification removes idiosyncratic risk; it does not eliminate the portfolio's common factor exposures.

Candidates need this distinction to interpret why APT assigns expected-return compensation to multiple factor exposures.

Complete Module 12 Errata Index

Scope: Module 12, pp. 467–505 (printed page numbers).

What this review covers. Errors in the printed curriculum that would change a candidate's answer or understanding: wrong numbers, wrong formulas, reversed logic, and statements that contradict the module's own data. It does not list spelling mistakes, equation-numbering slips, or wording that is loose but defensible.

The table below lists all high-value, objectively confirmed curriculum errors covered by this article. Import-only defects, question errors not printed in the module source, disputed or reasonably defensible claims, and low-value editorial corrections such as typos or numbering and cross-reference errors are outside scope.

References

• Robert S. Hamada, “The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks”
• NYU Stern: Betas and Leverage—Derivation and Extensions
• NYU Stern: CAPM Historical Risk Premium Problems and Data
• Stephen A. Ross, “The Arbitrage Theory of Capital Asset Pricing”

This article is an independent candidate-focused analysis of confirmed errors in the CFA Level I 2027 Curriculum, Volume 5 Equity Investments, Module 12 The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models. It is not an official CFA Institute errata notice, and inclusion here must not be read as CFA Institute confirmation, endorsement, or approval.