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Percentage Returns:Div Yield+ Capital GainTotal Return=Div(t+1) / P(t) + (P(t+1) – Pt) / P(t)R(t+1)=.05+ .09=.15Suppose you had 5k investedTotal dollar return = 5k x .15If you know the total dollar return on the stockYou do notneed to know how many shares you would have to purchase to figure out how much money you would have made.Three year holding period return(1 + R1) x (1 + R2) x (1 + R3) = 1.15 (15% total return … holding period return)Ch. 10:Variance / Standard Deviation Calculation:1. Calculate expected return:Average Return (A)=Abar=.175Average Return (B)=Bbar=.0552. Deviation from expected return: RA – Abar (For each state)3. Square each deviation4. Average of all the squares = Variance5. Sq. Rt. Of Variance = St. DeviationOR:Var(Rn) = Expected valued of (Rn – Rbar)^2Covariance and Correlation:1. Multiply respective deviations / residuals together2. Come up with an average of multiplied residualsCov (Ra,Rb) = Expcected (Avg.) of Residuals1. A’s return generally above its avg. when B’s return above avgpositive dependency / relationship … POSITIVE Covariance2. A’s return generally about avg. when B’s below B’s avg.Negative Covariance3. No relation = Covariance of 0Correlation (A,B) = Covariance (A,B) / (St. DevA x S. DevB)Var (Port) = (XaVar (a))^2 + 2XaXbCov(a,b) + (XbVar(b))^2NOTE: Cov(a,b) = Corr(a,b) x SD(A) x SD(B)1. Expected Return of the Portfolio = Xa E(a) + Xb E(b)= .60(.175) + .40 (.055)= .127Note: a positive relationship or Cov between variables increases thevariance for the entire portfolio which is undesirableAs long as Corr < 1 … SD(port) is < Wt avg of a and b DIVERSIFICATIONThe Efficient Set for Two Assets:1. Diversification occurs when Corr < 12. MV = minimum Var / minimum SD3. Cannot achieve point outside feasible set b/c cannot decrease SD of securites or correlation between securitesHow can an increase in the proportion of risky security (B)?5. No investorwould want to hold a portfolio with an expected return below that of the MV portfolio6. Straight Line comes form Corr = 1 (No diversification)Variance(port) (As N tends to Infinity) = CovBar*** Variance(port) (As N tends to Infinity) = CovBar ***Optimal Portfolio:LINE 2: Efficient set of all assets(1)m = intercept = Rf = Risk-free rate(2)Line tangential to optimal curve(3)All $ in Pt. A, just how much to Lend/BorrowMarket Equilibrium Portfolio:*In a world with homogenous expectations, all investors wouldhold the portfolio of risky assets represented by point A1 Estimate expected returns and var for individuals securities2 Covariances btwn pairs of securiteies3 Efficient set of risky assets4 Pt A from line 25 choose pt based on internal characteristics such as risk adversPlot expected returns for Market and Stock in each StateLine Joining = Characteristic line of securityBeta =Chg in E(stock) / Chg in E(mkt) =Responsiveness Coefficient=Slope of Characteristic Line=1.5=returns of Stock magnified 1.5x over market= Contribution of risk for stock