Percentage Returns: Div Yield + Capital Gain Total Return = Div(t+1) / P(t) + (P(t+1) – Pt) / P(t) R(t+1) = .05 + .09 = .15 Suppose you had 5k invested Total dollar return = 5k x .15 If you know the total dollar return on the stock You do not need 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 = .175 Average Return (B) = Bbar = .055 2. Deviation from expected return: RA – Abar (For each state) 3. Square each deviation 4. Average of all the squares = Variance 5. Sq. Rt. Of Variance = St. Deviation OR: Var(Rn) = Expected valued of (Rn – Rbar)^2 Covariance and Correlation: 1. Multiply respective deviations / residuals together 2. Come up with an average of multiplied residuals Cov (Ra,Rb) = Expcected (Avg.) of Residuals 1. A’s return generally above its avg. when B’s return above avg positive dependency / relationship … POSITIVE Covariance 2. A’s return generally about avg. when B’s below B’s avg. Negative Covariance 3. No relation = Covariance of 0 Correlation (A,B) = Covariance (A,B) / (St. DevA x S. DevB) Var (Port) = (XaVar (a))^2 + 2XaXbCov(a,b) + (XbVar(b))^2 NOTE: 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) = .127 Note: a positive relationship or Cov between variables increases the variance for the entire portfolio which is undesirable As long as Corr < 1 … SD(port) is < Wt avg of a and b DIVERSIFICATION The Efficient Set for Two Assets: 1. Diversification occurs when Corr < 1 2. MV = minimum Var / minimum SD 3. Cannot achieve point outside feasible set b/c cannot decrease SD of securites or correlation between securites How can an increase in the proportion of risky security (B)? Due to diversification effect. Risk of portfolio is reduced thus backward bending . Eventually the high SD of B causes the SD of the entire portfolio to rise 5. No investor would want to hold a portfolio with an expected return below that of the MV portfolio 6. 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/Borrow Market Equilibrium Portfolio: *In a world with homogenous expectations, all investors would hold the portfolio of risky assets represented by point A 1 Estimate expected returns and var for individuals securities 2 Covariances btwn pairs of securiteies 3 Efficient set of risky assets 4 Pt A from line 2 5 choose pt based on internal characteristics such as risk advers Plot expected returns for Market and Stock in each State
This is the end of the preview.
access the rest of the document.