Session 5: Measuring equity risk with
“diversified investors”
Aswath Damodaran
Aswath Damodaran
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Risk to diversified investors…
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If investors are diversified, the only risk that they should care about,
when investing in an asset, is the risk that it adds to a portfolio.
While all conventional risk and return models in finance share the
assumption that investors are diversified, they vary on how best to
measure this non-diversifiable risk.
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Aswath Damodaran
In the CAPM, with its assumptions of no transactions costs and no private
information, every investor holds a supremely diversified portfolio (the market
portfolio) and the non-diversifiable risk is measured relative to this portfolio with a
beta.
In the APM and multi-factor models, you allow for multiple sources of market risk
and betas relative to each one.
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Estimating Beta: Market Regression
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The standard procedure for estimating betas is to regress stock returns (Rj)
against market returns (Rm) Rj = a + b Rm
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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:
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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.
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Beta Estimation: The Noise Problem
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Beta Estimation: The Index Effect
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Solutions to the Regression Beta Problem
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Modify the regression beta by
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Estimate the beta for the firm using
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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
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changing the index used to estimate the beta
adjusting the regression beta estimate, by bringing in information about the
fundamentals of the company
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.
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Determinants of Betas
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Bottom-up Betas
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Bottom-up Beta: Firm in Multiple Businesses
SAP in 2004
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Approach 1: Based on business mix
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SAP is in three business: software, consulting and training. We will aggregate the
consulting and training businesses
Business
Revenues EV/Sales
Value
Weights
Beta
Software
$ 5.3
3.25
17.23
80%
1.30
Consulting $ 2.2
2.00
4.40
20%
1.05
SAP
$ 7.5
21.63
1.25
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Approach 2: Customer Base
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Why bottom-up betas?
The standard error in a bottom-up beta will be significantly lower than the
standard error in a single regression beta. Roughly speaking, the standard error
of a bottom-up beta estimate can be written as follows:
Std error of bottom-up beta =Average Std Error across Betas
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Number of firms in sample
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The bottom-up beta can be adjusted to reflect changes in the firm’s business
mix and financial leverage. Regression betas reflect the past.
You can estimate bottom-up betas even when you do not have historical stock
prices. This is the case with initial public offerings, private businesses or
divisions of companies.
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