Note 17 - CFA PDF

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Extend the reach of inference because they make few assumptions, can use ranked data, and may address questions unrelated to parameters

Makes minimal assumptions about the population from which the sample comes

Used when data does not meet distributional assumptions, data is given in ranks, or when the hypothesis does not concern a parameter

Parametric draws sharper conclusions

Least appropriate for numerical values

Normal density of normal distribution - u = 1 Std = 0

Normal distribution ____ extreme returns - Underestimates

Normal distribution has - A skewness of 0

A kurtosis of 3

0 excess kurtosis

The mean median and life are all equal for a normal random variable

Tends to underestimate the probability of extreme returns

null hypothesis - Designated H0, it is the hypothesis the researcher wants to reject. It is the hypothesis that is actually tested and is the basis for the selection of the test statisics

Objective probability - They do not differ from person to person

Aka priori and empirical

One tailed tests - If you are testing the lower bound: Reject if the test statistic is below the critical value

If you are testing the upper bound: Reject if the test statistic is above the critical value

Ordinal scales - Sorts data into categories that are ordered with respect to some characteristic

Ordinary annuity - has a first cash flow that occurs one period from now (indexed at t=1)

Other confidence interval calc - Upper (UL - Mean)/STD Lower (LL - Mean)/STD

P value - The smallest level of significance at which the null hypothesis can be rejected

It is the probability of obtaining a test statistic that rejects the null

Paired comparisons t statistic - (Sample mean difference - hypothesized mean)/ standard error of the mean difference

Paired comparisons test - A statistical test for differences in dependent items Used if the observations in the two samples both depend on some other factor

Panel data - Contains observations over time of multiple characteristics of the same entity

Parameter - Descriptive measure of a populations characteristics

Parameters of a multivariate normal distribution for n stocks - The list of mean returns on the individual securities The list of securities variances of return The list of all distinct pairwise correlations

Parametric test - Concerned with parameters Validity depends on a definite set of assumptions

They rely on assumptions regarding the distribution of the population and are specific to pop parameters

Not suitable for ranked observations Only for ordinal

Percentile calc - =(n+1)(y/100)

Y is the percentile you wanna find

The answer is the term number that the percentile is, meaning if the answer is 9, then it is the 9th term on the list in order from lowest to highest

Permutation Formula - nPr = n!/(n-r)!

The number of ways that we can choose r objects from a total of n objects, when the order of r objects does matter

Answers the question of how many different groups of size r in specific order can be chosen from b objects

Used for 2 subgroups where order is important

Perpetuity - Set of level never ending sequential cash flows

Platykurtic - normal curves that are short and more dispersed (broader)

Has thinner tails then normal

Point estimate - The calculated value of the sample mean in a given sample used as an estimate of the popular mean

Pooled variance - Population variance (sp^2) : ((N1-1)s^2 + (N2-1)s^2)/(N1+N2-2)

T statistic:

X1 - X2 / (sqreroot(sp^2/N1 + sp^2/N2))

Used with t test for testing the hypothesis that the means of 2 normally distributed pops are equal, when variances are unknown but assumed to be equal

population standard error - Std/square root of n

Portfolio variance - E(Wi*Wj*Cov(i,j)) ^with two variables, this is added 4 times)

Positive skewed data - Frequent small losses and a few extreme gains Has a long tail on its right side

The mean is greater than the median

Possible outcomes for a binomial distribution - Starts at 0, goes to upper limit

Power of a test - The probability of correctly rejecting the null

=1 - P(Type 2 error)

One should always choose the test with the highest power

Priori probability - One based on logical analysis rather than on observation or personal judgement

Probability of x successes in n trials - (Combination form) p^x (1-p)^n-x

Pseudo-random numbers - Random numbers that have sufficient levels of randomness to be practical in use, but are not truly random since all numbers sequences eventually repeat

An example is the numbers that random number generators create are based off a seed value and can be repeated if the same seed is inputted

Pv annuity - A((1-(1/(1+r)^N)/r)

PV of a perpetuity - A/r

Random variable follows Lognormal Distribution when - A random variable Y follows a lognormal distribution if its natural logarithm Ln Y is normally distributed

The reverse is true If the natural logarithm of random variable Y,Ln Y, is normally distributed, Y follows a lognormal distribution

Log is normal

Ratio scales - represent the highest form of measurement in that they have all the properties of interval scales with the additional attribute of representing absolute quantities; characterized by a meaningful absolute zero

Relative frequency - The absolute frequency of each interval divided by the total number of observations

Roy's Safety first ratio - (ERP- RL)/std p

Is maximized by the safety first optimal portfolio

This optimal portfolio minimizes the probability that portfolio return falls below a certain threshold level (RL)

Choose the portfolio with the highest ratio

S^2 - sample variance

Sample excess Kurtosis - ((N/(n-1)(n-2)(n-3)) x (E(Xi-XM)^4)/s^4) ---------------------------------3(n-1)^2/(n-2)(n-3)

I don't know what s is

sample skewness and sample kurtosis - Skewness

(E (X - U)^3) / s^3

Kurtosis (E (X - U)^4) / s^4

Sample soreness formula - (N/(n-1)(n-2)) x (E(Xi-XM)^3)/s^3

I don't know what s is...