Using Regression Analysis to Determine Stock Beta

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Using Regression Analysis to Determine Stock Beta
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Regression Analysis

• Regression provides a methodology of uncovering
  relationships between variables of interest using
  past data.
• The estimated relationships can then be used to
  make forecasts based on known parameters.

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Example

• Say you want to know what the expected return on
  a stock should be.
• You can estimate the relationship to the market
  portfolio using a regression
• Then use the expected future market return to
  calculate the expected return of the stock.

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Relationship between Stock A and the SP 500

• Always a good idea to graph the variables
• X (market excess return)
• Y (stock A excess return)
• Gives you a feel for the relationship
• Should be a positive relationship

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Example Sample of 10 houses
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Graph
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A Regression Model

• Assuming that the relationship between y and x
  is linear we can estimate the regression
  coefficients by OLS (Ordinary Least Squares)

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A Regression Model-The Capital Asset Pricing
Model
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A Regression Model-The Capital Asset Pricing
Model

• In estimating beta, we often use excess returns,
  the return above the risk free rate.

In other words, regress the excess stock return
on the excess market return to determine the
stocks beta.
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Steps in a Regression Analysis

• Identify the dependent variable (stock return)
  the variable you wish to forecast.
• Identify the independent variable (market
  return).
• Adjust the variables for the risk free rate.
• Run the analysis.

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Outputs from a regression

• Regression coefficients
• intercept and slopes.
• CAPM predicts zero intercept.
• Uncertainty in coefficients
• How confident are we in our estimates of the
  intercept and slope? Standard error. T-Test.
  Confidence interval.
• Explanatory power
• Standard Error (Deviation) of Residuals
• R-squared.

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Regression Output
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Graph
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Prediction of future stock returns using Beta

• We have estimated the beta as 1.65. Now we can
  use this to calculate the expected stock returns
  next year. Suppose we expect the market return
  to be 10 next year and the risk free rate will
  be 3. Then