Quantitative Methods - Distributions - Lognormal, T, Chi-Square, and F Distributions

Question 1

if a variable is normally distributed, how is the lognormal distribution denoted?

Answer 1

e^x

Question 2

what are the parameters for lognormal distributions?

Answer 2

always positive (bound by 0 on the x axis) and skewed to the right

Question 3

why are lognormal distributions used to model asset prices?

Answer 3

• asset prices can’t be negative (bounded by 0)
• using a normal distribution of returns would admit the possibility of returns less than -100% (suggesting asset prices are less than zero)

Question 4

how are price relatives distributed?

Answer 4

lognormally

Question 5

what is continuous compounding?

Answer 5

when the number of compounding periods becomes infinitesimally small

Question 6

what are the properties of a student’s t-distribution?

Answer 6

• symmetrical (mean=median=mode & 0 skewness)
• fatter tails than a normal distribution (higher probability of witnessing extreme observations and increased confidence intervals. Makes the null hypothesis harder to reject)
• defined by a single parameter, degrees of freedom (df) where df=n-1 (n being number of observations in your sample)
• as df increase, t-distribution approaches normal distribution

Question 7

what can be said about when you have more numbers of observations for a t-distribution?

Answer 7

it becomes more spiked and has thinner tails

Question 8

describe the properties of chi-squared distribution

Answer 8

• distribution of squared values of ‘n’ independent standard normal random variables
• bounded from below by zero (this is because any negative value squared would be +ve)
• asymmetric (bounded by 0 so skewed to the right)
• degrees of freedom = n-1
• as df increase, t-distribution approaches normal distribution

Question 9

when is chi-squared distribution normally used?

Answer 9

in hypothesis testing to test the variance of a normally distributed population

Question 10

describe the the properties of an f-distribution

Answer 10

• quotient of two chi-squared distributions with ‘m’ and ‘n’ degrees of freedom
• bounded by 0
• asymmetric
• as df increases, approaches normal distribution

Question 11

when would you use an f-distribution?

Answer 11

when you have 2 populations and want to test the hypothesis of 2 population variances

Question 12

what is the Monte Carlo Simulation?

Answer 12

simulation can be used to estimate a distribution of any asset prices or of net present values (the latter when looking at project appraisal)

Question 13

what are the Monte Carlo Simulation procedures?

Answer 13

1) Specify the probability distributions of random variables, such as interest rates and underlying stock prices
2) Use computer random generation of variables
3) Price the derivative using those values
4) Repeat steps 2 and 3 thousands of times
5) Calculate mean/variance of distribution of outcomes