Lecture Investments (6/e) - Chapter 7 "Capital allocation between the risky and the risk-free asset" presents the following content: allocating capital - risky & risk free assets, expected returns for combinations, possible combinations, variance for possible combined portfolios, combinations without leverage,. | Chapter 7 Capital Allocation Between The Risky And The Risk-Free Asset It’s possible to split investment funds between safe and risky assets. Risk free asset: proxy; T-bills Risky asset: stock (or a portfolio) Allocating Capital: Risky & Risk Free Assets Issues Examine risk/return tradeoff. Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets. Allocating Capital: Risky & Risk Free Assets rf = 7% rf = 0% E(rp) = 15% p = 22% y = % in p (1-y) = % in rf Example Using Chapter Numbers E(rc) = yE(rp) + (1 - y)rf rc = complete or combined portfolio For example, y = .75 E(rc) = .75(.15) + .25(.07) = .13 or 13% Expected Returns for Combinations Possible Combinations E(r) E(rp) = 15% rf = 7% 22% 0 P F c E(rc) = 13% C p c = Since rf y = 0, then * Rule 4 in Chapter 6 * Variance For Possible Combined Portfolios c = .75(.22) = .165 or If y = .75, then c = 1(.22) = .22 or 22% If y = 1 c = (.22) = .00 or 0% If y = 0 Combinations Without Leverage Borrow at the Risk-Free Rate and invest in stock. Using 50% Leverage, rc = () (.07) + () (.15) = .19 c = () (.22) = .33 Capital Allocation Line with Leverage CAL (Capital Allocation Line) E(r) E(rp) = 15% rf = 7% p = 22% 0 P F ) S = 8/22 E(rp) - rf = 8% CAL with Higher Borrowing Rate E(r) 9% 7% ) S = .36 ) S = .27 P 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 Allocation Utility Function U = E ( r ) - .005 A s2 Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion s2 = variance of returns CAL with Risk Preferences E(r) 7% P Lender Borrower p = 22% The lender has a larger A when compared to the borrower | Chapter 7 Capital Allocation Between The Risky And The Risk-Free Asset It’s possible to split investment funds between safe and risky assets. Risk free asset: proxy; T-bills Risky asset: stock (or a portfolio) Allocating Capital: Risky & Risk Free Assets Issues Examine risk/return tradeoff. Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets. Allocating Capital: Risky & Risk Free Assets rf = 7% rf = 0% E(rp) = 15% p = 22% y = % in p (1-y) = % in rf Example Using Chapter Numbers E(rc) = yE(rp) + (1 - y)rf rc = complete or combined portfolio For example, y = .75 E(rc) = .75(.15) + .25(.07) = .13 or 13% Expected Returns for Combinations Possible Combinations E(r) E(rp) = 15% rf = 7% 22% 0 P F c E(rc) = 13% C p c = Since rf y = 0, then * Rule 4 in Chapter 6 * Variance For Possible Combined Portfolios c = .75(.22) = .165 or If y = .75, then c = 1(.22) = .22 or 22% If y = 1 c = (.22) = .00 or 0% If y = 0 .
