Reading 8
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