Individual Securities Characteristics of: 1) expected return – return an individual expects over the next period 2) variance and sd – measure of volatility of a security’s return and it’s sqr root covariance and correlation – cov and corr measures interraltionship btwn 2 securities Exected return, variance, and covariance Expected return and variance Four equally likely states of co: depression, recession, normal, and boom times Suprtech rtrns (Rat) Slowpoke (Rbt) Deprsn-20 5 Recessn 10 20 Norm 30-12 Boom 50 9 1) expected return is mean of all Rat and Rbt 2) deviation Rat-Rabar (mean of Ra) 3) squared deviations 4) ave sqrd deviation is variance 5) std dev is sqr root of variance std dev(r) = sqrrt(var(r)) Covariance and correlation Measurements of how two random varies are related Find covariance: 1) Product of deviations: (Rat-Rabar)*(Rbt-Rbbar) 2) Average of 1 = Cov(Ra,Rb) = σab = expected val of (1) ~no relationship btwn vars, cov=0; positive relationship, cov<0 Correlation = cov(Ra,Rb)/(SDa*SDb) Return and risk for portfolios How to choose best combo or portfolio of securities given expected returns and SDs? The Example of Supertech and Slowpoke ~The expected return on a Portfolio Expected rtn = weighted ave of expected return of invidl securities ~ Variance and SD of a portfolio Var(portfolio) = Xa^2vara+2XaXbcov(A,B)+Xb^2varb, where Xa and Xb are fraction of a and fraction of b that are in portfolio Covar(a,b) = corr(a,b)*SDa*SDb As long as p (corr) < 1, SD of portfolio of 2 securities is less than the weighted ave of the SDs of of the indivdl securities (b/c weighted ave is
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