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READING 9. COMMON PROBABILITY DISTRIBUTIONS (Jan 31)
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 the 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, describe and inter- pret the choice of the null and alternative hypotheses, and distinguish between one-tailed and two-tailed tests of hypotheses;
b explain a test statistic, Type I and Type II errors, a significance level, and how significance levels are used in hypothesis testing;
c explain a decision rule, the power of a test, and the relation between confidence intervals and hypothesis tests;
d distinguish between a statistical result and an economically meaningful result;
e explain and interpret the p-value as it relates to hypothesis testing;
f 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;
g 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 sam- ples with 1) equal or 2) unequal assumed variances;
h identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations;
i 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;
j distinguish between parametric and nonparametric tests and describe the situa- tions in which the use of nonparametric tests may be appropriate.
READING 12. TECHNICAL ANALYSIS
The candidate should be able to:
a explain the principles of technical analysis, its applications, and its underlying assumptions;
b describe the construction of and interpret different types of technical analysis charts;
c explain the uses of trend, support, resistance lines, and change in polarity;
d identify and interpret common chart patterns;
e describe common technical analysis indicators: price-based, momentum oscilla- tors, sentiment, and flow of funds;
f explain the use of cycles by technical analysts;
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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