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Quantitative Methods - PR

Quantitative Methods

Economics - PR

Economics

Portfolio Management (Part One)

Corporate Issuers

Financial Statement Analysis - PR

Financial Statement Analysis

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Fixed Income

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Alternative Investments

Portfolio Management (Part Two)

Ethics

PR1. Interest Rates, Present Value, and Future Value

  • a. interpret interest rates as required rates of return, discount rates, or opportunity costs
  • b. explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk
  • c. calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows
  • d. demonstrate the use of a time line in modeling and solving time value of money problems
  • e. calculate the solution for time value of money problems with different frequencies of compounding
  • f. calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding

PR2. Organizing, Visualizing, and Describing Data

  • a. identify and compare data types
  • b. describe how data are organized for quantitative analysis
  • c. interpret frequency and related distributions
  • d. interpret a contingency table
  • e. describe ways that data may be visualized and evaluate uses of specific visualizations
  • f. describe how to select among visualization types
  • g. calculate and interpret measures of central tendency
  • h. evaluate alternative definitions of mean to address an investment problem
  • i. calculate quantiles and interpret related visualizations
  • j. calculate and interpret measures of dispersion
  • k. calculate and interpret target downside deviation

PR3. Probability Concepts

  • a. define a random variable, an outcome, and an event
  • b. identify the two defining properties of probability, including mutually exclusive and exhaustive events, and compare and contrast empirical, subjective, and a priori probabilities
  • c. describe the probability of an event in terms of odds for and against the event
  • d. calculate and interpret conditional probabilities
  • e. demonstrate the application of the multiplication and addition rules for probability
  • f. compare and contrast dependent and independent events
  • g. calculate and interpret an unconditional probability using the total probability rule
  • h. identify the most appropriate method to solve a particular counting problem and analyze counting problems using factorial, combination, and permutation concepts

PR4. Common Probability Distributions

  • a. define a probability distribution and compare and contrast discrete and continuous random variables and their probability functions
  • b. calculate and interpret probabilities for a random variable given its cumulative distribution function
  • c. describe the properties of a discrete uniform random variable, and calculate and interpret probabilities given the discrete uniform distribution function
  • d. describe the properties of the continuous uniform distribution, and calculate and interpret probabilities given a continuous uniform distribution
  • e. describe the properties of a Bernoulli random variable and a binomial random variable, and calculate and interpret probabilities given the binomial distribution function
  • f. explain the key properties of the normal distribution
  • g. contrast a multivariate distribution and a univariate distribution, and explain the role of correlation in the multivariate normal distribution
  • h. calculate the probability that a normally distributed random variable lies inside a given interval
  • i. explain how to standardize a random variable
  • j. calculate and interpret probabilities using the standard normal distribution
  • k. describe the properties of the Student�s t-distribution, and calculate and interpret its degrees of freedom
  • l. describe the properties of the chi-square distribution and the F-distribution, and calculate and interpret their degrees of freedom

PR5. Sampling and Estimation

  • a. identify and describe desirable properties of an estimator
  • b. contrast a point estimate and a confidence interval estimate of a population parameter
  • c. calculate and interpret a confidence interval for a population mean, given a normal distribution with 1) a known population variance, 2) an unknown population variance, or 3) an unknown population variance and a large sample size
  • d. describe the issues regarding selection of the appropriate sample size, data snooping bias, sample selection bias, survivorship bias, look-ahead bias, and time-period bias

PR6. Basics of Hypothesis Testing

  • a. define a hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null and alternative hypothesis
  • b. compare and contrast one-tailed and two-tailed tests of hypotheses
  • c. explain a test statistic, Type I and Type II errors, a significance level, how significance levels are used in hypothesis testing, and the power of a test
  • d. explain a decision rule and the relation between confidence intervals and hypothesis tests, and determine whether a statistically significant result is also economically meaningful
  • e. explain and interpret the p-value as it relates to hypothesis testing
  • f. describe how to interpret the significance of a test in the context of multiple tests
  • g. identify the appropriate test statistic and interpret the results for a hypothesis test concerning the population mean of both large and small samples when the population is normally or approximately normally distributed and the variance is (1) known or (2) unknown
  • h. identify the appropriate test statistic and interpret the results for a hypothesis test concerning the equality of the population means of two at least approximately normally distributed populations based on independent random samples with equal assumed variances
  • i. identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations
  • j. identify the appropriate test statistic and interpret the results for a hypothesis test concerning (1) the variance of a normally distributed population and (2) the equality of the variances of two normally distributed populations based on two independent random samples

PR7. Appendices

  • a. Cumulative Probabilities for a Standard Normal Distribution
  • b. Table of the Student�s t-Distribution (One-Tailed Probabilities)
  • c. Values of X2 (Degrees of Freedom, Level of Significance)
  • d. Table of the F-Distribution

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