V1 Module 8 Errata: The Return and Risk of a Financial Portfolio

1. Example 3 Switches between Covariance and Correlation

Curriculum location: Calculating Portfolio Statistics, Example 3, pp. 392–393.

"Furthermore, assume that the covariance of the returns between these two indices is 0.0050."

"${\sigma }_P=\sqrt{0.0228}=0.1510=15.10\%.$"

Curriculum location: Calculating Portfolio Statistics, Exhibit 2, Portfolio 9, p. 393.

Portfolio number:

"9"

S&P 500 Index weight:

"80"

MSCI Emerging Markets Index weight:

"20"

Standard deviation:

"14.59"

The 15.10% calculation inserts 0.0050 as covariance. The exhibit and chart instead use 0.0050 as correlation, which produces approximately 14.59%.

Correct reading: Treat 0.0050 as correlation, first compute covariance as $\rho {\sigma }_A{\sigma }_B$, and then calculate portfolio standard deviation. The 80/20 portfolio result is approximately 14.59%.

This distinction determines whether a candidate inserts a dimensionless correlation or a covariance into the portfolio-variance formula.

2. Exhibit 3 Reverses the Direction of Expected Return

Curriculum location: Calculating Portfolio Statistics, Exhibit 3 interpretation, p. 393.

"As the weight of the MSCI Emerging Markets Index increases, the color of the dots changes from purple to blue to yellow, and the portfolio risk and return decreases first (from P11 to P9) before increasing."

The exhibit shows standard deviation falling from 16.21% to 14.59% from P11 to P9, but expected return rises from 9.93% to 11.58%.

Correct reading: From P11 to P9, portfolio risk decreases while expected return increases. Beyond P9, both risk and expected return increase.

A candidate could otherwise trace the return axis in the wrong direction.

3. Equation 19 Uses $r_{i,M}$ Instead of $r_{i,M^{\prime }}$

Curriculum location: Calculating Portfolio Statistics, Equation 19, p. 400.

"${\sum }_{M^{\prime }=1}^M{p}_{M^{\prime }}{\sum }_{i=1}^N{w}_i{r}_{i,M}$"

The return inside the $M^{\prime }$ expectation retains the outer index $M$. That prevents the inner term from ranging across scenarios.

Correct reading: The final return term must be $r_{i,M^{\prime }}$: ${\sum }_{M^{\prime }}{p}_{M^{\prime }}{\sum }_i{w}_i{r}_{i,M^{\prime }}$.

Using the printed subscript can make a candidate calculate deviations from the wrong expected return.

4. Equation 20 Omits the Equal-Weight Condition

Curriculum location: Calculating Portfolio Statistics, The Benefits of Diversification, p. 405.

"If all assets have the same variance, ${\sigma }^2$, and the average correlation between assets is $\bar{\rho }$, then the portfolio variance simplifies to:"

The displayed coefficients ${\sigma }^2/N$ and $(1-1/N)\bar{\rho }{\sigma }^2$ also depend on every asset having weight $1/N$.

Correct reading: Equation 20 applies to an equally weighted $N$-asset portfolio whose assets have the stated common variance and average pairwise correlation.

Without that condition, a candidate could use the shortcut for an unequal-weight portfolio.

5. The Minimum-Variance Formula Ignores Its No-Short Constraint

Curriculum location: The Minimum–Variance Portfolio and the Efficient Frontier, two-asset setup, p. 416.

"the portfolio weights must be non-negative:"

"$w_A,w_B\ge 0.$"

Curriculum location: The Minimum–Variance Portfolio and the Efficient Frontier, Equations 23–24 conclusion, p. 417.

"These weights minimize the portfolio’s variance"

Equations 23–24 give the unconstrained interior stationary point. If a calculated weight is negative or above 1, it is infeasible under the stated constraint.

Correct reading: Use the formula directly only when both weights lie in $[0,1]$. Otherwise, the constrained minimum occurs at a feasible boundary, so compare the 100% Asset A and 100% Asset B endpoint portfolios.

A candidate could otherwise present a prohibited short position as the no-short minimum.

6. Example 11 Omits the Second Covariance Term but Prints the Intended Result

Curriculum location: The Minimum–Variance Portfolio and the Efficient Frontier, Example 11, p. 418.

"$w_A=\frac{0.1096-0.0107}{0.0263+0.1096-0.0107}=\frac{0.0989}{0.1144}\approx 0.864$"

The symbolic denominator subtracts the covariance only once, which would give 0.1252. The governing formula requires two covariance terms. The printed numerical denominator and reported weight reflect that intended structure rather than the expression as typeset.

Correct reading: Insert the missing factor: $0.0263+0.1096-2(0.0107)$. Using the displayed rounded components gives approximately $0.1145$; the reported $w_A\approx 0.864$ remains substantively correct at source precision.

The correction belongs in the symbolic expression, not in the reported portfolio weight.

7. The Frontier Rule Assumes $r_A>r_B$ despite the Module's $r_A<r_B$

Curriculum location: The Minimum–Variance Portfolio and the Efficient Frontier, p. 421.

"If $w_A$ is to be positive, $r_P$ must be at least as large as $r_B$."

"Covering all possible weights for $w_A$ from $w_{\min ,A}$ to 1 will generate the entire efficient frontier."

From $w_A=(r_P-r_B)/(r_A-r_B)$, both the sign condition and the direction of the upper frontier depend on the sign of $r_A-r_B$. In the module’s own asset assignment, $r_A<r_B$.

Correct reading: If $r_A>r_B$, $w_A\ge 0$ requires $r_P\ge r_B$, and the efficient branch moves from $w_{\min ,A}$ toward 1. If $r_A<r_B$, $w_A\ge 0$ requires $r_P\le r_B$, and the efficient branch moves from $w_{\min ,A}$ toward 0. The module’s own asset assignment is the second case.

The printed rule can send a candidate onto the inefficient branch.

8. A Complete Portfolio Is Misnamed the Optimal Risky Portfolio

Curriculum location: The Minimum–Variance Portfolio and the Efficient Frontier, transition to Example 13, p. 422.

"We need the risk-free asset to create the optimal risky portfolio, as the following example shows."

Curriculum location: The Minimum–Variance Portfolio and the Efficient Frontier, Example 13, p. 422.

"A portfolio manager creates an optimal risky portfolio by combining the risky portfolio, proxied by the MSCI World Index, and a risk-free asset"

The optimal risky portfolio is the risky-asset tangency portfolio. Combining a risky portfolio with the risk-free asset creates a complete portfolio on a capital allocation line.

Example 13 does not establish that the MSCI World proxy is the tangency portfolio; it supplies the chosen risky portfolio for the allocation calculation.

Correct reading: Identify the tangency portfolio first. Investor risk aversion then determines the allocation between that risky portfolio and the risk-free asset, producing the investor’s complete portfolio.

Confusing the two steps can make a candidate treat investor risk aversion as determining the risky fund itself.

9. Exhibit 22 Mixes Fixed-Risk and Fixed-Return Comparisons

Curriculum location: Optimal Portfolio Selection, Exhibit 22, p. 431.

"Higher return and higher risk at any given level of return"

"Higher return and lower risk at any given level of return"

The risk-seeking and risk-averse cells say that return is both higher and held fixed. They have merged two different dominance comparisons into one contradictory phrase.

Correct reading: At a given level of risk, an investor prefers higher expected return. At a given expected return, a risk-seeking investor prefers higher risk, while a risk-averse investor prefers lower risk.

A candidate could otherwise hold the wrong variable constant when classifying investor preferences.

10. Exhibit 24 Conflates Two Different Tangencies

Curriculum location: Optimal Portfolio Selection, Exhibit 24 description, p. 435.

"Exhibit 24 shows the highest attainable utility curve that is tangent to the efficient frontier."

The investor’s highest attainable indifference curve is tangent to the capital allocation line (CAL). A different tangency determines the optimal CAL: the CAL is tangent to the risky-asset efficient frontier.

Correct reading: First identify the risky tangency portfolio where the optimal CAL touches the risky-asset efficient frontier. Then identify the investor’s complete portfolio where the highest attainable indifference curve touches that CAL.

Conflating the two tangencies can make a candidate select the wrong portfolio point.

11. Beta Is Defined as ${\sigma }_p/{\sigma }_m$, Omitting Correlation

Curriculum location: Optimal Portfolio Selection, CAPM and its estimation, p. 439.

"${\beta }_i$ is the beta value of asset $i$ and is equal to ${\sigma }_p/{\sigma }_m$."

For a general asset, beta depends on both relative volatility and correlation with the market. The p.439 definition omits the correlation term and conflicts with Equation 33.

Correct reading: Use ${\beta }_i={\rho }_{i,m}{\sigma }_i/{\sigma }_m$ for a general asset.

Using volatility alone can make a candidate rank total risk as though it were systematic risk.

Complete Module 8 Body-Text Errata Index

Scope: Module 8, pp. 381–452 (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.

References

• CFA Institute: Portfolio Risk and Return, Part I
• CFA Institute: Portfolio Risk and Return, Part II

This article is an independent candidate-focused analysis of confirmed errors in the CFA Level I 2027 Curriculum, Volume 1 Quantitative Methods, Module 8 The Return and Risk of a Financial Portfolio. It is not an official CFA Institute errata notice, and inclusion here must not be read as CFA Institute confirmation, endorsement, or approval.