Reading 8

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Covariance (Ri,Rx)

= E(Ret. i - expected ret.i)*(Ret X- expected ret. x)

Covariance of any data with itself

= to variance

Correlation Equation and how to interpret

Cov (R1,R2)/(St. Dev R1*Std Dev R2) falls between -1 and 1. 0 indicates no correlation

total probability for expected values

E(X)= E(X l S)P(S)+ E(X l S)P(S)

Odds against equation

E=(1-P(event))/P(E)

Permutation Formula

How many ways can you select r object from n objects when order does matter n!/(n-r)!

Conditional Probability example and how to read

P(A l B) probability of event A given B

Conditional probability formula

P(A l B)= P(AB)/P(B)

P( A or B) =

P(A) + P(B)- P(AB)

Probability AB

P(AB)= P(A l B) *P(B)

Probability of P(AB) given uncorrelated random variable

P(AB)= P(A)*P(B)

Multiplication rule of independent events

P(AB)= P(A)*P(B)...could go further how ever many events there are if they are independent then you multiply

P(Pass) with survivor non survivor using total probability rule

P(Pass l Survivor)*P(survivor)+P(Pass l non surv.)*P(non surv.)

Variance of probabilities

P(X)(value of x-expected vlaue x)^2+ P(X2)(value X2-expected value x)^2

expected value

P(X)X+ P(X2)(X2) .....n

Bayes formula for probabilities

P(event l Information)= (P(information l Event)/P(information))*P(event)

Variance on portfolio of weighted assets

weight^2*Variance^2+weight^2*Variance^2+2*weight1*weight2*Cov(1,2,)

P(A l B)=

[P(B l A)/P(B)]* P(A)

conditional variances do what

allow us to asses risk given a particular scenario

Independent events

do not affect one another such that P(A l B)= P(A)

Probability based on historical data

empirical probability

Multiplication rule of counting

if something can be done N1 ways, step 2 n2 ways, step 3 n3 ways. total ways is N1*n2*n3

unconditional probability also called

marginal probability

Combination formula

number of ways to choose r objects from n objects when order does not matter, N!/(N-R)!R!

multinomeal labeling formula

number of ways to lable n things in k groups is N factorial/ (n1factorial*n2factorial*up to Nk factorial) with N1 meaning number labled first type, n2 number labled second type

A priori probability

one created from deductive reasoning. a priori and empirical probabilities do not change person to person

For probability solving

page 445 is important

Exhaustive probability

probability of all options adds up to 1

pairs arbitrage trade

probability on closely related stocks are not equally weighted in marketplace

Probability of A or B means

probability that either even a or b or both happen

based on our judgement and assessment

subjective probability

Covariance calculation using probability

sum all possible cross product deviations from mean weighted by joint probability of events and summed (page 464)

What does a negative covariance indicate

that is the return on asset 1 is above average the return on asset 2 should be below average

Covariance of 0 indicates

that the two assets are unrelated


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