Common Probability Distributions Flashcards
Probability Distribution
- describes the probabilities of all possible outcomes for a random variable
- all probabilities must sum to 1
Discrete random variable
a variable where the number of possible outcomes can be counted, measured, and given a positive probability
p (x)
probability function
A probability functions two key properties
- Each individual prob must be between 1 & 0
2. All probabilities must sum to 1
Continuous Randndom Variable
possible outcomes are infinate
p (x) is read as…
“The probability that random variable X=x”
Cumulative distribution function (cdf)
- 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
Discrete uniform random variable
probabilities for all possible outcomes for a discrete random variable are equal
Binomial Random Variable
Defined as the number or “successes” in a given number of trials, where the outcome is either a failure or a success
Binomial random variable with 1 trial
Bernoulli Trial
What does “p” denote with a binomial random variable?
“p” in a binomial distribution stands for probability of success, NOT p(x)
Expected Value of a Binomial random variable equation
E(X)= np
-where n= number of trials and p= prob of success
Variance of Binomial random variable equation
Variance of X = np(1-p)
One important application of a Binomial Stock Price Model
pricing options, be shortening the length of periods and increasing the amount of periods
Tracking Error
The difference between the total return on a portfolio and the total return on the benchmark against which its performance is measured
Other name for Tracking Error
Tracking Risk
Continuous Uniform Distribution
defined over a range that spans between a lower limit (a) and an upper limit (b), which serve as parameters
90% Confidence Interval number
1.65
95% Confidence Interval number
1.96
99% Confidence Interval Number
2.58
Lognormal Distribution
similar to the normal distribution, but is bound from going below zero, making it more applicable
z score equation
(X-mean)/ STDV
A z-score of 1 means that
the observation is 1 STDV above the mean
Roys Safety First Equation
(E(Rp) - RL) / STDV
Essentially the Sharpe equation but with min threshold level instead of rFr
SFR measures what
the STDVs below the mean
Min Threshold equation (RL)
(min portfolio value - portfolio value) / portfolio value
SFR rule
Choose the portfolio with the highest SFR
Discretely Compounded returns
compounded returns (geo mean), with some discrete compounding period such as semiannual or quarterly
Continuous compounding EAR equation
e^(Rcc)-1
Rcc is the
effective annual rate based on continous compounding
Rcc equation
ln (1+HPR) or ln(S1/S0)
Historical Simulation
based on actual changes in value or actual changes in risk over some prior period
Historical Simulation Downfalls (2)
- past changes in risk factors might may not indicate future changes
- Cannot address “what ifs” like the monte carlo can
