Tài chính doanh nghiệp - Chapter 7: Capital allocation between the risky and the risk - Free asset

Chapter 7Capital Allocation Between The Risky And The Risk-Free AssetIt’s possible to split investment funds between safe and risky assets.Risk free asset: proxy; T-billsRisky asset: stock (or a portfolio)Allocating Capital: Risky & Risk Free AssetsIssuesExamine risk/return tradeoff.Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets.Allocating Capital: Risky & Risk Free Assetsrf = 7%rf = 0%E(rp) = 15%p = 22%y = % in p(1-y) = % in rfExample Using Chapter 7.3 NumbersE(rc) = yE(rp) + (1 - y)rfrc = complete or combined portfolioFor example, y = .75E(rc) = .75(.15) + .25(.07)= .13 or 13%Expected Returns for CombinationsPossible CombinationsE(r)E(rp) = 15%rf = 7%22%0PFcE(rc) = 13%Cpc=Sincerfy= 0, then* Rule 4 in Chapter 6*Variance For Possible Combined Portfoliosc= .75(.22) = .165 or 16.5%If y = .75, thenc= 1(.22) = .22 or 22%If y = 1c= (.22) = .00 or 0%If y = 0Combinations Without LeverageBorrow at the Risk-Free Rate and invest in stock.Using 50% Leverage,rc = (-.5) (.07) + (1.5) (.15) = .19c = (1.5) (.22) = .33Capital Allocation Line with LeverageCAL (Capital Allocation Line)E(r)E(rp) = 15%rf = 7% p = 22%0PF ) S = 8/22E(rp) - rf = 8%CAL with Higher Borrowing RateE(r)9%7%) S = .36) S = .27Pp = 22%Greater levels of risk aversion lead to larger proportions of the risk free rate.Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets.Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations.Risk Aversion and AllocationUtility FunctionU = E ( r ) - .005 A s2Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion s2 = variance of returnsCAL with Risk PreferencesE(r)7%PLenderBorrowerp = 22% The lender has a larger A when compared to the borrower