CFA Level 2 · Free topic practice

CFA Level 2 Quantitative Methods: notes and free practice

CFA Level 2 Quantitative Methods uses models to analyze investment data. Diagnose assumptions, interpret estimated relationships and assess model limitations before using a fitted result as a forecast.

The key ideas, at a glance

Level 2 · Visual study guide Study illustration of an analyzed worksheet, calculator and checked answer.

Translate the regression

Read the visual, then follow the worked example below. Use the stated case assumptions.

Illustrative worked case

Read the slope as a conditional relationship

% forecast

0%: 2
2%: 3.4
4%: 4.8
5%: 5.5
6%: 6.2
8%: 7.6

Forecast = 2 + 0.7 × market return in percentage points. A 5% market input gives 5.5%; the line is not a guaranteed return.

Key methods and mistakes for CFA Level 2 Quantitative Methods
Concept	Rule or decision	Common mistake
Translate the regression	Prediction = intercept + Σ coefficient × predictor	Entering 0.05 when the model expects 5 understates that predictor’s contribution.
Test the claim, then fit	t = (estimate - null) / SE; R² = 1 - SSE / SST	Statistical significance does not establish a large economic effect or causation.
Identify the failure mode	Unequal error variance changes conventional inference	Robust standard errors do not cure omitted-variable bias.
Forecast without hindsight	AR(1): next mean = a + b × latest x; long-run mean = a / (1 - b)	Repeated tuning against the test sample makes it another training signal.

01Translate the regression
Prediction = intercept + Σ coefficient × predictor
Watch for: Entering 0.05 when the model expects 5 understates that predictor’s contribution.
02Test the claim, then fit
t = (estimate - null) / SE; R² = 1 - SSE / SST
Watch for: Statistical significance does not establish a large economic effect or causation.
03Identify the failure mode
Unequal error variance changes conventional inference
Watch for: Robust standard errors do not cure omitted-variable bias.
04Forecast without hindsight
AR(1): next mean = a + b × latest x; long-run mean = a / (1 - b)
Watch for: Repeated tuning against the test sample makes it another training signal.

Selected 2026 study concepts. Match your preparation to your registered exam-year curriculum. These notes are not complete curriculum coverage.

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CFA Level II: 20 practice MCQs

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Put the method to work

One worked example, from facts to answer

Given
Forecast = 2 + 0.7 × market return; market return is 5 percentage points.
Method
2 + 0.7 × 5 = 5.5.
Answer and interpretation
The conditional forecast is 5.5%, not a guaranteed return.

Original independent teaching example. Assumptions are stated above; this is not an official exam question or scoring key.

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10 free Quantitative Methods questions

Five mini-cases, two questions each. Read the case facts, choose an answer and review the method. Short teaching cases, not complete exam item sets or a mock.

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Question 1 of 10Level II topic sample · Case 1 of 5Quantitative MethodsMultiple choice
Case facts
Lena models annual stock return in percentage points as 1.5 + 0.8 × market return - 0.4 × a rate-change variable. Both predictors are in percentage points. Her scenario sets market return to 6 and the rate variable to 2. Interpret slopes holding the other predictor fixed.
Under Lena’s supplied scenario, the predicted annual stock return is:
Answer and explanations
1.5 + 0.8 × 6 - 0.4 × 2 = 5.5 percentage points, or 5.5%.
Review the method
- A: 4.7% subtracts the rate effect twice.
- B: 7.1% adds the rate effect despite its negative coefficient.
- C - correct: 1.5 + 0.8 × 6 - 0.4 × 2 = 5.5 percentage points, or 5.5%.
Question 2 of 10Level II topic sample · Case 1 of 5Quantitative MethodsMultiple choice
Case facts
Lena models annual stock return in percentage points as 1.5 + 0.8 × market return - 0.4 × a rate-change variable. Both predictors are in percentage points. Her scenario sets market return to 6 and the rate variable to 2. Interpret slopes holding the other predictor fixed.
Holding market return fixed, a one-percentage-point rise in the rate variable changes the forecast by:
Answer and explanations
The rate coefficient is -0.4 in percentage-point units, holding market return fixed.
Review the method
- A - correct: The rate coefficient is -0.4 in percentage-point units, holding market return fixed.
- B: The rate coefficient is negative, not positive.
- C: Multiplying the coefficient by 100 misreads the supplied units.
Question 3 of 10Level II topic sample · Case 2 of 5Quantitative MethodsMultiple choice
Case facts
Omar estimates a multiple regression under the classical assumptions. A slope estimate is 0.60 with standard error 0.20. The two-sided critical t value for testing a zero slope is 2.05. Total sum of squares is 200 and residual sum of squares is 50.
What is Omar’s t statistic for the supplied zero-slope test?
Answer and explanations
(0.60 - 0) / 0.20 = 3.00, exceeding the supplied cutoff of 2.05.
Review the method
- A: Multiplying estimate and standard error is not the test statistic.
- B - correct: (0.60 - 0) / 0.20 = 3.00, exceeding the supplied cutoff of 2.05.
- C: 2.05 is the critical value, not the calculated statistic.
Question 4 of 10Level II topic sample · Case 2 of 5Quantitative MethodsMultiple choice
Case facts
Omar estimates a multiple regression under the classical assumptions. A slope estimate is 0.60 with standard error 0.20. The two-sided critical t value for testing a zero slope is 2.05. Total sum of squares is 200 and residual sum of squares is 50.
How much sample variation does Omar’s regression explain, as measured by R²?
Answer and explanations
R² = 1 - 50 / 200 = 0.75, or 75% of sample variation.
Review the method
- A: 25% is the unexplained share, SSE / SST.
- B: 50% does not follow from the supplied sums of squares.
- C - correct: R² = 1 - 50 / 200 = 0.75, or 75% of sample variation.
Question 5 of 10Level II topic sample · Case 3 of 5Quantitative MethodsMultiple choice
Case facts
Nia fits OLS with exogenous predictors. Residuals fan out as firm size rises; there is no serial correlation. In a separate model, two predictors are almost linear copies of one another. She wants reliable coefficient inference, not just high in-sample fit.
For Nia’s fan-shaped residuals, which response addresses conventional slope-inference risk?
Answer and explanations
Under exogeneity, unequal error variance undermines conventional standard errors; robust inference addresses this issue.
Review the method
- A - correct: Under exogeneity, unequal error variance undermines conventional standard errors; robust inference addresses this issue.
- B: Heteroskedasticity alone does not necessarily bias OLS slopes with exogenous predictors.
- C: Automatically deleting observations can introduce a different estimation problem.
Question 6 of 10Level II topic sample · Case 3 of 5Quantitative MethodsMultiple choice
Case facts
Nia fits OLS with exogenous predictors. Residuals fan out as firm size rises; there is no serial correlation. In a separate model, two predictors are almost linear copies of one another. She wants reliable coefficient inference, not just high in-sample fit.
In Nia’s separate model, nearly redundant predictors most directly create:
Answer and explanations
Strong predictor correlation can inflate slope standard errors and destabilize individual estimates.
Review the method
- A: Redundancy does not guarantee accuracy on new observations.
- B - correct: Strong predictor correlation can inflate slope standard errors and destabilize individual estimates.
- C: A unit root concerns time-series persistence, not predictor redundancy.
Question 7 of 10Level II topic sample · Case 4 of 5Quantitative MethodsMultiple choice
Case facts
Theo fits a stationary AR(1): x(t) = 3 + 0.6 × x(t-1) + error. The latest observation is 10. Future errors have conditional mean zero and coefficients remain fixed. There is no deterministic time trend.
Theo’s one-period-ahead conditional forecast is:
Answer and explanations
The conditional forecast is 3 + 0.6 × 10 = 9.0 because the next error has mean zero.
Review the method
- A: 6.0 omits the intercept from 0.6 × 10.
- B: 7.5 is the long-run mean rather than the next forecast.
- C - correct: The conditional forecast is 3 + 0.6 × 10 = 9.0 because the next error has mean zero.
Question 8 of 10Level II topic sample · Case 4 of 5Quantitative MethodsMultiple choice
Case facts
Theo fits a stationary AR(1): x(t) = 3 + 0.6 × x(t-1) + error. The latest observation is 10. Future errors have conditional mean zero and coefficients remain fixed. There is no deterministic time trend.
Under Theo’s stationary model, the long-run mean is:
Answer and explanations
The mean solves μ = 3 + 0.6μ, so μ = 3 / 0.4 = 7.5.
Review the method
- A - correct: The mean solves μ = 3 + 0.6μ, so μ = 3 / 0.4 = 7.5.
- B: The intercept is not the mean when the autoregressive coefficient is nonzero.
- C: The latest observation is not the process’s long-run mean.
Question 9 of 10Level II topic sample · Case 5 of 5Quantitative MethodsMultiple choice
Case facts
A team predicts next-month defaults. Model A has lower training error but higher untouched test error than Model B. A proposed input is a restatement published two months after the prediction date. Settings are chosen using validation data, with a separate final test sample.
The default team’s training-versus-test results warn that Model A may be:
Answer and explanations
The deterioration outside training is consistent with fitting sample-specific noise rather than generalizable relationships.
Review the method
- A: Lower training error with higher test error does not establish stability.
- B - correct: The deterioration outside training is consistent with fitting sample-specific noise rather than generalizable relationships.
- C: Neither model is shown to eliminate estimation uncertainty.
Question 10 of 10Level II topic sample · Case 5 of 5Quantitative MethodsMultiple choice
Case facts
A team predicts next-month defaults. Model A has lower training error but higher untouched test error than Model B. A proposed input is a restatement published two months after the prediction date. Settings are chosen using validation data, with a separate final test sample.
How should the team treat the later restatement when reconstructing historical predictions?
Answer and explanations
The restatement was unavailable then; using it would introduce look-ahead information into the backtest.
Review the method
- A: Later accuracy does not establish historical availability.
- B: Outcome-dependent inclusion adds another source of hindsight.
- C - correct: The restatement was unavailable then; using it would introduce look-ahead information into the backtest.

Four ideas to put to work

Find the method you need

Start with: Regression vocabulary, conditional averages, hypothesis tests and percentage-point units.

METHOD 01

Translate the regression

Prediction = intercept + Σ coefficient × predictor

Keep predictors in the units used to estimate their coefficients.
Interpret each slope holding the other predictors fixed.
Conditional association does not by itself establish causation.

Worked example

Given: Forecast = 2 + 0.7 × market return; market return is 5 percentage points.
Calculate / decide: 2 + 0.7 × 5 = 5.5.
Result: The conditional forecast is 5.5%, not a guaranteed return.

Watch for: Entering 0.05 when the model expects 5 understates that predictor’s contribution.

Practise this idea

METHOD 02

Test the claim, then fit

t = (estimate - null) / SE; R² = 1 - SSE / SST

Specify the null and tail before reading the test.
Compare absolute t with the supplied two-sided cutoff.
R² measures explained sample variation, not future predictive success.

Worked example

Given: Slope 0.45, null zero, SE 0.15; critical t is 2.10.
Calculate / decide: t = 0.45 / 0.15 = 3.00, exceeding 2.10.
Result: Reject the zero-slope null under the stated assumptions.

Watch for: Statistical significance does not establish a large economic effect or causation.

Practise this idea

METHOD 03

Identify the failure mode

Unequal error variance changes conventional inference

A fan-shaped residual plot suggests heteroskedasticity.
With exogenous predictors, consider heteroskedasticity-robust standard errors.
Closely related predictors can inflate individual slope uncertainty.

Worked example

Given: Large firms have wider residual dispersion than small firms.
Calculate / decide: Investigate error variance that depends on size.
Result: Use an appropriate inference method instead of assuming constant variance.

Watch for: Robust standard errors do not cure omitted-variable bias.

Practise this idea

METHOD 04

Forecast without hindsight

AR(1): next mean = a + b × latest x; long-run mean = a / (1 - b)

A stationary AR(1) needs |b| < 1 and stable assumptions.
Use only information available at the prediction date.
Tune on validation data; reserve an untouched final test sample.

Worked example

Given: x(t) = 4 + 0.5 × x(t-1) + error; latest x is 12.
Calculate / decide: Next forecast = 10; long-run mean = 4 / 0.5 = 8.
Result: The forecast moves toward 8 rather than extrapolating 12 forever.

Watch for: Repeated tuning against the test sample makes it another training signal.

Practise this idea

Questions about this topic

Does a high R² establish a good forecast?: No. It describes a form of in-sample fit under the model. Assumptions, specification, overfitting and out-of-sample performance still require evaluation.
Why do regression diagnostics matter?: Violations of assumptions can affect inference or forecasting. Read residual patterns and the stated error structure before relying on a coefficient test or a prediction interval.
What is the risk of fitting and testing on the same data?: A model can capture sample-specific noise as though it were a stable relationship. Appropriate validation separates model fitting from evaluating performance on information not used to fit it.

Sources and curriculum scope

Official outlines establish curriculum scope. The explanations and worked examples are independent teaching material; the sources do not verify or endorse them.

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One worked example, from facts to answer

Given

Method

Answer and interpretation

10 free Quantitative Methods questions

Under Lena’s supplied scenario, the predicted annual stock return is:

Holding market return fixed, a one-percentage-point rise in the rate variable changes the forecast by:

What is Omar’s t statistic for the supplied zero-slope test?

How much sample variation does Omar’s regression explain, as measured by R²?

For Nia’s fan-shaped residuals, which response addresses conventional slope-inference risk?

In Nia’s separate model, nearly redundant predictors most directly create:

Theo’s one-period-ahead conditional forecast is:

Under Theo’s stationary model, the long-run mean is:

The default team’s training-versus-test results warn that Model A may be:

How should the team treat the later restatement when reconstructing historical predictions?

Find the method you need

Translate the regression

Worked example

Test the claim, then fit

Worked example

Identify the failure mode

Worked example

Forecast without hindsight

Worked example

Questions about this topic

Sources and curriculum scope