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(9) Common Probability Distributions
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Terms in this set (22)
Discrete Random Variable
One for which the number of possible outcomes can be counted, and for each possible outcome there is a measurable and positive probability
Continuous Random Variable
One for which the number of possible outcomes is infinite
Discrete Uniform Random variable
one for which the probabilities for all possible outcomes for a discrete random variable are equal (1/n)
Binomial Random variable
Defined as the number of successes in a given number of trials, where by the outcome can be either "success" or "failure"
Probability of x successes in n trials
P(x)= n!/(n-x)! x! × P^x × (1-P)^n-x
Variance of a binomial random variable
np(1-p)
Probability of outcomes for a Continuous Uniform Distribution
X2-X1/b-a
Normal Distribution for x
X is normally distributed with mean μ and variance σ²
90, 95, and 99% CI Z-Stats
1.645, 1.96, 2.58
How do you build a confidence interval (CI)?
x ± Z-Value σ
What is a Standard Normal Distribution?
A normal distribution that has been standardized so that it has a mean 0 and standard deviation 1
What is the calculation for a Z-Value?
X-μ/σ
What is short-fall risk?
Short-Fall risk is the probability that a portfolio value or return will fall below a particular value or return over a given period of time
Roy's safety-first criterion
States that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable threshold level
What does a bigger Roy's Safety Ratio tell you?
The bigger the Safety Ratio, the lower the probability of negative returns
(more safety in positive returns??)
Why is the lognormal distribution good for modeling asset prices?
Because it is bounded by 0, and therefore cannot have a negative value, the same as assets can't have a negative value
What is a price relative?
Price Relative is the end of period price of the asset divided by the beginning of period price of the asset
Equals (1+Holding Period Return)
How do you calculate EAR with continuous compounding?
EAR= e^Rcc -1
where Rcc= Continuously compounding rate
How do you find a particular Holding Period Return for a Lognormally distributed random variable?
Ln(S1/S0)= ln(1+HPR) = Rcc
How do you find the Holding Period Return (HPR) for multiple periods?
HPR= e^(Rcc×T) -1
What is a Monte Carlo simulation?
A Monte Carlo simulation is a technique based on the repeated generation of one or more risk factors that affect security values, in order to generate a distribution of security values
What is the limitation of a Monte Carlo simulation?
It is way too complex, it's statistical and not analytical
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