Common Probability Distributions Flashcards
The average return of a mutual fund is 10.5% per year and the standard deviation of annual returns is 18%. If returns are approximately normal, what is the 95% confidence interval for the mutual fund return next year?
What is the formula
Answer:
Here µ and σ are 10.5% and 18%, respectively. Thus, the 95% confidence interval for the return, R, is:
10.5 ± 1.96(18) = –24.78% to 45.78%
Mean ± Confidence Interval X (SD)
What is a Z value and how do you standardize an observation into a Z value?
The z-value represents the number of standard deviations a given observation is from the population mean. Standardization is the process of converting an observed value for a random variable to its z-value. The following formula is used to standardize a random variable:
Observation - Population mean
/
Standard Deviation
What is a Z value and how do you standardize an observation into a Z value?
The z-value represents the number of standard deviations a given observation is from the population mean. Standardization is the process of converting an observed value for a random variable to its z-value. The following formula is used to standardize a random variable:
Observation - Population mean
/
Standard Deviation
Explain and calculate Shortfall Ratio / Roy’s safety first criterion
What criteria must the portfolio have
What is the formula / what are the steps?
Roy’s safety-first criterion states that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level. This minimum acceptable level is called the threshold level. Symbolically, Roy’s safety-first criterion can be stated as:
minimize P(Rp < RL)
In summary, when choosing among portfolios with normally distributed returns using Roy’s safety-first criterion, there are two steps:
Portfolio Return - Threashold level return
/
Standard Deviation of returns
= SF ratio
The higher the SF ratio the better
Calculate discretely compounded rate of return
1 + ( 0.10 / 12) ^12 -1
would be 10% compounded monthly for 12 periods (1 year)
Calculating continuously compounded return
Calculate EAY w/ continuous compounding
LN (1+HPR)
Ei - 1
What are the properties of a student’s t- distribution?
It is symmetrical.
It is defined by a single parameter, the degrees of freedom (df), where the degrees of freedom are equal to the number of sample observations minus 1, n – 1, for sample means.
It has more probability in the tails (“fatter tails”) than the normal distribution.
As the degrees of freedom (the sample size) gets larger, the shape of the t-distribution more closely approaches a standard normal distribution.
What is a probability function, what is the abbreviation?
What is a continuous probability function, what is the abbreviation?
The probability that a discrete random variable will take on the value X
p(X)
The probability that a discrete random variable will be less than or equal to a given value
F(x)
Define a probability distribution, a discrete distribution and a continuous distribution.
Probability distribution: gives the probabilities for all possible outcomes for a random variable
Discrete: countable number of possible outcomes. Continuous = unlimited
What is a probability function?
Gives the probability that a discrete random variable will take on the value x
What is a cumulative distribution function?
The probability a random variable will be less than or equal to a given value
What is the difference between p(x) and f(x)
P(x) = probability function, probability variable will take on a discrete random variable
F(x) = cumulative distribution function
Calculate a binominal random variable
nCr (n = number of trials, r = number of successes)
x
P Success (to the power of the number of successes)
x
P Failure (power of the number of failures)
What are the confidence intervals for x?
68% = x +- 1 SD
90% = x +- 1.65 SD
95% = x +- 1.96 SD
99% = x +- 2.58 SD
When calculating confidence intervals, how do you enter the percentages?
As whole numbers
