Beta

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Beta
or.

• What Is Beta and How Is It Calculated?

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Beta

• A coefficient measuring a stocks relative
  volatility
  
• Beta measures a stocks sensitivity to overall
  market movements
  

SourceUBS Warburg Dictionary of Finance and
Investment Terms
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• In practice, Beta is measured by comparing
  changes in a stock price to changes in the value
  of the SP 500 index over a given time period
  
• The SP 500 index has a beta of 1

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A Generic Example

• Stock XYZ has a beta of 2
• The SP 500 index increases in value by 10
• The price of XYZ is expected to increase 20 over
  the same time period

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Beta can be Negative

• Stock XYZ has a beta of 2
• The SP 500 index INCREASES in value by 10
• The price of XYZ is expected to DECREASE 20 over
  the same time period
  

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• If the beta of XYZ is 1.5
• And the SP increases in value by 10
• The price of XYZ is expected to increase 15

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• A beta of 0 indicates that changes in the market
  index cannot be used to predict changes in the
  price of the stock
  
• The companys stock price has no correlation to
  movments in the market index

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Source taken from yahoo.finance.com, except PXLW
from bloomberg.com

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Beta and Risk

• Beta is a measure of volatility
• Volatility is associated with risk

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Risk-Reward Curve
Risk
Expected Return
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• If beta is a measure of risk, then investors who
  hold stocks with higher betas should expect a
  higher return for taking on that risk
  
• What does this remind you of?

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Beta and CAPM

• The capital asset pricing model
• E(R) Rf B(Rm-Rf)
• where
• E(R) Expected return
• Rf risk free rate of return
• B beta
• Rm market return

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WACC

• Weighted average cost of capital
• WACC (D/V)Rd(1-T) (E/V)Re
• where
• D market value of firms debt
• Rd return on debt securities
• T tax rate
• E market value of firms equity securities
• Re return on equity securities (from CAPM)
  
  
• V total value of firms securities (D V)

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WACC and Beta

• WACC increases as the beta and the rate of return
  on the equity securities increases (all else
  constant)
  
• WACC is used as the discount rate in DCF models
• Therefore, increasing WACC reduces the firms
  valuation to reflect the increase in risk

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How to Calculate Beta

• Beta Covariance(stock price, market index)
• Variance(market index)
• When calculating, you must compare the percent
  change in the stock price to the percent change
  in the market index

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How to Calculate Beta

• Easily calculated using Excel and Yahoo! Finance
  
  
• Use COVAR and VARP worksheet functions
• An example
• Calculate the beta of Citigroup stock over the
  5-yr time period from Jan. 1, 1997 Dec. 31, 2001

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SP 500 Adjusted Daily Closing Values January 1,
1997 - December 31, 1997
Citigroup Adjusted Daily Closing Prices January
1, 1997 - December 31, 1997
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