McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-1 Capital Allocation Between the Risky Asset and the Risk-Free Asset Chapter 7

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-2 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 Between Risky & Risk Free Assets

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-3 Issues Examine risk/return tradeoff. Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets. Allocating Capital Between Risky & Risk Free Assets (cont.)

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-4 r f = 7%  rf = 0% E(r p ) = 15%  p = 22% y = % in p(1-y) = % in r f Example Using the Numbers in Chapter 7.2

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-5 E(r c ) = yE(r p ) + (1 - y)r f r c = complete or combined portfolio For example, y =.75 E(r c ) =.75(.15) +.25(.07) =.13 or 13% Expected Returns for Combinations

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-6 Possible Combinations E(r) E(r p ) = 15% r f = 7% 22% 0 P F  cc E(r c ) = 13% C

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-7 p c = Since rfrf y = 0, then    * Rule 4 in Chapter 6 * Variance on the Possible Combined Portfolios

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-8 c =.75(.22) =.165 or 16.5% If y =.75, then c = 1(.22) =.22 or 22% If y = 1 c = (.22) =.00 or 0% If y = 0       Combinations Without Leverage

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 7-9 Borrow at the Risk-Free Rate and invest in stock. Using 50% Leverage, r c = (-.5) (.07) + (1.5) (.15) =.19  c = (1.5) (.22) =.33 Using Leverage with Capital Allocation Line

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved CAL (Capital Allocation Line) E(r) E(r p ) = 15% r f = 7%  p = 22% 0 P F ) S = 8/22 E(r p ) -r f = 8% 

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved CAL with Higher Borrowing Rate E(r)  9% 7% ) S =.36 ) S =.27 P  p = 22%

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved 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

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved Utility Function U = E ( r ) A  2 Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion   = variance of returns

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved CAL with Risk Preferences E(r)  7% P Lender Borrower  p = 22% The lender has a larger A when compared to the borrower

McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved Home Assignment Required: problems 1, 2, 5, 6, 7, 8, 9, 19 (3 rd ed). problems 1, 2, 5, 6, 7, 8, 9, 22 (5 rd ed). closely follow financial news!