Quantitative Methods: CFA® Level I

It is 11–14% of the 2027 Level I exam. 54 learning outcomes across 11 learning modules.

500+ practice questions and 31 formula cards on this topic in the app.

Returns of Financial Assets and Instruments

• Contrast the parts that make up an interest rate
• Explain required returns, the risk-free rate and risk premiums

Types of Financial Returns

• Work out a holding period return and explain what it means
• Work out an annualised return and explain what it means
• Contrast gross with net, pre-tax with after-tax, and real with nominal returns

Benchmarking Returns

• Contrast money-weighted with time-weighted rates of return
• Work out values and returns for indexes weighted by price, by market capitalisation and equally

The Time Value of Money in Finance

• Work out what a cash flow will be worth in future
• Work out what one cash flow is worth today
• Work out what an annuity and a perpetuity are worth today
• Contrast a stated annual rate with the effective annual rate
• Work out net present value and the internal rate of return
• Work out, from market prices, the return implied by a bond and the growth rate implied by a stock
• Explain cash flow additivity and apply it to derive an implied forward rate

Statistical Characteristics of Asset Returns

• Explain what measures of central tendency show
• Work out measures of dispersion and explain what they show
• Explain what skewness and kurtosis say about a return distribution
• Work out quantiles and explain what they show
• Work out covariance and correlation and explain what they show
• Work out the coefficient of variation and semi-deviation and explain what they mean

Statistical Distributions for Financial Asset Prices and Returns

• Use the probability rules for addition and multiplication
• Work out a random variable's expected value and variance
• Use Bayes' formula to revise a probability
• Explain the discrete uniform and the binomial distribution
• Use the normal distribution to work out probabilities
• Explain continuous compounding and the lognormal distribution
• Explain the chi-square, F and Student's t distributions
• Work out expected values and variances conditional on given information

Estimation and Hypothesis Testing

• Explain what a confidence interval around a population mean tells you
• Say what the central limit theorem states and what follows from it
• Contrast ways of sampling and explain sampling error
• Set up the null and the alternative hypothesis
• Explain what a p-value means and the two kinds of testing error
• Choose the right test for a hypothesis concerning a mean
• Explain how a correlation coefficient is tested
• Contrast parametric with non-parametric tests and recognise when each is appropriate

The Return and Risk of a Financial Portfolio

• Work out the asset weights giving the lowest-variance mix of two risky assets

Simulation of Financial Asset Prices and Returns

• Explain resampling techniques, the bootstrap among them
• Explain Monte Carlo simulation and what it is used for
• Explain historical simulation and how it is used in investing
• Contrast historical simulation with Monte Carlo simulation and with bootstrap resampling

Applications of Simple Linear Regression in Finance

• Set out what a simple linear regression assumes
• Explain what the intercept, slope and coefficient of determination mean
• Work out the standard error of estimate and explain what it shows
• Apply a regression model to produce a forecast
• Derive a stock's alpha and beta by regressing its excess returns on those of the market
• Explain what a simple linear regression's ANOVA table and F-statistic tell you

Introduction to Financial Data Science

• Explain which parts of fintech matter for collecting and analysing financial data
• Explain what is meant by machine learning, artificial intelligence and big data
• Explain how big data and data science are used in investment management
• Explain deep, supervised and unsupervised learning and how investment managers use them
• Explain how training works for large language models and the way they produce text
• Explain how investment managers put large language models and generative AI to use
• Explain where AI and large language models fall short or pose risks in investment work