Study Session 2 syllabus

STUDY SESSION 2
QUANTITATIVE METHODS:
Basic Concepts

This introductory study session presents the fundamentals of those quantitative
techniques that are essential in almost any type of financial analysis, and which
will be used throughout the remainder of the CFA curriculum. This session introduces
two main building blocks of the quantitative analytical tool kit: (1) the time
value of money and (2) statistics and probability theory.
The time value of money concept is one of the main principles of financial valuation.
The calculations based on this principle (e.g., present value, future value,
and internal rate of return) are the basic tools used to support corporate finance
decisions and estimate the fair value of fixed income, equity, or any other type of
security or investment.
Similarly, the basic concepts of statistics and probability theory constitute the
essential tools used in describing the main statistical properties of a population
and understanding and applying various probability concepts in practice.

LEARNING OUTCOMES
Reading 5: The Time Value of Money
The candidate should be able to:
a. interpret interest rates as required rate of return, discount rate, or opportunity
cost;
b. explain an interest rate as the sum of a real risk-free rate, expected inflation, and
premiums that compensate investors for distinct types of risk;
c. calculate and interpret the effective annual rate, given the stated annual interest
rate and the frequency of compounding, and solve time value of money problems
when compounding periods are other than annual;
d. 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;
e. draw a time line, specify a time index, and solve time value of money applications


Reading 6: Discounted Cash Flow Applications
The candidate should be able to:
a. calculate and interpret the net present value (NPV) and the internal rate of return
(IRR) of an investment, contrast the NPV rule to the IRR rule, and identify problems
associated with the IRR rule;
b. define, calculate, and interpret a holding period return (total return);
c. calculate, interpret, and distinguish between the money-weighted and timeweighted
rates of return of a portfolio and appraise the performance of portfolios
based on these measures;
d. calculate and interpret the bank discount yield, holding period yield, effective
annual yield, and money market yield for a U.S. Treasury bill; and convert among
holding period yields, money market yields, effective annual yields, and bond
equivalent yields.
Reading 7: Statistical Concepts and Market Returns
The candidate should be able to:
a. differentiate between descriptive statistics and inferential statistics, between a
population and a sample, and among the types of measurement scales;
b. explain a parameter, a sample statistic, and a frequency distribution;
c. calculate and interpret relative frequencies and cumulative relative frequencies,
given a frequency distribution, and describe the properties of a dataset presented
as a histogram or a frequency polygon;
d. define, calculate, and interpret measures of central tendency, including the population
mean, sample mean, arithmetic mean, weighted average or mean (including
a portfolio return viewed as a weighted mean), geometric mean, harmonic
mean, median, and mode;
e. describe, calculate, and interpret quartiles, quintiles, deciles, and percentiles;
f. define, 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;
g. calculate and interpret the proportion of observations falling within a specified
number of standard deviations of the mean, using Chebyshev’s inequality;
h. define, calculate, and interpret the coefficient of variation and the Sharpe ratio;
i. define and interpret skewness, explain the meaning of a positively or negatively
skewed return distribution, and describe the relative locations of the mean,
median, and mode for a nonsymmetrical distribution;
j. define and interpret measures of sample skewness and kurtosis.
Reading 8: Probability Concepts
The candidate should be able to:
a. define a random variable, an outcome, an event, mutually exclusive events, and
exhaustive events;
b. explain the two defining properties of probability, and distinguish among
empirical, subjective, and a priori probabilities;
c. state the probability of an event in terms of odds for or against the event;
Study Session 2 169
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d. distinguish between unconditional and conditional probabilities;
e. 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;
f. distinguish between dependent and independent events;
g. calculate and interpret, using the total probability rule, an unconditional probability;
h. explain the use of conditional expectation in investment applications;
i. diagram an investment problem, using a tree diagram;
j. calculate and interpret covariance and correlation;
k. calculate and interpret the expected value, variance, and standard deviation of a
random variable and of returns on a portfolio;
l. calculate and interpret covariance given a joint probability function;
m. calculate and interpret an updated probability, using Bayes’ formula;
n. identify the most appropriate method to solve a particular counting problem,
and solve counting problems using the factorial, combination, and permutation
notations.