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Capital Allocation Between the Risky Asset and the Risk-Free Asset

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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

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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.)

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r f = 7% rf = 0% E(r p ) = 15% p = 22% w = % in p(1-w) = % in r f Example

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E(r c ) = wE(r p ) + (1 - w)r f r c = complete or combined portfolio For example, w =.75 E(r c ) =.75(.15) +.25(.07) =.13 or 13% Expected Returns for Combinations

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Possible Combinations E(r) E(r p ) = 15% r f = 7% 22% 0 P F cc E(r c ) = 13% C

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p c = Since rfrf w = 0, then * Variance on the Possible Combined Portfolios

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c =.75(.22) =.165 or 16.5% If w =.75, then c = 1(.22) =.22 or 22% If w = 1 c = (.22) =.00 or 0% If w = 0 Combinations Without Leverage

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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

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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%

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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

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Example 1. Given the above data, suppose you want to achieve 10% of rate of return, how much do you want to invest in the risky asset p? 2. Again, suppose you want to maintain your risk level with standard deviation at 11%, what’s the maximum return you can achieve? r f = 7% rf = 0% E(r p ) = 15% p = 22% w = % in p(1-w) = % in r f

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Risk and Return Professor Thomas Chemmanur. 22 1. Risk Aversion ASSET – A: EXPECTED PAYOFF = 0.5(100) + 0.5(1) = $50.50 ASSET – B:PAYS $50.50 FOR SURE.

Risk and Return Professor Thomas Chemmanur. 22 1. Risk Aversion ASSET – A: EXPECTED PAYOFF = 0.5(100) + 0.5(1) = $50.50 ASSET – B:PAYS $50.50 FOR SURE.

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