4.2: Normal Distributions

Question 1

The Central Limit Theorem states that the sum (and mean) of a…

Answer 1

Large number of independent random variables (with finite variance) is approximately normally distributed.

Question 2

The normal (univariate) distribution is completely described by two parameters:

Answer 2

Its mean, μ, and variance, σ2.

Question 3

The normal (univariate) distribution has:
Skewness of…
Kurtosis of…
Its excess kurtosis (kurtosis − 3.0) equals…

Answer 3

0 (it is symmetric).

Kurtosis of 3.

0

Question 4

Multivariate Normal Distribution - a probability distribution for a…

Answer 4

Group of random variables that is completely defined by the means and variances of the variables plus all the correlations between pairs of the variables.

Question 5

Standardizing - a transformation that..

Answer 5

Involves subtracting the mean and dividing the result by the standard deviation.

Question 6

Formula for computing Z-score (std. normal distribution):

Answer 6

Z = (X − μ)/σ

Question 7

Safety-first rules - rules for portfolio selection that focus on…

Answer 7

The risk that portfolio value or portfolio return will fall below some minimum acceptable level over some time horizon.

Question 8

Safety-first ratio formula (SFRatio):

Answer 8

SFRatio = [E(RP) − RL]/σP

If returns are normally distributed.

Question 9

There are two steps in choosing among portfolios using Roy’s criterion (assuming normality):

Answer 9

1 - Calculate each portfolio’s SFRatio.

2 - Choose the portfolio with the highest SFRatio.

Question 10

Formula for finding X (rearrange z-score formula):

Answer 10

X = µ + Zσ

Question 11

Formula for finding variance (rearrange z-score formula):

Answer 11

σ = (X − μ)/Z