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Analytical Methods for Lawyers (Finance) Risk Discount rate Capital Asset Pricing Model (CAPM) (last updated 20 Apr 09)

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Merton on risk

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What is the value of $1000?

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Nominal? When? Risk?

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Value a business YearRevenuesEarnings 11,600,000134,000 21,755,000256,000 31,259,000122,000 41,560,000195,000 51,900,000220,000 Thereafter2,100,000234,000 spreadsheet

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What is risk? How do markets “price” risk? What is ECMH? What is CAPM?

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ECMH Market InformationPrice Ronald Gilson (Stanford) Reinier Kraakman (Harvard) Can you beat the market?

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Brownian motion (Louis Bachelier)

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One hundred thousand lemings can’t all be wrong

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How does the market value risk and return?

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Which investment would you choose?

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Return Risk

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What is beta? The Beta coefficient is a key parameter in CAPM. It measures the part of the asset's statistical variance that cannot be mitigated by portfolio diversification, and thus is correlated with the return of assets in the portfolio.

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Stock AStock B Compare returns to market average

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Market average Stock A Market average Stock B

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Market average Stock A Market average Stock B Slope = 1.7Slope = 0.6

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Return (%) Risk (measured as beta) Risk vs. Return Stock A = 1.7 Stock B = 0.6 Mkt = 1.0

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Return Risk vs. Return Stock A = 1.7 Stock B = 0.6 Mkt = 1.0 Return (%) Risk (measured as beta)

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Capital Asset Pricing Model Mkt = 1.0 rfrf rmrm Risk (measured as beta) Return (%)

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Capital Asset Pricing Model E(r) = r f + r m - r f ) Beta = 1.7 Beta = 0.6 Mkt = 1.0 rfrf rmrm E(r) Return (%) Risk (measured as beta)

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Solve for beta …

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Beta = 0.6 Mkt = 1.0 r f = 3.2% r m = 11.7% E(r) Return (%) Risk (measured as beta) Assume: r m = 11.7% / r f = 3.2% E(r) = r f + r m - r f ) E(r) = 3.2% + 0.6*(11.7% – 3.2%) E(r) = 3.2% + 0.6*(8.5%) E(r) = 3.2% + 5.1% = 8.3%

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Beta = 1.7 Mkt = 1.0 E(r) Return (%) Risk (measured as beta) Assume: r m = 11.7% / r f = 3.2% E(r) = r f + r m - r f ) E(r) = 3.2% + 1.7*(11.7% – 3.2%) E(r) = 3.2% + 1.7*(8.5%) E(r) = 3.2% + 13.45% = 16.65% r m = 11.7% r f = 3.2%

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It’s better to be vaguely right, than precisely wrong … Study after study has found that beta isn't a good measure of risk …

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Return and Risk: The Capital-Asset Pricing Model (CAPM) Expected Returns (Single assets & Portfolios), Variance, Diversification, Efficient Set, Market.

Return and Risk: The Capital-Asset Pricing Model (CAPM) Expected Returns (Single assets & Portfolios), Variance, Diversification, Efficient Set, Market.

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