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CFA Level 1 – Quantitative Methods

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Study Session 2: Quantitative Methods (1)
Reading 7 Statistical Concepts and Market Returns 13 LOSs | 1 Quiz
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Reading 8 Probability Concepts 15 LOSs | 1 Quiz
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State the two defining properties of probability and distinguish among empirical, subjective, and a priori probabilities
Define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events
State the probability of an event in terms of odds for and against the event
Distinguish between unconditional and conditional probabilities
Explain the multiplication, addition, and total probability rules
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
Distinguish between dependent and independent events
Calculate and interpret an unconditional probability using the total probability rule
Explain the use of conditional expectation in investment applications
Explain the use of a tree diagram to represent an investment problem
Calculate and interpret covariance and correlation and interpret a scatterplot
Calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio
Calculate and interpret covariance given a joint probability function
Calculate and interpret an updated probability using Bayes’ formula
Identify the most appropriate method to solve a particular counting problem and solve counting problems using factorial, combination, and permutation concepts
Study Session 3: Quantitative Methods (2)
Reading 9 Common Probability Distributions 17 LOSs | 1 Quiz
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Define a probability distribution and distinguish between discrete and continuous random variables and their probability functions
Describe the set of possible outcomes of a specified discrete random variable
Interpret a cumulative distribution function
Calculate and interpret probabilities for a random variable, given its cumulative distribution function
Define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable
Calculate and interpret probabilities given the discrete uniform and the binomial distribution functions
Construct a binomial tree to describe stock price movement
Define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution
Explain the key properties of the normal distribution
Distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution
Determine the probability that a normally distributed random variable lies inside a given interval
Define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution
Define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion
Explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices
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
Explain Monte Carlo simulation and describe its applications and limitations
Compare Monte Carlo simulation and historical simulation
Reading 11 Hypothesis Testing 12 LOSs | 1 Quiz
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Define a hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null and alternative hypotheses
Distinguish between one-tailed and two-tailed tests of hypotheses
Explain a test statistic, Type I and Type II errors, a significance level, and how significance levels are used in hypothesis testing
Explain a decision rule, the power of a test, and the relation between confidence intervals and hypothesis tests
Distinguish between a statistical result and an economically meaningful result
Explain and interpret the p-value as it relates to hypothesis testing
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
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
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations
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
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
Distinguish between parametric and nonparametric tests and describe situations in which the use of nonparametric tests may be appropriate