II. QUANTITATIVE METHODS
К оглавлению1 2 3 4 5 6 7 8 9 10 11A. Time Value of Money
1. Future value of a single cash flow
a. Calculating the future value of a single cash flow
b. Frequency of compounding
c. Continuous compounding
d. Annual and effective interest rates
2. Future value of a series of cash flows
a. Equal cash flows
(1) Ordinary annuity
(2) Annuity due
b. Unequal cash flows
3. Present value of a single cash flow
a. Calculating the present value of a single cash flow
b. Frequency of compounding
4. Present value of a series of cash flows
a. Calculating the present value of a series of equal cash flows
(1) Ordinary annuity
(2) Annuity due
b. Present value of a series of unequal cash flows
c. Present value of an infinite series of equal cash flows (perpetuity)
5. Equivalence of present and future value
6. Other applications of the time value of money
a. Solving for interest rates and growth rates
b. Solving for the number of periods
c. Solving for the size of annuity payments
7. Discounted cash flow analysis
a. Net present value rule
b. Internal rate of return rule
c. Problems with the internal rate of return rule
8. Simple interest and money-market conventions
a. Bank-discount yield
b. Periodic yield
c. Bond-equivalent yield
d. Effective annual yield
e. CD-equivalent yield
9. Investment measures of return
a. Dollar-weighted rate of return
b. Time-weighted rate of return
B. Basic Statistical Concepts
1. Nature of statistics
a. Populations and samples
b. Types of statistical data
(1) Nominal data
(2) Ordinal data
(3) Interval data
(4) Ratio data
2. Frequency distributions
3. Measures of central tendency
a. Population mean
b. Sample mean
c. Median
d. Mode
e. Quartiles, quintiles, deciles, and percentiles
f. Weighted mean
g. Geometric mean
(1) Geometric mean return
(2) Relationship to arithmetic mean return
4. Measures of dispersion
a. Measures of absolute dispersion
(1) Range
(2) Mean absolute deviation
(3) Variance and standard deviation
(a) Population variance and standard deviation
(b) Sample variance and standard deviation
b. Relative dispersion
5. Measures of skewness
6. Measures of kurtosis
C. Probability Concepts and Random Variables
1. Probability concepts
a. Definitions, including outcome, event, sample space, and mutually exclusive
b. Objective probability
(1) Classical probability
(2) Empirical concept
(3) Subjective probability
2. Methods of counting
a. Multiplication rule of counting
b. Factorial rule
c. Permutation rule
d. Combination rule
3. Random variables and probability
a. Random variable
b. Univariate probability distribution
c. Discrete versus continuous random variables
d. Probability density function
e. Cumulative density function
4. Probability theorems/axioms
a. The complement rule
b. The special rule of addition
c. General rule of addition
d. Rule of multiplication
(1) Independent events
(2) Dependent events
(3) Decision trees
(4) Bayes’ Theorem
5. Expected value, variance, and covariance/correlation
a. Expected value
(1) Random variable
(2) Constant times a random variable
(3) Sum of random variables
(4) Weighted sum
b. Multivariate probability distribution
c. Variance
(1) Random variable
(2) Constant times a random variable
(3) Random variable plus a constant
d. Covariance
(1) Between two random variables
(2) Constant times a random variable
e. Correlation coefficient between two random variables
f. Covariance among more than two random variables
6. Standardized random variables
D. Common Probability Distributions
1. Discrete random variables
a. Discrete uniform distribution
b. Binomial distribution
c. Expected value and variance of a binomial random variable
2. Continuous probability distributions
a. Uniform distribution
b. Normal distribution
c. Standard normal distribution
d. Cumulative density for the standard normal distribution
e. Finding standard normal distribution areas
f. Confidence intervals
g. Mean-variance portfolio selection
h. Monte Carlo simulation
3. Lognormal distribution
a. Lognormal stock prices
b. Price relatives
E. Sampling and Estimation
1. Random samples
a. Sampling in investment analysis
b. Time series and cross-sectional data
c. Data-snooping bias
d. Sample selection bias
(1) Survivorship bias
(2) Delisting bias
2. Distribution of the sample mean
3. Point and interval estimates of the population mean
a. Point estimators
b. Confidence intervals when sampling from a normal distribution with known
variance
c. Confidence intervals when sampling from a normal distribution with unknown
variance
d. Using t distribution tables
e. Confidence intervals when sampling from a non-normal population
F. Statistical Inference and Hypothesis Testing
1. Establishing hypotheses
a. Null hypothesis
b. Alternative hypothesis
2. Testing hypotheses
a. Test criterion
b. Two-tail tests
c. One-tail tests
d. Type I error (rejecting a true null hypothesis)
e. Type II error (failing to reject a false null hypothesis)
3. Types of hypothesis testing
a. Testing the mean of a single sample when the population standard deviation is not
known
b. Testing the difference between the population means of two samples
(1) Population variances are known
(2) Population variances are not known but assumed equal
(3) Dependent samples: paired data
c. Testing the proportion of a single sample: significance tests with small samples
d. Significance tests and confidence intervals for a single variance
(1) Confidence interval for the sample variance
(2) Hypothesis test about a single population variance
(3) Testing the equality of two variances: the F-distribution
4. Analysis of variance (ANOVA)
a. Single-Factor analysis of variance
b. F-test for equality of factor-level means
c. Computing sums of squares
d. Degrees of freedom
G. Correlation Analysis and Linear Regression
1. Correlation analysis
a. Scatter plots and correlation analysis
b. Computing the correlation coefficient
c. Testing the significance of the correlation coefficient
2. Linear regression
a. Linear regression with one independent variable
b. Assumptions of the linear regression model
c. Standard error of estimate
d. Coefficient of determination
e. Confidence intervals and testing hypotheses
(1) Significance level
(2) Standard error of the estimated coefficient
(3) Critical value for rejecting the null hypothesis
f. Prediction intervals
g. Limitations to regression analysis
H. Multivariate Regression
1. Multiple linear regression
a. Assumptions of the multiple linear regression model
b. Standard error of estimate in multiple linear regression
c. Predicting the dependent variable in a multiple regression model
d. Testing whether all the regression coefficients are equal to zero
2. Using dummy variables in regressions
3. Heteroskedasticity
a. Types of heteroskedasticity
b. Tests that evaluate heteroskedasticity
c. Correcting for heteroskedasticity
4. Serial correlation and Durbin-Watson test
a. Consequences of serial correlation
b. Durbin-Watson statistic to test for serial correlation
c. Correcting for serial correlation
d. Generalized least squares
5. Multicollinearity
6. Models with qualitative dependent variables
I. Time Series Analysis
1. Trends
2. Limitations to trends
3. Fundamental issues in time series
4. Autoregressive time series models
a. Mean reversion
b. Multiperiod forecasts
c. Instability of regression coefficients
5. Random walks and unit roots
6. Moving-average time series models
a. Smoothing past values with a moving average
b. Moving average models for forecasting
7. Seasonality in time-series models
J. Portfolio Concepts
1. Optimal portfolios with three assets
2. Minimum Variance Frontier for many assets
3. Instability in the Minimum Variance Frontier
4. Diversification and portfolio size
5. Risk free assets and the trade-off between risk and return
6. The Capital Allocation Line
7. The Capital Asset Pricing Model (CAPM)
8. Estimates based on historical means, variances and covariances
9. The Market Model
10. Adjusted-beta Market Models
11. The structure of factor models
12. Arbitrage Pricing Theory (APT) and the factor model
13. Multifactor models in current practice
A. Time Value of Money
1. Future value of a single cash flow
a. Calculating the future value of a single cash flow
b. Frequency of compounding
c. Continuous compounding
d. Annual and effective interest rates
2. Future value of a series of cash flows
a. Equal cash flows
(1) Ordinary annuity
(2) Annuity due
b. Unequal cash flows
3. Present value of a single cash flow
a. Calculating the present value of a single cash flow
b. Frequency of compounding
4. Present value of a series of cash flows
a. Calculating the present value of a series of equal cash flows
(1) Ordinary annuity
(2) Annuity due
b. Present value of a series of unequal cash flows
c. Present value of an infinite series of equal cash flows (perpetuity)
5. Equivalence of present and future value
6. Other applications of the time value of money
a. Solving for interest rates and growth rates
b. Solving for the number of periods
c. Solving for the size of annuity payments
7. Discounted cash flow analysis
a. Net present value rule
b. Internal rate of return rule
c. Problems with the internal rate of return rule
8. Simple interest and money-market conventions
a. Bank-discount yield
b. Periodic yield
c. Bond-equivalent yield
d. Effective annual yield
e. CD-equivalent yield
9. Investment measures of return
a. Dollar-weighted rate of return
b. Time-weighted rate of return
B. Basic Statistical Concepts
1. Nature of statistics
a. Populations and samples
b. Types of statistical data
(1) Nominal data
(2) Ordinal data
(3) Interval data
(4) Ratio data
2. Frequency distributions
3. Measures of central tendency
a. Population mean
b. Sample mean
c. Median
d. Mode
e. Quartiles, quintiles, deciles, and percentiles
f. Weighted mean
g. Geometric mean
(1) Geometric mean return
(2) Relationship to arithmetic mean return
4. Measures of dispersion
a. Measures of absolute dispersion
(1) Range
(2) Mean absolute deviation
(3) Variance and standard deviation
(a) Population variance and standard deviation
(b) Sample variance and standard deviation
b. Relative dispersion
5. Measures of skewness
6. Measures of kurtosis
C. Probability Concepts and Random Variables
1. Probability concepts
a. Definitions, including outcome, event, sample space, and mutually exclusive
b. Objective probability
(1) Classical probability
(2) Empirical concept
(3) Subjective probability
2. Methods of counting
a. Multiplication rule of counting
b. Factorial rule
c. Permutation rule
d. Combination rule
3. Random variables and probability
a. Random variable
b. Univariate probability distribution
c. Discrete versus continuous random variables
d. Probability density function
e. Cumulative density function
4. Probability theorems/axioms
a. The complement rule
b. The special rule of addition
c. General rule of addition
d. Rule of multiplication
(1) Independent events
(2) Dependent events
(3) Decision trees
(4) Bayes’ Theorem
5. Expected value, variance, and covariance/correlation
a. Expected value
(1) Random variable
(2) Constant times a random variable
(3) Sum of random variables
(4) Weighted sum
b. Multivariate probability distribution
c. Variance
(1) Random variable
(2) Constant times a random variable
(3) Random variable plus a constant
d. Covariance
(1) Between two random variables
(2) Constant times a random variable
e. Correlation coefficient between two random variables
f. Covariance among more than two random variables
6. Standardized random variables
D. Common Probability Distributions
1. Discrete random variables
a. Discrete uniform distribution
b. Binomial distribution
c. Expected value and variance of a binomial random variable
2. Continuous probability distributions
a. Uniform distribution
b. Normal distribution
c. Standard normal distribution
d. Cumulative density for the standard normal distribution
e. Finding standard normal distribution areas
f. Confidence intervals
g. Mean-variance portfolio selection
h. Monte Carlo simulation
3. Lognormal distribution
a. Lognormal stock prices
b. Price relatives
E. Sampling and Estimation
1. Random samples
a. Sampling in investment analysis
b. Time series and cross-sectional data
c. Data-snooping bias
d. Sample selection bias
(1) Survivorship bias
(2) Delisting bias
2. Distribution of the sample mean
3. Point and interval estimates of the population mean
a. Point estimators
b. Confidence intervals when sampling from a normal distribution with known
variance
c. Confidence intervals when sampling from a normal distribution with unknown
variance
d. Using t distribution tables
e. Confidence intervals when sampling from a non-normal population
F. Statistical Inference and Hypothesis Testing
1. Establishing hypotheses
a. Null hypothesis
b. Alternative hypothesis
2. Testing hypotheses
a. Test criterion
b. Two-tail tests
c. One-tail tests
d. Type I error (rejecting a true null hypothesis)
e. Type II error (failing to reject a false null hypothesis)
3. Types of hypothesis testing
a. Testing the mean of a single sample when the population standard deviation is not
known
b. Testing the difference between the population means of two samples
(1) Population variances are known
(2) Population variances are not known but assumed equal
(3) Dependent samples: paired data
c. Testing the proportion of a single sample: significance tests with small samples
d. Significance tests and confidence intervals for a single variance
(1) Confidence interval for the sample variance
(2) Hypothesis test about a single population variance
(3) Testing the equality of two variances: the F-distribution
4. Analysis of variance (ANOVA)
a. Single-Factor analysis of variance
b. F-test for equality of factor-level means
c. Computing sums of squares
d. Degrees of freedom
G. Correlation Analysis and Linear Regression
1. Correlation analysis
a. Scatter plots and correlation analysis
b. Computing the correlation coefficient
c. Testing the significance of the correlation coefficient
2. Linear regression
a. Linear regression with one independent variable
b. Assumptions of the linear regression model
c. Standard error of estimate
d. Coefficient of determination
e. Confidence intervals and testing hypotheses
(1) Significance level
(2) Standard error of the estimated coefficient
(3) Critical value for rejecting the null hypothesis
f. Prediction intervals
g. Limitations to regression analysis
H. Multivariate Regression
1. Multiple linear regression
a. Assumptions of the multiple linear regression model
b. Standard error of estimate in multiple linear regression
c. Predicting the dependent variable in a multiple regression model
d. Testing whether all the regression coefficients are equal to zero
2. Using dummy variables in regressions
3. Heteroskedasticity
a. Types of heteroskedasticity
b. Tests that evaluate heteroskedasticity
c. Correcting for heteroskedasticity
4. Serial correlation and Durbin-Watson test
a. Consequences of serial correlation
b. Durbin-Watson statistic to test for serial correlation
c. Correcting for serial correlation
d. Generalized least squares
5. Multicollinearity
6. Models with qualitative dependent variables
I. Time Series Analysis
1. Trends
2. Limitations to trends
3. Fundamental issues in time series
4. Autoregressive time series models
a. Mean reversion
b. Multiperiod forecasts
c. Instability of regression coefficients
5. Random walks and unit roots
6. Moving-average time series models
a. Smoothing past values with a moving average
b. Moving average models for forecasting
7. Seasonality in time-series models
J. Portfolio Concepts
1. Optimal portfolios with three assets
2. Minimum Variance Frontier for many assets
3. Instability in the Minimum Variance Frontier
4. Diversification and portfolio size
5. Risk free assets and the trade-off between risk and return
6. The Capital Allocation Line
7. The Capital Asset Pricing Model (CAPM)
8. Estimates based on historical means, variances and covariances
9. The Market Model
10. Adjusted-beta Market Models
11. The structure of factor models
12. Arbitrage Pricing Theory (APT) and the factor model
13. Multifactor models in current practice