Learning Outcome Statements

1. Basic Definitions

a. define a probability distribution and distinguish between discrete and continuous random variables and their probability functions;

b. describe the set of possible outcomes of a specified discrete random variable;

2. Probability Function

c. interpret a cumulative distribution function;

d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;

3. Cumulative Distribution Function

c. interpret a cumulative distribution function;

d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;

4. The Discrete Uniform Distribution

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 binomial 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 probabilities, given a continuous uniform distribution;

5. The Binomial Distribution

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 binomial 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 probabilities, given a continuous uniform distribution;

6. The Normal Distribution

j. explain the key properties of the normal distribution;

7. The Univariate and Multivariate Distributions

k. distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution;

8. The Standard 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;

9. Shortfall Risk and Roy's Safety-First Criterion

n. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy's safety-first criterion;

10. The Lognormal Distribution

o. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices;

11. Discretely and Continuously Compounded Rates of Return

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;

12. Monte Carlo Simulation

q. explain Monte Carlo simulation and describe its applications and limitations;

r. compare Monte Carlo simulation and historical simulation.