# Ch7 - – slope c p f p f c r r E r r E σ ] ) ( [ ) (-+ =...

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Capital Allocation Chapter 7

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Capital allocation Two fund separation Invest into riskfree asset and risky portfolio Examine the risk-return trade-off How risk aversion affect the allocation decision
Example Given r f = 7% σ rf = 0% E(r p ) = 15% σ p = 22% y = % in p (1-y) = % in r f

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Expected return Return of the portfolio is 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%
Variance Variance of the portfolio is

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Combinations E(r) E(r p ) = 15% r f = 7% 22% 0 P F σ E(r c ) = 13% C
Leverage effect Borrow at the Risk-Free Rate and invest in stock. Using 50% Leverage, r c = (-.5) (.07) + (1.5) (.15) = .19 σ c = (1.5) (.22) = .33

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Capital allocation line E(r) r f = 7% σ p = 22% 0 P F ) S = 8/22 E(r p ) - r f = 8% σ E(r p ) = 15%
Equation Investment opportunity set Equation of CAL Reward-to-variability ratio

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Unformatted text preview: – slope c p f p f c r r E r r E σ ] ) ( [ ) (-+ = Higher borrowing rate • Normally the borrowing rate is higher, eg 9%, Risk aversion and allocation • Choosing optimal portfolio • 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. Utility function • U = E ( r ) - .005 A σ 2 Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion σ 2 = variance of returns Optimal portfolio • Expected return: • Variance: • Optimal portfolio Optimal portfolio • • • • Example • 2 * 01 . ) ( p f p A r r E y σ-=...
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## This note was uploaded on 07/12/2011 for the course FINA 221 taught by Professor Na during the Spring '09 term at HKUST.

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Ch7 - – slope c p f p f c r r E r r E σ ] ) ( [ ) (-+ =...

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