calculation-reference

CFA Level I Quantitative Methods Calculation Guide

Formulas, examples, and calculator workflows for CFA Level I quantitative methods.

TL;DR

Quantitative Methods covers TVM, descriptive statistics, probability, sampling, hypothesis testing, and regression. The fastest study path is to master TVM first, then mean/variance, probability trees, and regression interpretation.

Formula Reference

Expected value

E(X) = sum[p_i x x_i]

Weight each outcome by its probability.

Sample variance

s^2 = sum[(x_i - mean)^2] / (n - 1)

Use n - 1 for sample variance.

Z-score

z = (x - mean) / standard deviation

Standardizes an observation.

Bayes

P(A|B) = P(B|A) x P(A) / P(B)

Useful for updated probabilities after a signal.

BA II Plus Keystrokes

Use DATA and STAT worksheets for mean and standard deviation.
Use STO/RCL for probability tree intermediate values.
Use TVM keys for compounding and discounting.

Worked Example

Problem: Outcomes are 5 percent, 9 percent, and 14 percent with probabilities 0.2, 0.5, and 0.3.
Expected return = 0.2 x 5 + 0.5 x 9 + 0.3 x 14 = 9.7 percent.
Store each product before summing if doing this under time pressure.

Common Mistakes

Using sample standard deviation when the question asks for population standard deviation.
Not checking whether probability weights sum to 1.
Mixing decimals and percentages.

Related Guides

CFA Level I Quantitative Methods Formula Sheet - Public formula sheet for CFA Level I quantitative methods calculations.
Time Value of Money Calculations on the BA II Plus - CFA Level I TVM reference for present value, future value, annuities, perpetuities, and BA II Plus inputs.
Time-Weighted vs Money-Weighted Return - Compare TWR and MWR with formulas, examples, and CFA Level I interpretation rules.