Common Probability Distributions

Question 1

Probability Distribution

Answer 1

• describes the probabilities of all possible outcomes for a random variable
• all probabilities must sum to 1

Question 2

Discrete random variable

Answer 2

a variable where the number of possible outcomes can be counted, measured, and given a positive probability

Question 3

p (x)

Answer 3

probability function

Question 4

A probability functions two key properties

Answer 4

1. Each individual prob must be between 1 & 0

2. All probabilities must sum to 1

Question 5

Continuous Randndom Variable

Answer 5

possible outcomes are infinate

Question 6

p (x) is read as…

Answer 6

“The probability that random variable X=x”

Question 7

Cumulative distribution function (cdf)

Answer 7

• defines that prob that random variable X, is equal to or less than the specific value of x.
• Represents the summ of probs for outcomes up to and including that specific outcome

Question 8

Discrete uniform random variable

Answer 8

probabilities for all possible outcomes for a discrete random variable are equal

Question 9

Binomial Random Variable

Answer 9

Defined as the number or “successes” in a given number of trials, where the outcome is either a failure or a success

Question 10

Binomial random variable with 1 trial

Answer 10

Bernoulli Trial

Question 11

What does “p” denote with a binomial random variable?

Answer 11

“p” in a binomial distribution stands for probability of success, NOT p(x)

Question 12

Expected Value of a Binomial random variable equation

Answer 12

E(X)= np

-where n= number of trials and p= prob of success

Question 13

Variance of Binomial random variable equation

Answer 13

Variance of X = np(1-p)

Question 14

One important application of a Binomial Stock Price Model

Answer 14

pricing options, be shortening the length of periods and increasing the amount of periods

Question 15

Tracking Error

Answer 15

The difference between the total return on a portfolio and the total return on the benchmark against which its performance is measured

Question 16

Other name for Tracking Error

Answer 16

Tracking Risk

Question 17

Continuous Uniform Distribution

Answer 17

defined over a range that spans between a lower limit (a) and an upper limit (b), which serve as parameters

Question 18

90% Confidence Interval number

Answer 18

1.65

Question 19

95% Confidence Interval number

Answer 19

1.96

Question 20

99% Confidence Interval Number

Answer 20

2.58

Question 21

Lognormal Distribution

Answer 21

similar to the normal distribution, but is bound from going below zero, making it more applicable

Question 22

z score equation

Answer 22

(X-mean)/ STDV

Question 23

A z-score of 1 means that

Answer 23

the observation is 1 STDV above the mean

Question 24

Roys Safety First Equation

Answer 24

(E(Rp) - RL) / STDV

Essentially the Sharpe equation but with min threshold level instead of rFr

Question 25

SFR measures what

Answer 25

the STDVs below the mean

Question 26

Min Threshold equation (RL)

Answer 26

(min portfolio value - portfolio value) / portfolio value

Question 27

SFR rule

Answer 27

Choose the portfolio with the highest SFR

Question 28

Discretely Compounded returns

Answer 28

compounded returns (geo mean), with some discrete compounding period such as semiannual or quarterly

Question 29

Continuous compounding EAR equation

Answer 29

e^(Rcc)-1

Question 30

Rcc is the

Answer 30

effective annual rate based on continous compounding

Question 31

Rcc equation

Answer 31

ln (1+HPR) or ln(S1/S0)

Question 32

Historical Simulation

Answer 32

based on actual changes in value or actual changes in risk over some prior period

Question 33

Historical Simulation Downfalls (2)

Answer 33

1. past changes in risk factors might may not indicate future changes
2. Cannot address “what ifs” like the monte carlo can