Estimating Beta - New York University

Estimating Beta

The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) -

Rj = a + b Rm

? where a is the intercept and b is the slope of the regression.

The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock.

This beta has three problems:

? It has high standard error

? It reflects the firm's business mix over the period of the regression, not the current

mix

? It reflects the firm's average financial leverage over the period rather than the

current leverage.

Aswath Damodaran

63

Beta Estimation: The Noise Problem

Aswath Damodaran

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Beta Estimation: The Index Effect

Aswath Damodaran

65

Solutions to the Regression Beta Problem

Modify the regression beta by

? changing the index used to estimate the beta

? adjusting the regression beta estimate, by bringing in information about the

fundamentals of the company

Estimate the beta for the firm using

? the standard deviation in stock prices instead of a regression against an index

? accounting earnings or revenues, which are less noisy than market prices.

Estimate the beta for the firm from the bottom up without employing the regression technique. This will require

? understanding the business mix of the firm

? estimating the financial leverage of the firm

Use an alternative measure of market risk not based upon a regression.

Aswath Damodaran

66

The Index Game...

Aracruz ADR Aracruz

Aracruz ADR vs S&P 500

80

60

40 20

0

- 20

- 40

-20

- 10

0

10

S&P

A r a c r u z ADR = 2.80% + 1.00 S&P

Aracruz vs Bovespa

1 40

1 20

1 00

80

60

40

20

0

- 20

- 40

20

-50

-40

- 30

-20 -10

0

10

20

30

BOVESPA

A r a c r u z = 2.62% + 0.22 Bovespa

Aswath Damodaran

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