CFA Level 1: Quantitative Methods, Economics, and Corporate Issuers

Comprehensive practice flashcards covering Quantitative Methods, Economics, and Corporate Issuers for the CFA Level 1 2026 exam.

What are the three components of a stated interest rate?

A real risk-free rate, an expected inflation rate, and a risk premium.

How is the nominal risk-free rate calculated?

$$\text{Nominal risk-free rate} = \text{real risk-free rate} + \text{expected inflation rate}$$

Define Default Risk.

The risk that a borrower will not make the promised payments on a timely basis.

Define Liquidity Risk.

The risk of receiving less than fair value for an investment if it must be sold quickly for cash.

Define Maturity Risk.

The risk that the prices of longer-term bonds are more volatile than those of shorter-term bonds.

What is the formula for the Effective Annual Rate ($EAR$) given a stated annual rate and compounding frequency ($m$)?

$$EAR = (1 + \frac{\text{stated rate}}{m})^m - 1$$

In the Future Value ($FV$) formula, what does $n$ represent?

The number of compounding periods.

What is the formula for continuous compounding future value?

$$FV = PV \times e^{r \times t}$$

What is an annuity?

A finite set of equal cash flows occurring at equal intervals over a defined period.

What is the difference between an ordinary annuity and an annuity due?

In an ordinary annuity, cash flows occur at the end of each period; in an annuity due, they occur at the beginning.

Define a perpetuity.

A series of equal cash flows expected to continue indefinitely into the future.

What is the formula for the present value of a perpetuity?

$$PV_{perpetuity} = \frac{PMT}{r}$$

What happens to the present value ($PV$) when the discount rate ($r$) increases?

The present value decreases.

What is the 'Net Present Value' ($NPV$)?

The sum of the present values of all expected incremental cash flows of a project.

Define the 'Internal Rate of Return' ($IRR$).

The discount rate that makes the $NPV$ of a series of cash flows equal to zero.

What is the Money-Weighted Rate of Return?

The internal rate of return calculated on a portfolio based on all its actual cash inflows and outflows.

Define the Time-Weighted Rate of Return.

A measure of compound growth; it is the geometric mean of a series of return periods, unaffected by cash inflows or outflows.

What is a 'Descriptive Statistic'?

A summary of data that characterizes its important features, such as mean or variance.

Define 'Inferential Statistics'.

The process of making forecasts, estimates, or judgments about a large data set based on a smaller sample.

What is the 'Geometric Mean' formula?

$$G = \sqrt[n]{x_1 \times x_2 \times \dots \times x_n}$$

What is the 'Arithmetic Mean' formula?

$$\mu = \frac{\sum x_i}{n}$$

Define 'Skewness'.

A measure of the degree to which a distribution is not symmetric around its mean.

Define 'Kurtosis'.

A measure of the degree to which a distribution is more or less 'peaked' than a normal distribution.

What is 'Leptokurtic'?

A distribution that is more peaked than a normal distribution (excess kurtosis > 0).

What is 'Platykurtic'?

A distribution that is less peaked (flatter) than a normal distribution.

Define 'Variance'.

The average of the squared deviations from the mean.

Define 'Standard Deviation'.

The positive square root of the variance.

What is the 'Coefficient of Variation' ($CV$)?

$CV = \frac{s}{\bar{x}}$, measuring the amount of risk per unit of return.

Define 'Probability'.

The likelihood of an event occurring, expressed as a number between 0 and 1.

Contrast 'Empirical Probability' and 'Subjective Probability'.

Empirical is based on historical data; subjective is based on personal judgment or experience.

What are 'Mutually Exclusive Events'?

Events that cannot happen at the same time.

What is the 'Addition Rule' for non-mutually exclusive events?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

What is the 'Multiplication Rule' for independent events?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Define 'Conditional Probability'.

The probability of event A occurring given that event B has occurred, denoted $P(A|B)$.

What is 'Bayes' Theorem'?

A method to update the probability of a hypothesis as more evidence or information becomes available; $P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}$.

Define a 'Binomial Distribution'.

A probability distribution of the number of successes in a fixed number of independent trials with a constant probability of success.

What is a 'Normal Distribution'?

A symmetric, bell-shaped distribution defined by its mean ($\mu$) and variance ($\sigma^2$).

Approximately what percentage of observations fall within one standard deviation of the mean in a normal distribution?

$$68\%$$

Approximately what percentage of observations fall within two standard deviations of the mean in a normal distribution?

$$95\%$$

What is a 'Standard Normal Distribution'?

A normal distribution with a mean of 0 and a standard deviation of 1.

Define 'Z-score'.

The number of standard deviations an observation is from the mean; $z = \frac{x - \mu}{\sigma}$.

What is 'Shortfall Risk'?

The probability that the value of a portfolio will fall below a minimum acceptable target level.

Define 'Simple Random Sampling'.

A sampling method where every item in the population has the same probability of being selected.

Define 'Stratified Random Sampling'.

Dividing the population into subpopulations (strata) based on specific characteristics and sampling from each.

What is the 'Central Limit Theorem'?

States that the distribution of sample means will be approximately normal if the sample size is sufficiently large, regardless of the population's distribution.

Define 'Standard Error of the Sample Mean'.

The standard deviation of the distribution of the sample mean; $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$.

Define 'Confidence Interval'.

A range of values within which a population parameter is expected to fall with a specific level of probability.

What is 'Data Mining Bias'?

Bias introduced by repeatedly searching a dataset for patterns until a statistically significant one is found.

What is 'Survivorship Bias'?

A bias caused by including only entities that have 'survived' to the end of the period, ignoring those that were removed.

Define a 'Null Hypothesis' ($H_0$).

The hypothesis the researcher wants to reject; usually represents the status quo or 'no effect'.

Define an 'Alternative Hypothesis' ($H_a$).

The hypothesis that is accepted if there is sufficient evidence to reject the null hypothesis.

What is a 'Type I Error'?

Rejecting a true null hypothesis (false positive).

What is a 'Type II Error'?

Failing to reject a false null hypothesis (false negative).

Define 'Significance Level' ($\alpha$).

The probability of committing a Type I error.

Define 'P-value'.

The smallest level of significance at which the null hypothesis can be rejected.

When is a 't-test' used instead of a 'z-test'?

When the population variance is unknown and the sample size is small, or for any sample from a normal population with unknown variance.

What is 'Correlation'?

A measure of the linear relationship between two variables, ranging from -1 to +1.

Define 'Spurious Correlation'.

A correlation that is either the result of chance or produced by a third variable, rather than a direct relationship.

Define 'Elasticity' in economics.

A measure of the sensitivity of one variable to changes in another variable.

What is the formula for 'Price Elasticity of Demand'?

$$\frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$$

What is 'Inelastic Demand'?

When the absolute value of the price elasticity of demand is less than 1.

What is 'Elastic Demand'?

When the absolute value of the price elasticity of demand is greater than 1.

Define 'Unitary Elastic Demand'.

When the percentage change in quantity demanded is exactly equal to the percentage change in price (elasticity = 1).

What is the 'Substitution Effect'?

The change in consumption resulting from a change in relative price, holding utility constant.

What is the 'Income Effect'?

The change in consumption resulting from a change in real income or purchasing power caused by a price change.

Define a 'Normal Good'.

A good for which demand increases as income increases (positive income elasticity).

Define an 'Inferior Good'.

A good for which demand decreases as income increases (negative income elasticity).

What is a 'Giffen Good'?

An inferior good for which the negative income effect outweighs the substitution effect, leading to an increase in demand when price increases.

What is a 'Veblen Good'?

A good for which demand increases as price increases because of its status symbol or 'snob' appeal.

Define 'Marginal Cost' ($MC$).

The increase in total cost resulting from producing one additional unit of output.

What are 'Economies of Scale'?

Reductions in average cost that occur as a firm increases its scale of production in the long run.

Define 'Perfect Competition'.

A market structure with many small firms, identical products, no barriers to entry, and perfectly elastic demand for individual firms.

Define 'Monopoly'.

A market structure where a single firm produces a product with no close substitutes and high barriers to entry.

Define 'Oligopoly'.

A market structure with a few large firms that are interdependent and have significant barriers to entry.

Define 'Monopolistic Competition'.

A market structure with many firms selling differentiated products and low barriers to entry.

What is a 'Natural Monopoly'?

A situation where economies of scale are so large that a single firm can supply the entire market at a lower cost than multiple firms.

What is the 'GDP Deflator'?

A price index used to convert nominal GDP into real GDP; $\frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100$.

Define 'Gross Domestic Product' ($GDP$).

The total market value of all final goods and services produced within a country's borders in a specific period.

What is the 'Expenditure Approach' to GDP?

$GDP = C + I + G + (X - M)$ (Consumption + Investment + Government Spending + Net Exports).

Define 'Personal Income'.

The total income received by households from all sources.

Define 'Aggregate Demand' ($AD$).

The total quantity of goods and services demanded in an economy at different price levels.

Define 'Aggregate Supply' ($AS$).

The total quantity of goods and services produced in an economy at different price levels.

What causes a shift in the Aggregate Demand curve?

Changes in household wealth, consumer expectations, investment, or fiscal and monetary policy.

What is the 'Fisher Effect'?

The theory that the nominal interest rate is the sum of the real interest rate and expected inflation.

Define 'Stagflation'.

An economic condition characterized by high inflation and high unemployment (stagnant growth).

What are the three types of unemployment?

Frictional, Structural, and Cyclical.

Define 'Inflation'.

A persistent increase in the general price level of goods and services.

Define 'Deflation'.

A persistent decrease in the general price level (negative inflation).

What is the 'Consumer Price Index' ($CPI$)?

A measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods.

Define 'Cost-Push Inflation'.

Inflation resulting from an increase in the costs of production, such as wages or raw materials.

Define 'Demand-Pull Inflation'.

Inflation resulting from an increase in aggregate demand that exceeds the economy's productive capacity.

What is 'Fiscal Policy'?

Government use of spending and taxation to influence the economy.

What is 'Monetary Policy'?

Central bank actions that influence the quantity of money and credit in the economy.

What are the three main tools of the Federal Reserve?

Open market operations, the discount rate, and reserve requirements.

Define 'Expansionary Monetary Policy'.

Actions taken to increase the money supply and lower interest rates to stimulate economic growth.

Define 'Contractionary Monetary Policy'.

Actions taken to decrease the money supply or raise interest rates to slow inflation.

What is a 'Budget Deficit'?

When government spending exceeds tax revenue.

What is a 'Budget Surplus'?

When tax revenue exceeds government spending.

Define 'Ricardian Equivalence'.

The theory that consumers anticipate future taxes to pay for current government debt, so they increase savings and offset the deficit spending.

What is an 'Exchange Rate'?

The price of one currency in terms of another.