CFA Level 1 Study Notes – Quantitative Methods

Study Session 2

Reading 6 – The Time Value of Money

LOS 6a: interpret interest rates as required rates of return, discount rates, or opportunity costs
LOS 6b: explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk
LOS 6c: calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding
LOS 6d: solve time value of money problems for different frequencies of compounding
LOS 6e: 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
LOS 6f: demonstrate the use of a time line in modeling and solving time value of money problems

Reading 7 – Statistical Concepts and Market Returns

LOS 7a: distinguish between descriptive statistics and inferential statistics, between a population and a sample, and among the types of measurement scales
LOS 7b: define a parameter, a sample statistic, and a frequency distribution
LOS 7c: calculate and interpret relative frequencies and cumulative relative frequencies, given a frequency distribution
LOS 7d: describe the properties of a data set presented as a histogram or a frequency polygon
LOS 7e: calculate and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean, geometric mean, harmonic mean, median, and mode
LOS 7f: calculate and interpret quartiles, quintiles, deciles, and percentiles
LOS 7g: calculate and interpret 1) a range and a mean absolute deviation and 2) the variance and standard deviation of a population and of a sample
LOS 7h: calculate and interpret the proportion of observations falling within a specified number of standard deviations of the mean using Chebyshev’s inequality
LOS 7i: calculate and interpret the coefficient of variation and the Sharpe ratio
LOS 7j: explain skewness and the meaning of a positively or negatively skewed return distribution
LOS 7k: describe the relative locations of the mean, median, and mode for a unimodal, nonsymmetrical distribution
LOS 7l: explain measures of sample skewness and kurtosis
LOS 7m: compare the use of arithmetic and geometric means when analyzing investment returns

Reading 8 – Probability Concepts

LOS 8a: define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events
LOS 8b: state the two defining properties of probability and distinguish among empirical, subjective, and a priori probabilities
LOS 8c: state the probability of an event in terms of odds for and against the event
LOS 8d: distinguish between unconditional and conditional probabilities
LOS 8e: explain the multiplication, addition, and total probability rules
LOS 8f: calculate and interpret 1) the joint probability of two events, 2) the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events, and 3) a joint probability of any number of independent events
LOS 8g: distinguish between dependent and independent events
LOS 8h: calculate and interpret an unconditional probability using the total probability rule
LOS 8i: explain the use of conditional expectation in investment applications
LOS 8j: explain the use of a tree diagram to represent an investment problem
LOS 8k: calculate and interpret covariance and correlation
LOS 8l: calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio
LOS 8m: calculate and interpret covariance given a joint probability function
LOS 8n: calculate and interpret an updated probability using Bayes’ formula
LOS 8o: identify the most appropriate method to solve a particular counting problem and solve counting problems using factorial, combination, and permutation concepts

Study Session 3

Reading 9 – Common Probability Distributions

LOS 9a: define a probability distribution and distinguish between discrete and continuous random variables and their probability functions
LOS 9b: describe the set of possible outcomes of a specified discrete random variable
LOS 9c: interpret a cumulative distribution function
LOS 9d: calculate and interpret probabilities for a random variable, given its cumulative distribution function
LOS 9e: define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable
LOS 9f: calculate and interpret probabilities given the discrete uniform and the binomial distribution functions
LOS 9g: construct a binomial tree to describe stock price movement
LOS 9h: define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution
LOS 9i: explain the key properties of the normal distribution
LOS 9j: distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution
LOS 9k: determine the probability that a normally distributed random variable lies inside a given interval
LOS 9l: define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution
LOS 9m: define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion
LOS 9n: explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices
LOS 9o: 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
LOS 9p: explain Monte Carlo simulation and describe its applications and limitations
LOS 9q: compare Monte Carlo simulation and historical simulation

Reading 10 – Sampling and Estimation

LOS 10a: define simple random sampling and a sampling distribution
LOS 10b: explain sampling error
LOS 10c: distinguish between simple random and stratified random sampling
LOS 10d: distinguish between time-series and cross-sectional data
LOS 10e: explain the central limit theorem and its importance
LOS 10f: calculate and interpret the standard error of the sample mean
LOS 10g: identify and describe desirable properties of an estimator
LOS 10h: distinguish between a point estimate and a confidence interval estimate of a population parameter
LOS 10i: describe properties of Student’s t-distribution and calculate and interpret its degrees of freedom
LOS 10j: 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 variance and a large sample size
LOS 10k: describe the issues regarding selection of the appropriate sample size, datamining bias, sample selection bias, survivorship bias, look-ahead bias, and timeperiod bias

Reading 11 – Hypothesis Testing

LOS 11a: define a hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null and alternative hypotheses
LOS 11b: distinguish between one-tailed and two-tailed tests of hypotheses
LOS 11c: explain a test statistic, Type I and Type II errors, a significance level, and how significance levels are used in hypothesis testing
LOS 11d: explain a decision rule, the power of a test, and the relation between confidence intervals and hypothesis tests
LOS 11e: distinguish between a statistical result and an economically meaningful result
LOS 11f: explain and interpret the p-value as it relates to hypothesis testing
LOS 11g: 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
LOS 11h: 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 1) equal or 2) unequal assumed variances
LOS 11i: identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations
LOS 11j: 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
LOS 11k: formulate a test of the hypothesis that the population correlation coefficient equals zero and determine whether the hypothesis is rejected at a given level of significance
LOS 11l: distinguish between parametric and nonparametric tests and describe situations in which the use of nonparametric tests may be appropriate

(2020 – Deleted – Discounted Cash Flow Applications)

LOS 7a: calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment
LOS 7a: Part 2
LOS 7b: contrast the NPV rule to the IRR rule, and identify problems associated with the IRR rule
LOS 7c: calculate and interpret a holding period return (total return)
LOS 7d: calculate and compare the money-weighted and time-weighted rates of return of a portfolio and evaluate the performance of portfolios based on these measures
LOS 7d: Part 2
LOS 7e: calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money market yield for US Treasury bills and other money market instruments
– LOS 7f: convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields

(2020 – Moved to Portfolio Management – Technical Analysis)

LOS 13a: explain principles of technical analysis, its applications, and its underlying assumptions
LOS 13b: describe the construction of different types of technical analysis charts and interpret them
LOS 13c: explain uses of trend, support, resistance lines, and change in polarity
LOS 13d: describe common chart patterns
LOS 13e: describe common technical analysis indicators (price-based, momentum oscillators, sentiment, and flow of funds)
LOS 13f: explain how technical analysts use cycles
LOS 13g: describe the key tenets of Elliott Wave Theory and the importance of Fibonacci numbers
LOS 13h: describe intermarket analysis as it relates to technical analysis and asset allocation


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