LM 6: Simulation Methods

Question 1

What is a lognormal distribution?

Answer 1

positive skew for returns, used for asset prices since asset prices can’t go below 0.

Question 2

What is the formula to determine an asset’s continuously compounded rate of return?

Answer 2

r0, t = ln (St / S0)

S0 = initial price
St = price at end of investment horizon

Question 3

What is the formula for assets’ future expected price with continuous compound rate of return?

Answer 3

St = S0 * e^(r0,t)

S0 = initial price
St = price at end of investment horizon

Question 4

What is Monte Carlo simulation?

Answer 4

predicts possible outcomes of an uncertain event. Computer programs use this method to analyze past data and predict a range of future outcomes based on a choice of action.

uses computers to generate a large number of outcomes for a variable of interest based on random samples taken from one or more input variables

Question 5

What is bootstrapping?

Answer 5

statistical procedure that resamples a single data set to create many simulated samples

bootstrap, the analyst repeatedly draws samples from the original sample and not population, where each individual resample has the same size as the original sample and each item drawn is replaced for the next draw

Question 6

What is resampling?

Answer 6

process of repeatedly drawing samples from a larger pool of sample data in order to make statistical inferences about the population parameters

Question 7

How do you turn a periodic variance into an annualized standard deviation?

Answer 7

1. multiple the variance * periodicity
2. square root the number to get annualized returns

Question 8

What 2 parameters do you need for a normal distribution?

Answer 8

1. mean
2. variance