Quantitative Methods Application
　　This study session introduces some of the discrete and continuous probability dis?tributions most commonly used to describe the behavior of random variables. Probability theory and calculations are widely used in finance, for example, in the field of investment and project valuation and in financial risk management.
　　Furthermore, this session explains how to estimate different parameters (e.g., mean and standard deviation) of a population if only a sample, rather than the whole population, can be observed. Hypothesis testing is a closely related topic. This session presents techniques that are used to accept or reject an assumed hypothesis (null hypothesis) about various parameters of a population.
　　The final reading introduces the fundamentals of technical analysis and illustrates how it is used to analyze securities and securities markets. Technical analysis is an investment approach that often makes use of quantitative methods.
　　READING ASSIGNMENTS
　　Reading 9 Common Probability Distributions Quantitative Methods for Investment Analysis, Second Edition, by Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
　　Reading 10 Sampling and Estimation Quantitative Methods for Investment Analysis, Second Edition, by Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
　　Reading 11 Hypothesis Testing Quantitative Methods for Investment Analysis, Second Edition, by Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
　　Reading 11 Hypothesis Testing Quantitative Methods for Investment Analysis, Second Edition, by Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
　　Reading 12 Technical Analysis by Barry M. Sine, CFA, and Robert A. Strong, CFA
　　LEARNING OUTCOMES
　　READING 9. COMMON PROBABILITY DISTRIBUTIONS
　　The candidate should be able to:
　　a define a probability distribution and distinguish between discrete and continu?ous random variables and their probability functions;
　　b describe the set of possible outcomes of a specified discrete random variable;
　　c interpret a cumulative distribution function;
　　d calculate and interpret probabilities for a random variable, given its cumulative distribution function;
　　e define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable;
　　f calculate and interpret probabilities given the discrete uniform and the bino?mial distribution functions;
　　g construct a binomial tree to describe stock price movement;
　　h calculate and interpret tracking error;
　　i define the continuous uniform distribution and calculate and interpret proba?bilities, given a continuous uniform distribution;
　　j explain the key properties of the normal distribution;
　　k distinguish between a univariate and a multivariate distribution, and explain the role of correlation in the multivariate normal distribution;
　　l determine the probability that a normally distributed random variable lies inside a given interval;
　　m define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution;
　　n define shortfall risk, calculate the safety-first ratio, and select an optimal portfo?lio using Roy’s safety-first criterion;
　　o explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices;
　　p distinguish between discretely and continuously compounded rates of return, and calculate and interpret a continuously compounded rate of return, given a specific holding period return;
　　q explain Monte Carlo simulation and describe its major applications and limitations;
　　r compare Monte Carlo simulation and historical simulation.
　　READING 10. SAMPLING AND ESTIMATION
　　The candidate should be able to:
　　a define simple random sampling and a sampling distribution;
　　b explain sampling error;
　　c distinguish between simple random and stratified random sampling;
　　d distinguish between time-series and cross-sectional data;
　　e explain the central limit theorem and its importance;
　　f calculate and interpret the standard error of the sample mean;
　　g identify and describe desirable properties of an estimator;
　　h distinguish between a point estimate and a confidence interval estimate of a population parameter;
　　i describe properties of Student’s t-distribution and calculate and interpret its degrees of freedom;
　　j calculate and interpret a confidence interval for a population mean, given a nor?mal distribution with 1) a known population variance, 2) an unknown popula?tion variance, or 3) an unknown variance and a large sample size;
　　k describe the issues regarding selection of the appropriate sample size, data-mining bias, sample selection bias, survivorship bias, look-ahead bias, and time-period bias.
　　READING 11. HYPOTHESIS TESTING
　　The candidate should be able to:
　　a define a hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null and alternative hypotheses;
　　b distinguish between one-tailed and two-tailed tests of hypotheses;
　　c explain a test statistic, Type I and Type II errors, a significance level, and how significance levels are used in hypothesis testing;
　　d explain a decision rule, the power of a test, and the relation between confidence intervals and hypothesis tests;
　　e distinguish between a statistical result and an economically meaningful result;
　　f explain and interpret the p-value as it relates to hypothesis testing;
　　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 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 approxi?mately normally distributed populations, based on independent random samples with 1) equal or 2) unequal 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;
　　k distinguish between parametric and nonparametric tests and describe situations in which the use of nonparametric tests may be appropriate.
　　READING 12. TECHNICAL ANALYSIS
　　The candidate should be able to:
　　a explain principles of technical analysis, its applications, and its underlying assumptions;
　　b describe the construction of different types of technical analysis charts and interpret them;
　　c explain uses of trend, support, resistance lines, and change in polarity;
　　d describe common chart patterns;
　　e describe common technical analysis indicators (price-based, momentum oscil?lators, sentiment, and flow of funds);
　　f explain how technical analysts use cycles;
　　g describe the key tenets of Elliott Wave Theory and the importance of Fibonacci numbers;
　　h describe intermarket analysis as it relates to technical analysis and asset allocation.
　　　
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