V9 Portfolio Construction Errata: Portfolio Risk, Factor Models, and Behavioral Biases

1. Module 1 — Example 5 Replaces the Covariance Product with an Addition

Curriculum location: Portfolio Risk & Portfolio of Two Risky Assets, Example 5, solution 2, p. 29.

In the numerical substitution, the contribution inside the square root is printed as:

$2\times 0.33\times 0.040+0.090$

The symbolic formula immediately above this line uses the product $2\rho {\sigma }_{lc}{\sigma }_{FX}$. With local-currency volatility of $4.0\%$, exchange-rate volatility of $9.0\%$, and correlation of $0.33$, both standard deviations must remain factors in that product.

The numerical line instead adds $0.090$. Evaluating the complete expression as printed gives

$$\sqrt{0.040^2+0.090^2+2\times 0.33\times 0.040+0.090}\approx 0.355106$$

or $35.51\%$. It cannot reproduce the curriculum's stated $11.0\%$ risk. The preceding formula and final answer are correct; the error lies in the intervening substitution.

Correct reading: Replace the final addition in the covariance contribution with multiplication:

$${\sigma }_D=\sqrt{0.040^2+0.090^2+2\times 0.33\times 0.040\times 0.090}\approx 0.109891\approx 11.0\%$$

The printed final answer remains correct.

When entering a portfolio-risk calculation, preserve the product of correlation and both standard deviations; copying the printed addition produces a substantially overstated risk estimate.

2. Module 2 — The Market-Weight Denominator Excludes the Asset Being Weighted

Curriculum location: Capital Market Theory: Risk-Free and Risky Assets, market-portfolio construction, p. 66.

"In constructing the market portfolio, Siemens’s weight in the market portfolio will be equal to its market value divided by the value of all other assets included in the market portfolio."

The portfolio definition on p. 63 requires asset weights to sum to one. Excluding the asset being weighted breaks that requirement. For an illustrative market with asset values of 60 and 40, the printed rule gives weights of $60/40=1.5$ and $40/60=2/3$, which sum to $13/6$. The correct weights are $0.6$ and $0.4$.

Correct reading: An asset’s market-portfolio weight is its market value divided by the total value of all assets in that portfolio, including the asset itself: $w_i=V_i/{\sum }_j{V}_j$.

Use the full portfolio value as the denominator when calculating capitalization weights, weighted returns, or portfolio exposures.

3. Module 2 — The Active-Portfolio Description Equates Positive Holdings with Overweighting

Curriculum location: Capital Market Theory: The Capital Market Line, Passive and Active Portfolios, pp. 66–67.

"In an actively managed portfolio, assets that are undervalued, or have a chance of offering above-normal returns, will have a positive weight (i.e., overweight compared to the market weight in the benchmark index), whereas other assets will have a zero weight, or even a negative weight if short selling is permitted (i.e., some assets will be underweighted compared with the market weight in the benchmark index)."

The short-selling condition makes clear that the passage is discussing absolute holdings. Its benchmark comparisons concern a different quantity: active weight. A positive holding of $2\%$ against a benchmark weight of $5\%$ is underweight by $3$ percentage points. Underweighting can therefore leave a positive holding; it does not require a zero holding or a short position.

Correct reading: Overweight and underweight compare portfolio weight with benchmark weight: $w_i^{\mathrm{active}}=w_i^{\mathrm{portfolio}}-w_i^{\mathrm{benchmark}}$. Positive active weight means overweight; negative active weight means underweight. A negative absolute portfolio weight represents a short position.

Compare a holding with its benchmark weight before classifying it as overweight or underweight.

4. Module 2 — The Insurance Example Infers Market Beta from Personal-Loss Protection

Curriculum location: Calculation and Interpretation of Beta, Beta and Expected Return, p. 83.

"Insurance gives a positive return when the insured’s wealth is reduced because of a catastrophic loss."

"Thus, insurance has a negative beta and a negative expected return, but helps in reducing overall risk."

The curriculum defines beta using covariance with market returns on p. 80 and selects the S&P 500 as its market proxy on p. 67. The example instead describes a relationship with one insured person’s wealth. A personal loss can occur independently of market returns: protection against that loss can reduce personal risk without producing negative market covariance. The stated protection therefore does not establish the negative beta used in the conclusion.

Correct reading: Insurance can hedge an individual loss without having negative market beta. Negative market beta requires negative covariance with market returns. Under the CAPM, a negative beta implies an expected return below the risk-free rate, which need not be a negative expected return.

Distinguish a hedge against an individual loss from a hedge against systematic market risk before inferring a beta or required return.

5. Module 2 — The APT Description Assigns Factor Identification to No-Arbitrage

Curriculum location: Beyond CAPM: Limitations and Extensions of CAPM, Theoretical Models, p. 93.

"A no-arbitrage condition in asset markets is used to determine the risk factors and estimate betas for the risk factors."

The very next paragraph says that APT does not specify the risk factors and identifies factor selection and beta estimation as practical difficulties. The pricing equation on the same page relates expected return to factor premiums and factor sensitivities; it does not identify those factors or estimate their sensitivities. Huberman and Wang’s account likewise starts from a factor structure before deriving the no-arbitrage return relation. Huberman and Wang, Arbitrage Pricing Theory.

Correct reading: Given a factor structure and factor sensitivities, no-arbitrage constrains the relationship between expected returns and factor risk premiums. Identifying factors and estimating betas require additional specification and empirical work.

Keep APT’s pricing restriction separate from the data and estimation choices needed to implement a factor model.

6. Module 2 — The Four-Factor Discussion Treats Stock Returns as Unrelated to the Market

Curriculum location: Beyond CAPM: Limitations and Extensions of CAPM, Practical Models, p. 94.

"Historical analysis shows that the coefficient on $MKT$ is not significantly different from zero, which implies that stock return is unrelated to the market."

The preceding model identifies $MKT$ as market excess return and its coefficient as an asset’s factor loading. That identifies the object being discussed, but does not establish its empirical value. Fama and French’s original paper distinguishes weak cross-sectional explanatory power of market beta for differences in average returns from time-series market exposure. In regressions including size and value factors, their stock portfolios had market-factor slopes close to one. A finding about differences in average returns cannot establish that stock returns are unrelated to market movements. Nor would failure to reject a zero coefficient prove the absence of a relationship. Fama and French, Common risk factors in the returns on stocks and bonds.

Correct reading: The model includes market excess return, size (small versus large companies), value (high versus low book-to-market companies), and momentum (past winners versus past losers). Evidence that market beta explains little of the differences in average returns across stocks does not imply zero market-factor exposure or returns unrelated to the market.

Keep factor exposure distinct from evidence about how that exposure explains differences in average returns.

7. Module 3 — Bond Fund NAV Counts Only Bonds, Omitting Other Assets

Curriculum location: Pooled Interest – Mutual Funds, Bond Mutual Funds, p. 148.

"The net asset value of the fund is the sum of the value of each bond in the portfolio divided by the number of shares."

The preceding sentence expressly allows a bond fund to hold preferred shares. Those shares remain fund assets, but the quoted rule counts only bonds. Even with no liabilities, it omits the value of any preferred shares when valuing a fund share. An all-bond illustration could use that subtotal, but the paragraph does not impose that restriction. Reading "each bond" as every holding would erase the distinction the preceding sentence makes between bonds and preferred shares.

The complete calculation uses all assets and deducts liabilities before dividing by outstanding shares. The SEC's definition confirms both the net-assets numerator and the distinction between total NAV and NAV per share. SEC Investor.gov: Net Asset Value.

Correct reading: The net asset value per share of the fund is the value of all its assets less its liabilities, divided by the number of shares outstanding: $\mathrm{NAV}\mathrm{per}\mathrm{share}=\frac{\mathrm{Total}\mathrm{assets}-\mathrm{Total}\mathrm{liabilities}}{\mathrm{Shares}\mathrm{outstanding}}$.

Using bond values alone can misstate a fund's NAV per share and, consequently, the share count or redemption value calculated from it.

8. Module 4 — The Paragraph After Example 9 Incorrectly Singles Out Emerging Markets

Curriculum location: Strategic Asset Allocation, paragraph following Example 9, p. 181.

"Using correlation as a metric, Example 9 tends to indicate that only emerging markets were well differentiated from European equities."

Exhibit 5 on p. 180 contradicts this conclusion. European equities have correlations of $0.88$ with US equities, $0.84$ with emerging-market equities, $0.64$ with Japanese equities, and $0.79$ with US small-cap equities. Japanese equities have the lowest correlation with European equities among these alternatives. US small-cap equities also have a lower correlation than emerging-market equities.

The preceding worked solution uses the lowest correlation to identify the equity class most differentiated from US equities. Applying that same rule to the European-equity comparison cannot single out emerging markets. Although “well differentiated” has no specified cutoff, any lower-correlation cutoff that admits emerging markets must also admit both alternatives with lower correlations. The following discussion of organizational reasons for keeping equity subclasses does not change these data. Naming Japanese equities as the tentative exception also preserves the transition to the question of why investors subdivide otherwise highly correlated equities.

Correct reading: Among the other equity categories in Exhibit 5, Japanese equities are the most differentiated from European equities when correlation is the metric. Their correlation is $0.64$, compared with $0.84$ for emerging-market equities. Emerging markets are not uniquely differentiated on this evidence.

For a correlation-matrix question, compare the entries for the specified reference asset; an emerging-market label cannot substitute for the actual pairwise relationship.

9. Module 4 — The Minimum-Variance Definition Confuses a Single Portfolio with a Frontier

Curriculum location: Strategic Asset Allocation, efficient-frontier definition, pp. 183–184.

"The line that connects those portfolios with the minimal risk for each level of expected return (above that of the minimum-variance portfolio—the portfolio with the minimum variance for each given level of expected return) is the efficient frontier."

The parenthetical needs one portfolio whose expected return marks the lower boundary of the efficient upper branch. Its explanation instead describes minimizing variance separately for each given expected return. That description is the standard definition of a minimum-variance portfolio in the non-global sense, and it is correct on its own. The problem is that it is attached here to a singular boundary portfolio. Those are different optimization problems: changing the required return generally changes the minimizing portfolio. Together, these target-return minima form the minimum-variance frontier; they do not identify one common endpoint.

The curriculum's own attainable-set diagram in Exhibit 10 on p. 186 makes the distinction visible. There is a leftmost point with the lowest attainable risk, and a lower branch containing portfolios with lower expected returns. The portfolio at the leftmost point is the global minimum-variance portfolio. A portfolio on the lower branch can minimize risk for its particular expected return while remaining inefficient, because a higher return is attainable at the same risk.

The words “above that of” signal the intended global minimum, but they do not repair the explicit definition that follows. This distinction is also supported by the definition in Appendix B of CFA Institute Research Foundation's Investing Separately in Alpha and Beta.

Correct reading: The global minimum-variance portfolio has the lowest variance among all attainable portfolios, without imposing a particular expected-return target. The efficient frontier is the upper part of the minimum-variance frontier, beginning at that portfolio.

When identifying an efficient portfolio, distinguish the single global minimum from a minimum at a chosen return target; minimizing variance for a target return does not by itself make a portfolio efficient.

10. Module 5 — Example 7 Assigns $67\%$ to the Normal One-Sigma Interval

Curriculum location: Cognitive Errors, Example 7, Effects of Framing Bias, p. 212.

"Assuming a normal return distribution, in a given year there is a $67\%$ probability that the return will fall within one standard deviation of the mean,"

Curriculum location: Cognitive Errors, Example 7, Portfolio ABC probability statement, p. 213.

"$67\%$ chance that the return earned by Portfolio ABC will be between $-6\%$ and $26\%$,"

The curriculum gives the correct normal-distribution coverage elsewhere in this volume: Module 1, Distributional Characteristics, p. 9 states that approximately $68\%$ of observations lie within one standard deviation of the mean. Example 7 instead prints $67\%$ and carries it into the worked probability for Portfolio ABC.

ABC’s mean return of $10\%$ and standard deviation of $16\%$ correctly produce the interval from $-6\%$ to $26\%$. For normal returns, its probability is approximately $68.27\%$, which rounds to $68\%$. NIST’s normal-distribution reference corroborates that coverage. The first questionnaire table displays approximately $95\%$, two-standard-deviation intervals; the second lists the same portfolios’ means and standard deviations. Both tables’ values and the framing-bias conclusion remain unchanged.

Correct reading: Under the stated normal-return assumption, approximately $68\%$ of returns fall within one standard deviation of the mean. Portfolio ABC therefore has approximately a $68\%$ probability of returning between $-6\%$ and $26\%$. Keep the interval endpoints, both questionnaire tables, and the framing conclusion unchanged.

Use the corrected probability when interpreting the worked ABC interval or applying the normal-coverage rule to another return distribution.

11. Module 5 — Example 14’s Question 6 Denies Jordan’s Appeal to Past Success

Curriculum location: Emotional Biases, Example 14, Question 6 solution, p. 226.

"Jordan is not relating her certainty about the future or her decision to hold losing positions back to anything she has done or experienced in the past."

The vignette explicitly makes that connection when Jordan reassures her team about retaining the strategy:

Curriculum location: Emotional Biases, Example 14, Jordan’s response to Tang, p. 224.

"She reassures the team that this strategy has performed well in the past and that the markets will revert, bringing the fund’s returns back to normal levels."

Question 6 asks which bias Jordan did not demonstrate (pp. 225–226). The solution’s factual denial conflicts with the vignette’s stated reliance on past performance. Its preceding rationale makes a narrower distinction: the case does not show Jordan classifying new information into a personalized category. Referring to past success alone does not establish representativeness bias, so correcting the denial does not require changing answer B, Representativeness.

Correct reading: Jordan does invoke the strategy’s past success when expressing confidence in recovery. That reference alone does not demonstrate representativeness bias; the relevant question is whether she classifies new information through a misleading resemblance to a familiar category. Retain B as the bias not demonstrated, and remove the claim that she makes no connection to past experience.

When identifying a behavioral bias, distinguish the case’s stated evidence from the additional reasoning needed to establish the bias; a reference to past experience is insufficient on its own.

12. Module 6 — The normal-tail recurrence times do not match the stated inputs

Curriculum location: Identification of Risk — Financial vs. Non-Financial Risk, S&P 500 monthly-return example, p. 260.

“With a normal distribution, we would find that a return that low would occur only once every $2,199,935$ years.”

The example gives a monthly mean of $0.70\%$ and standard deviation of $4.10\%$. Its quoted interval refers to the $-21.76\%$ return. Those inputs produce

$$z=\frac{-21.76-0.70}{4.10}=-5.47805,p=\Phi (z)\approx 2.15021\times 10^{-8}.$$

The average recurrence interval is therefore $1/(12p)\approx 3,875,594$ years. The other three intervals also fail the same numerical check:

These differences cannot be explained by ordinary rounding of the displayed mean, standard deviation, or returns. The correction uses the supplied parameters; it does not claim that the historical sample statistics have been independently re-estimated.

Correct reading: Using the stated monthly inputs, standardize each return and calculate the appropriate one-sided normal-tail probability. Convert its reciprocal from months to years by dividing by $12$. The resulting average intervals are approximately $3.88$ million, $9,866$, $860$, and $1,175$ years, respectively.

This restores a calculation candidates can reproduce. These are model-implied average intervals, not guaranteed waiting periods; the example's broader warning about relying on thin normal tails remains valid. The standardization and cumulative-probability method follow the NIST normal-distribution reference.

13. Module 6 — Example 4 drops the portfolio weight from the hedge cost

Curriculum location: Risk Modification: Transferring, Shifting, and How to Choose, Example 4, Question 2 solution, p. 278.

$3.87\%=3.9\%-0.03\%$.

The same solution says the hedge covers $40\%$ of current portfolio value and initially writes its return impact as $40\%\times -0.03\%$. Its final subtraction applies the entire currency discount to the portfolio, omitting that weight.

Even retaining the curriculum's rounded figures gives $3.9\%-0.4(0.03\%)=3.888\%$, approximately $3.89\%$. For a calculation that retains the precision of the supplied inputs, the expected unhedged return is

$$0.6(5.5\%)+0.4(1.6\%)=3.94\%.$$

The spot and forward quotes then give

$$R_{\mathrm{hedged}}=3.94\%+0.4\left(\frac{0.7038}{0.7040}-1\right)\times 100\%\approx 3.92864\%.$$

Correct reading: Apply the forward discount only to the share of current portfolio value hedged. Keeping the curriculum's displayed inputs gives $3.9\%-0.4(0.03\%)=3.888\%\approx 3.89\%$. Using the unrounded inputs gives approximately $3.93\%$. The initial $3.9\%$ is valid rounding; the error is dropping the $40\%$ weight in the later worked answer.

Candidates should weight a position's hedge cost consistently with its portfolio exposure and retain guard digits until the final result.

Complete Portfolio Construction Errata Index

Scope: Modules 1–6, pp. 3–60, 61–120, 121–158, 159–202, 204–237, and 239–289 (printed page numbers).

Reviewed coverage: Portfolio Construction: Module 1 (pp. 3–60, including Practice Problems and solutions), Module 2 (pp. 61–120), Module 3 (pp. 121–158), Module 4 (pp. 159–202, including embedded examples, Practice Problems and solutions), Module 5 (pp. 204–237, plus the unnumbered module opening; includes embedded examples, Practice Problems, and solutions), and Module 6 (pp. 239–289, including embedded examples and Practice Problems and solutions) (printed page numbers).

The table below lists all high-value, objectively confirmed curriculum errors covered by this article, including eligible errors in printed Practice Problems and their solutions. Repeated instances of the same defect are consolidated into one row. 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

• CFA Institute: Portfolio Risk and Return, Part I — supporting overview of how portfolio risk depends on asset weights, standard deviations, and covariance or correlation.
• Huberman and Wang, Arbitrage Pricing Theory
• Fama and French, Common risk factors in the returns on stocks and bonds
• U.S. Securities and Exchange Commission, Investor.gov — Net Asset Value
• CFA Institute — Portfolio Risk and Return: Part I: correlation, diversification, and the distinction among the minimum-variance frontier, efficient frontier, and global minimum-variance portfolio.
• CFA Institute Research Foundation — Investing Separately in Alpha and Beta, Appendix B: the global minimum-variance portfolio and portfolio optimization.
• NIST/SEMATECH e-Handbook of Statistical Methods: What do we mean by “Normal” data?
• NIST/SEMATECH e-Handbook: Normal Distribution — standardization and normal cumulative probabilities.

This article is an independent candidate-focused analysis of confirmed errors in the CFA Level I 2027 Curriculum, Volume 9 Portfolio Construction, Modules 1–6. It is not an official curriculum errata notice.