Kaplan CFA Practice Exam Flashcards - Quantitative Methods and Portfolio Management

Exactly 160 vocabulary flashcards covering CFA candidate exam questions about quantitative methods, bond pricing, and hypothesis testing based on the provided practice quiz.

Roy's Safety-First Criterion

A portfolio selection strategy used to minimize the probability that the portfolio return will fall below a minimum acceptable threshold.

Power of the Test

The probability of correctly rejecting the null hypothesis when it is false, which can be increased by enlarging the sample size.

Nonparametric Tests

Statistical tests that do not rely on population parameters or specific distribution assumptions, often used for hypothesis testing involving performance ranks.

Safety-First Ratio (SFRatio)

$SFRatio = \frac{E(R_P) - R_L}{\sigma_P}$, where $E(R_P)$ is the expected return, $R_L$ is the threshold return, and $\sigma_P$ is the standard deviation.

Covariance of Random Variables

A measure of the joint variability of two random variables, defined as $Cov(X,Y) = E[(X - E(X))(Y - E(Y))]$.

Simple Random Sampling

A sampling method where every possible sample of a given size has an equal probability of being selected from the population.

Expected Return of an Equally Invested Portfolio

The weighted average of the expected returns of the individual assets, calculated as $\frac{E(R_A) + E(R_B)}{2}$ for a two-asset portfolio.

Winsorized Mean

A measure of central tendency calculated by replacing extreme outliers in a data set with the nearest value that is not an outlier.

Bond Yield to Maturity (YTM)

The internal rate of return earned by an investor who buys the bond today at the market price and holds it until maturity.

Sample Standard Deviation

A measure of the dispersion of a sample of data points around their mean, calculated as the square root of the sample variance $\sqrt{s^2}$.

Geometric Mean as a Measure of Central Tendency

The rate of return that matches the actual cumulative investment performance over time; it is always less than or equal to the arithmetic mean.

Null Hypothesis Significance

If a test statistic is less than the critical value in a two-tailed test, the analyst will fail to reject the null hypothesis.

Correlation Coefficient (r)

A standardized measure of the linear relationship between two variables, calculated as $r_{X,Y} = \frac{Cov(X,Y)}{\sigma_X \times \sigma_Y}$.

Optimal Portfolio (Roy's Criterion)

Under Roy's safety-first criteria, the portfolio that maximizes the safety-first ratio is considered optimal for a given threshold.

Covariance Calculation (Correlation)

The covariance derived from standard deviations and correlation: $Cov(C,D) = \rho_{C,D} \times \sigma_C \times \sigma_D$.

Type I Error

The error committed when a true null hypothesis is rejected.

Confidence Level

The probability that a true null hypothesis will not be rejected, calculated as $1 - \alpha$, where $\alpha$ is the significance level.

Cash Flow Additivity Principle

A principle stating that the present value of a series of future cash flows is the sum of the present values of each individual cash flow.

Present Value of an Annuity

The current value of a series of equal annual payments, calculated using a discount rate: $PV = \frac{PMT}{r} \times (1 - \frac{1}{(1+r)^n})$.

Geometric Return Formula

$R_G = [\prod (1 + R_t)]^{\frac{1}{n}} - 1$; it represents the compound growth rate of an investment.

Variance of a Discrete Random Variable

Calculated as $\sigma^2 = \sum [P(x_i) \times (x_i - E(X))^2]$.

Chi-Square Test

A statistical test primarily used to test hypotheses concerning the value of a population variance.

Geometric Mean of Appreciation

The average percentage change in asset value over multiple periods, accounting for compounding.

Expected Returns Derivation Limitation

While correlation and standard deviation can derive covariance, they cannot be used to derive expected returns of assets independently.

Compound Annual Growth Rate (CAGR)

The geometric mean return that provides the average annual growth rate of an investment over multiple years.

Percentile Calculation

The value below which a given percentage of observations in a group of observations falls; for example, the $70\text{th}$ percentile.

Portfolio Standard Deviation

Calculated as $\sigma_P = \sqrt{w_R^2 \sigma_R^2 + w_S^2 \sigma_S^2 + 2 w_R w_S \sigma_R \sigma_S \rho_{R,S}}$.

Two-Stock Portfolio Standard Deviation (Correlation)

The dispersion of a portfolio where negative correlation reduces overall risk more effectively than positive correlation.

Z-Distributed Test Statistic

In a two-tailed test at a $5\%$ level of significance, a z-statistic must exceed $1.96$ (absolute value) to reject the null hypothesis.

Threshold Return ($R_L$)

The minimum acceptable return used in Roy's safety-first criterion calculations to evaluate portfolio downside risk.

Zero-Coupon Bond Pricing

The value of a bond that pays no interest and is sold at a discount: $P = \frac{Face\,Value}{(1+r)^n}$.

Implied Forward Rate

The interest rate for a future period that is implied by the current spot interest rates of different maturities.

Kurtosis Measure of 4.2

An indication that a distribution is leptokurtic, meaning it has a higher probability of extreme upside and downside returns (fatter tails) than a normal distribution.

Geometric vs. Arithmetic Return Relationship

Except when all returns are equal, the geometric return is always lower than the arithmetic return due to volatility.

Arithmetic Mean Return

The simple average of a series of returns, calculated by summing all returns and dividing by the number of observations.

Gordon Growth Model (Implied Required Return)

$k = \frac{D_1}{P_0} + g$, where $k$ is the required return, $D_1$ is the next dividend, $P_0$ is the price, and $g$ is the growth rate.

Dividend Discount Model (DDM) Constants

Estimates an equity share's required rate of return as the sum of its dividend yield and its constant growth rate.

Portfolio's Expected Return (Three Assets)

The sum of the products of each asset's weight and its expected return: $E(R_P) = w_1 E(R_1) + w_2 E(R_2) + w_3 E(R_3)$.

Preferred Stock Valuation

The price of preferred stock calculated as the annual dividend divided by the required rate of return: $P = \frac{D}{k}$.

Alternative Hypothesis ($H_a$)

A statement that contradicts the null hypothesis; for a 'different from' test, it is two-sided ($H_a: \mu \neq \mu_0$).

Correlation Coefficient ($r_{A,B}$)

The ratio of the covariance of two variables to the product of their standard deviations: $r = \frac{Cov_{A,B}}{\sigma_A \sigma_B}$.

Inverse Price-Yield Relationship

The fundamental bond market principle that bond prices increase when market yields to maturity decrease.

Current Market Value (Coupon Bond)

The present value of all future interest payments plus the present value of the par value, discounted at the market interest rate.

Test Statistic for the Mean

Calculated as $Z = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}$, where $\bar{X}$ is the sample mean and $s/\sqrt{n}$ is the standard error.

Annualized Rate of Return (Zero-Coupon)

The geometric rate of return for a bond that matures without coupons: $r = (\frac{FV}{PV})^{\frac{1}{n}} - 1$.

Expected Coefficient of Variation (CV)

A measure of relative risk, calculated as the standard deviation divided by the expected return: $CV = \frac{\sigma}{E(R)}$.

Present Value of $500

The current value of a single future payment: $PV = \frac{500}{(1+r)^n}$.

Type II Error Definition

Failing to reject a null hypothesis that is actually false.

Significance Level Risk

The probability of committing a Type I error, which is rejecting a null hypothesis that is actually true.

5% Trimmed Mean

A mean calculated by excluding the top $2.5\%$ and the bottom $2.5\%$ of all observations.

Negative Skewness Tails

A distribution where the mass of the distribution is concentrated on the right, resulting in a long tail on the left side.

Power of the Test Definition

The specific probability of rejecting the null hypothesis when the alternative hypothesis is true.

Present Value of Variable Cash Flows

Calculated by discounting each individual annual cash flow back to time zero and summing them.

Positively Skewed Central Tendency

The relationship where $Mean > Median > Mode$ due to a long right tail.

Negative Linear Association

Indicated by a negative correlation coefficient, meaning that as one variable increases, the other tends to decrease linearly.

Variance of a Two-Asset Portfolio

$\sigma_P^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \sigma_A \sigma_B \rho_{A,B}$.

Coefficient of Variation Formula

A ratio measuring the risk per unit of return: $CV = \frac{\sigma}{\bar{X}} \times 100\%$, often using the square root of variance for $\sigma$.

Interquartile Range (IQR)

The distance between the first quartile ($Q_1$) and the third quartile ($Q_3$), representing the middle $50\%$ of the data.

Perpetual Bond Price

Calculated as the annual interest payment divided by the market yield: $P = \frac{I}{r}$, assuming no maturity.

Value of a Coupon Bond

The present value of the stream of annual interest payments and the principal return at the bond's yield to maturity.

One-Tailed Z-Test Rejection

At a $5\%$ significance level, a true null hypothesis will be rejected $5\%$ of the time.

Mean Absolute Deviation (MAD)

The average of the absolute differences between each data point and the arithmetic mean: $MAD = \frac{\sum |X_i - \bar{X}|}{n}$.

Two-Stock Portfolio Standard Deviation Calculation

Calculating the portfolio risk using two stock weights, their standard deviations, and their correlation coefficient.

Required Return on Equity (Gordon Growth)

Calculated as $k = \frac{D_0 \times (1 + g)}{P} + g$ when starting with the most recent dividend ($D_0$).

Annualized Yield of Zero-Coupon Bond

The interest rate earned per year on a bond that does not pay coupons, often calculated with annual compounding.

Leptokurtic Distribution Definition

A distribution that is more peaked and has fatter tails than a normal distribution, with positive excess kurtosis.

Third Quartile ($Q_3$)

The value at or below which $75\%$ of all observations in a data set fall.

Safety-First Return Optimization

Selecting the portfolio with the highest safety-first ratio for a specific minimum acceptable return ($R_L$).

Sample Standard Deviation of Asset Returns

The square root of the sum of squared deviations from the mean divided by $n-1$ for a given set of returns.

Portfolio Selection (Risk-Free Rate = 3%)

Assessing the probability that returns fall below a threshold ($5\%$) using safety-first ratios.

Significance Level (Alpha)

The probability of a Type I error set by the researcher before the test.

Expected Return (Portfolio Weights)

The sum of weighted expected returns for multiple stocks in a single portfolio.

Equivalent Compound Annual Rate

The single annual rate of return that would produce the same total growth as a series of different annual returns.

No-Arbitrage Principle

The logic that two assets with identical future cash flows must have the same price, leading investors to buy the underpriced one.

Performance Rank Hypothesis Test

A test used to determine if performance in one period correlates with performance in another, typically a nonparametric test.

Sample Variance of ROE

The measurement of the spread of Return on Equity data from its mean, calculated using $\frac{\sum (X_i - \bar{X})^2}{n-1}$.

Excess Kurtosis

The difference between a distribution's kurtosis and the kurtosis of a normal distribution (which is $3$).

Sixty-Fifth Percentile Definition

The point where $65\%$ of all observations are below that specific value.

F-Statistic Utility

A test statistic used to compare the variances of two different populations.

Sample Standard Deviation (10-year Fund)

The measure of volatility calculated for a fund's annual returns over a decade.

Yield to Maturity Calculation (Price < Par)

When a bond is priced below its face value, its yield to maturity must be greater than its coupon rate.

Expected Return for a Probability Distribution

$E(R) = \sum [P(scenario_i) \times R_i]$.

Covariance of Random Variables X and Y

$Cov(X,Y) = E(XY) - E(X)E(Y)$, representing the linear relationship between the variables.

Portfolio Optimization (Roy's Criterion 3%)

Selecting the portfolio with the highest ratio relative to a $3\%$ threshold return.

Positively Skewed Distribution (Mean-Median)

A distribution where the mean is pulled right by outliers, making it larger than the median.

Positive Excess Kurtosis Distribution Shape

Characterized by a more peaked shape and fatter tails compared to a normal distribution.

Present Value of Uneven Cash Stream

The sum of individual cash flows each divided by $(1+r)^t$ for its respective time period $t$. defense.

Two-Tailed Test tail Choice

A test used when the alternative hypothesis specifies that a parameter is simply 'not equal to' a hypothesized value.

Gordon Growth Model Requirement

Requires estimating the dividend to be received next year ($D_1$) and a constant growth rate ($g$).

Type I Error in Hypothesis Testing

Occurs when a researcher rejects a null hypothesis that is true.

Relative Risk Measure

The coefficient of variation ($CV = \sigma/\mu$), used to compare the risk of different securities.

Type II Error in Hypothesis Testing

Occurs when a researcher fails to reject a null hypothesis that is false.

Pure Discount Instrument Price Calculation

$PV = \frac{FV}{(1+r)^n}$ for a single payment at maturity.

Average Compound Annual Rate (4 Years)

The geometric mean of four annual percentage returns.

Standard Deviation of Expected Returns (Events)

The square root of the variance, where variance is $\sum P_i (R_i - E(R))^2$ for multiple economic events.

Type I Error Medical Example

Rejecting the hypothesis that a condition exists (Appendicitis) when it is actually true (though the example logic focuses on the error of action).

Portfolio Standard Deviation (Economic States)

Risk calculated by weighting squared deviations from the expected return across boom and bust scenarios.

Type I vs Type II Error Result

Rejecting a mean length of 18 inches when it is actually 17.8 inches (rejecting a false null) is not an error, but the prompt explores error outcomes.

Test Statistic Calculation (CFA Starting Salary)

$Z = \frac{64,000 - 59,000}{5,500 / \sqrt{135}}$, comparing sample mean to hypothesized mean.

Perfectly Negatively Correlated Portfolio (Standard Deviation)

$\sigma_P = |w_A \sigma_A - w_B \sigma_B|$; risk is minimized or potentially eliminated.