Short note on Estimating Betas

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Short note on Estimating Betas

• CAPM Implementation Details

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Excess return on your stock
Excess return on the market
On average, excess return on your stock should
equal beta times excess return on the market
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Estimating beta
Monthly excess return on your stock
Monthly excess return on the SP 500
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From your statistics course
5
The Properties of Beta

• Portfolio b is linear in the components.
• Ex For a 50-50 portfolio, with one stock having
  b.6 and the other having b.8. The portfolio
  has b.7.
• The portfolio mean also has this property, while
  standard deviation doesnt.
• For the mathematically inclined this is because
  b is proportional to covariance, and covariance
  is linear.
• The b of the market portfolio is 1

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Hows your confidence?

• Recall that I said
• Confidence intervals for means are huge
• You cant estimate the mean of anything
• Lots of variation in realized stock returns
• This is not true for higher moments
• We can estimate variance and covariance
  relatively precisely.
• We can be relatively confident of our estimates
  of betas, but not alphas.

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Alpha

• ( Excess return that is not explained by
  movements in the market.)
• If the CAPM is correct, and if markets are
  efficient
• alphas should be zero in expectation
• But in any sample of data, realized alpha will
  differ wildly from zero (either or )
• Active portfolio management is all about the
  search for alpha
• Go visit Dr. Bob Litterman

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A detail
Excess return on your stock
Excess return on the market
So technically you should be estimating.
For high-frequency data (i.e. day, week, month)
the risk-free rate is very small and very stable,
so there is little change to beta from estimating
Practical application for Homework 5, just use
raw returns.