# R9-Probability-2

msk2222's version from 2018-02-18 16:29

## PORTFOLIO EXPECTED RETURN AND VARIANCE OF RETURN

Properties of Expected ValueThe expected value of a constant times a random variable equals the constant times the expected value of the random variableE(wiRi) = wiE(Ri)
Properties of Expected ValueThe expected value of a weighted sum of random variables equals the weighted sum of the expected values, using the same weights
Calculation of Portfolio Expected Return.Given a portfolio with n securities, the expected return on the portfolio is a weighted average of the expected returns on the component securitiesE(Rp)= E(w1R1....wnRn)
Definition of CovarianceCov(Ri,Rj) = E[(Ri-ERi)(Rj-ERj)]σ(Ri,Rj) and σij.
interpret the sign of covariance as followsnegativewhen the return on one asset is above its expected value, the return on the other asset tends to be below its expected value
interpret the sign of covariance as followspositive returns on both assets tend to be on the same side (above or below) their expected values at the same time
interpret the sign of covariance as follows0returns on the assets are unrelated
The covariance of a random variable with itself (own covariance) is its own varianceCov(R,R) = E{[R − E(R)][R − E(R)]} = E{[R − E(R)]2}σ2(R)
Definition of Correlation ρ(Ri,Rj) = Cov(Ri,Rj)/σ(Ri)σ(Rj). Alternative notations are Corr(Ri,Rj) and ρij.
Properties of CorrelationA correlation of 0 (uncorrelated variables) indicates an absence of any linear (straight-line) relationship between the variables.13 Increasingly positive correlation indicates an increasingly strong positive linear relationship (up to 1, which indicates a perfect linear relationship). Increasingly negative correlation indicates an increasingly strong negative (inverse) linear relationship (down to −1, which indicates a perfect inverse linear relationship)
joint probability function of two random variables X and Y, denoted P(X,Y)gives the probability of joint occurrences of values of X and Y. For example, P(3, 2), is the probability that X equals 3 and Y equals 2
Definition of Independence for Random VariablesTwo random variables X and Y are independent if and only if P(X,Y) = P(X)P(Y).
Multiplication Rule for Expected Value of the Product of Uncorrelated Random VariablesThe expected value of the product of uncorrelated random variables is the product of their expected values.