Capital Allocation Between The Risky And The RiskFree Asset

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Chapter 7

• Capital Allocation Between The Risky And The
  Risk-Free Asset

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Allocating Capital Risky Risk Free Assets

• Its possible to split investment funds between
  safe and risky assets.
• Risk free asset proxy T-bills
• Risky asset stock (or a portfolio)

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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.

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Example Using Chapter 7.3 Numbers
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Expected Returns for Combinations
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Possible Combinations
E(r)
E(rp) 15
P
E(rc) 13
C
rf 7
F
?
0
?c
22
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Variance For Possible Combined Portfolios

?
?
Rule 4 in Chapter 6
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Combinations Without Leverage
?
?
?
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Capital Allocation Line with Leverage

• Borrow at the Risk-Free Rate and invest in stock.
• Using 50 Leverage,
• rc (-.5) (.07) (1.5) (.15) .19
• ?c (1.5) (.22) .33

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CAL (Capital Allocation Line)
E(r)
P
E(rp) 15
E(rp) -
rf 8
) S 8/22
rf 7
F
?
0
?p 22
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CAL with Higher Borrowing Rate
E(r)
P
) S .27
9 7
) S .36
?
?p 22
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Risk Aversion and Allocation

• 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.

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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

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CAL with Risk Preferences
E(r)
The lender has a larger A when
compared to the borrower
P
Borrower
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Lender
?
?p 22