July 14 Slides.2

# July 14 Slides.2 - Chapter6 Graphically, .Thatis, E 1...

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7/13/2011 1 Chapter 6 Risk Aversion and Capital Allocation to Risky Assets Maximizing Expected Utility Graphically, to maximize utility an investor want to move to the indifference curve the farthest to the NW as possible. That is, attain the highest level of utility. E σ

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7/13/2011 2 By definition, a risk free asset is an asset with zero variance and a risky asset has a variance greater than zero. Risky and Risk Free Assets 2 2 (5 12) ps rs Er   Thus, by equation 5.12, a risk free asset must have in all possible scenarios. That is, the return is always the same, regardless of scenario, and is equal to the expected return. We will use to denote the return on a risk free asset.       (5.12) s     Er rs f r Assume we create the following portfolio, C, at the beginning of the month: Invest \$30 in Asset A Invest \$70 in Asset B Risky and Risk Free Assets At the end of the month we find the following: A earned a 20% return \$30 x 1.20 = \$36 B earned a 40% return \$70 x 1.40 = \$98 Total \$134 Thus the portfolio return was: \$134 \$100 34% \$100
7/13/2011 3 Another way to see this is: That is: Risky and Risk Free Assets       \$1001 \$301 \$701 CAB rrr   \$30 \$70 w r w r    Where the weights of the assets are: Now, lets apply the expectation operator to both sides of our equation: \$100 \$100 A A B B \$30 \$70 \$100 \$100

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July 14 Slides.2 - Chapter6 Graphically, .Thatis, E 1...

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