analytical methods for lawyers (finance)

Analytical Methodsfor Lawyers (Finance)

Risk

Discount rate

Capital Asset Pricing Model(CAPM)

(last updated 20 Apr 09)

Merton on risk

What is the value of $1000?

What is the value of $1000?

Nominal?When?Risk?

Value a business

Year Revenues Earnings

1 1,600,000 134,000

2 1,755,000 256,000

3 1,259,000 122,000

4 1,560,000 195,000

5 1,900,000 220,000

Thereafter 2,100,000 234,000

spreadsheet

What is risk?

How do markets “price” risk?

What is ECMH?

What is CAPM?

ECMH

MarketInformation Price

Ronald Gilson(Stanford)

Reinier Kraakman (Harvard)

Can you beat the market?

Brownian motion(Louis Bachelier)

One hundred thousandlemings can’t all be wrong

How does the market value

risk and return?

Which investment would you choose?

Which investment would you choose?

Return

Risk

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.

Stock A Stock B

Compare returns to market average

Market average

Stock A

Market average

Stock B

Market average

Stock A

Market average

Stock B

Slope = 1.7 Slope = 0.6

Return(%)

Risk (measured as beta)

Risk vs. Return

Stock A = 1.7

Stock B = 0.6

Mkt = 1.0

Return

Risk vs. Return

Stock A = 1.7

Stock B = 0.6

Mkt = 1.0

Return(%)

Risk (measured as beta)

Capital Asset Pricing Model

Mkt = 1.0

rf

rm

Risk (measured as beta)

Return(%)

Capital Asset Pricing ModelE(r) = rf + rm- rf )

Beta = 1.7

Beta = 0.6

Mkt = 1.0

rf

rm

E(r)

E(r)

Return(%)

Risk (measured as beta)

Solve for beta …

Beta = 0.6

Mkt = 1.0

rf = 3.2%

rm= 11.7%

E(r)

Return(%)

Risk (measured as beta)

Assume: rm = 11.7% / rf = 3.2%

E(r) = rf + rm- rf )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%

Beta = 1.7

Mkt = 1.0

E(r)

Return(%)

Risk (measured as beta)

Assume: rm = 11.7% / rf = 3.2%

E(r) = rf + rm- rf )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%

rm= 11.7%

rf = 3.2%

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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