V1 Module 9 Errata: Simulation of Financial Asset Prices and Returns

1. The 95% Parametric VaR Uses 1.96 Instead of 1.645

Curriculum location: Historical Simulation, historical VaR case, parametric comparison, p. 463.

${\mathrm{VaR}}_{95\%}=z_{95\%}\times {\sigma }_p=1.96\times 1.0656=\mathrm{HKD}2.0885\text{ million}.$

The case defines 95% VaR from the lower 5% tail. The one-sided standard-normal magnitude for that tail is approximately $1.645$; $1.96$ is the 97.5th percentile used for a two-sided 95% interval.

Correct reading: Use ${\mathrm{VaR}}_{95\%}=1.645\times 1.0656\approx \mathrm{HKD}1.7529\text{ million}$.

Candidates can otherwise apply a two-sided confidence-interval multiplier to a one-tailed risk measure.

2. The 2.5th Percentile Uses Ranks 2–3 Instead of 1–2

Curriculum location: Historical Simulation, sustainable-energy startup case, Step 2, p. 465.

"2.5th percentile (between ranks 2 and 3) using the linear interpolation formula:"

Curriculum location: Historical Simulation, sustainable-energy startup case, Step 2 substitution, p. 466.

$x=-25.60+\frac{2.5-2}{3-2}\times (-25.56-(-25.60))=-25.58\%.$

Curriculum location: Historical Simulation, sustainable-energy startup case, Step 3 downside, p. 466.

$-25.58\%\times 123,897.22/0.01\approx -3,170,000.$

The same case maps ranks 48 and 49 to the 96th and 98th percentiles. Under that convention, ranks 1 and 2 map to 2% and 4%, so the 2.5th percentile lies between ranks 1 and 2. This correction follows the case's own rank/$n$ mapping; under the CFA location convention $L=(n+1)y/100$, $L=(50+1)\times 2.5/100=1.275$, which likewise places the percentile between ranks 1 and 2.

Correct reading: Under the case's rank/$n$ mapping, interpolate between $-28.56\%$ and $-25.60\%$: $x=-28.56+\frac{2.5-2}{4-2}\times [-25.60-(-28.56)]=-27.82\%$. The downside impact is $-0.2782\times 123,897.22/0.01=-\mathrm{GBP}3,446,820.66$, approximately $-\mathrm{GBP}3.447\text{ million}$, and the resulting NPV is approximately $-\mathrm{GBP}2.447\text{ million}$.

Candidates can otherwise combine incompatible percentile coordinates and propagate the wrong downside valuation.

3. The Upper-Tail Interpolation Prints 6.89% Instead of 6.8475%

Curriculum location: Historical Simulation, sustainable-energy startup case, Step 2 upper-tail interpolation, p. 466.

$x=5.49+\frac{97.5-96}{98-96}\times (7.30-5.49)=6.89\%.$

Curriculum location: Historical Simulation, sustainable-energy startup case, Step 3 upside impact, p. 466.

$6.89\%\times 123,897.22/0.01\approx 854,000.$

Curriculum location: Historical Simulation, sustainable-energy startup case, Step 3 upside NPV, p. 466.

$1,000,000+854,000=1,854,000.$

The displayed interpolation equals $6.8475\%$, not $6.89\%$. Because the printed value is then used in both Step 3 lines, the arithmetic error propagates into the worked upside impact and NPV.

Correct reading: The interpolation is $6.8475\%$, displayed as $6.85\%$. If Step 3 uses that displayed $6.85\%$, the upside impact is approximately $\mathrm{GBP}849,000$ and the NPV is approximately $\mathrm{GBP}1,849,000$.

A candidate who performs the interpolation correctly otherwise cannot reproduce the official worked answer and may mistake a source error for a calculator error.

4. The 10,000-Run Standard Deviation Is Called Proof of Smoother Curves

Curriculum location: Bootstrapping, Brighton Rock 500-versus-10,000 run comparison, p. 476.

"Comparing the results of the 10,000-run simulations and the 500-run simulations, we observe smoother distribution curves in the 10,000-run graphs, as confirmed by the lower standard deviation."

Increasing the run count reduces sampling noise in the empirical histogram and stabilizes estimated summaries. It does not reduce the volatility of the underlying outcome distribution. The small differences between the reported sample standard deviations are simulation-to-simulation variation.

Correct reading: The 10,000-run histograms are smoother and their tail estimates are more stable because the larger run count reduces sampling noise; the lower reported sample standard deviation does not confirm that improvement.

Candidates should distinguish precision of an estimate from dispersion of the modeled outcome.

5. Bootstrap Resampling Is Said to Reduce Outlier Influence

Curriculum location: Bootstrapping, strengths, robust variability estimates, p. 480.

"Bootstrapping also reduces the impact of outliers in the data, relative to historical simulation."

Curriculum location: Bootstrapping, Question Set 2, item 2 solution, p. 481.

"The correct response is B. Bootstrapping, sampling with replacement, lessens the impact of outliers in the data."

In an ordinary size-$n$ bootstrap, every original observation has probability $1/n$ on each of $n$ draws, so its expected multiplicity is one. An outlier may be omitted from one resample and duplicated in another; resampling with replacement is not itself an outlier-robust method.

Correct reading: Ordinary bootstrap resampling inherits the observed sample's outliers. Outlier resistance requires a robust statistic or a specifically robust resampling procedure; it does not follow merely from sampling with replacement.

Candidates should not choose bootstrapping as an automatic cure for contaminated data.

6. One Asian Call Subtype Is Presented as the Definition of All Asian Options

Curriculum location: Monte Carlo Simulation, Asian Option Valuation Using Monte Carlo Simulation, p. 485.

"Asian-style options, also commonly referred to as Asian options, provide a payoff at maturity equal to the greater of zero or the difference between the underlying stock’s price at maturity and the average stock price over the life of the option."

The stated payoff is an average-strike, or floating-strike, Asian call. Average-price, or fixed-strike, Asian calls use the path average as the underlying value and compare it with a fixed strike.

Correct reading: The case studies an average-strike Asian call with payoff $\max (S_T-\bar{S},0)$. A fixed-strike Asian call instead has payoff $\max (\bar{S}-K,0)$.

Candidates need the strike convention before selecting or calculating an Asian-option payoff.

7. Practice Problem 6 Keys “Yes” When the Bond’s History Would Overstate Future Movements

Curriculum location: Historical Simulation, Practice Problem 6, p. 504.

"An analyst uses 5 years of historical data to model the potential price movements of a bond with an original maturity of 10 years and remaining maturity of 3 years."

"The yield curve is flat and interest rate volatility is relatively constant. Will the results of this simulation most likely reflect future price movements? A. Yes. B. No, it will probably overstate the potential for large movements."

Curriculum location: Historical Simulation, Practice Problem 6 solution, p. 506.

"The correct response is A. As a bond approaches maturity, its price volatility will decrease."

The solution's own premise contradicts its key. The five-year history covers periods when the bond had roughly eight to three years remaining. With the stated flat yield curve and relatively constant interest-rate volatility, the earlier observations came from when the bond had longer remaining maturity and higher duration. Replaying those own-price changes for the bond with three years remaining will probably overstate future large movements.

Correct reading: The correct response is B. The five-year own-price history includes observations from when the bond had longer remaining maturity and higher duration, so it will probably overstate large future price movements for the bond with three years remaining.

Candidates would select A (“Yes”) when B—the response stating that the simulation will probably overstate large movements—is defensible.

Complete Module 9 Errata Index

Scope: Module 9, pp. 453–508 (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

• NIST/SEMATECH: Cumulative Distribution Function of the Standard Normal Distribution
• SciPy: Bootstrap Confidence Intervals
• NIST/SEMATECH: Lognormal Distribution
• MathWorks: Pricing Asian Options

This article is an independent candidate-focused analysis of confirmed errors in the CFA Level I 2027 Curriculum, Volume 1 Quantitative Methods, Module 9 Simulation of Financial Asset Prices and Returns. It is not an official CFA Institute errata notice, and inclusion here must not be read as CFA Institute confirmation, endorsement, or approval.