This document discusses concepts related to measuring market risk and the Capital Asset Pricing Model (CAPM). It provides examples to illustrate how to calculate beta and the market risk premium. It also discusses limitations of CAPM and alternative models. The key points are:
1) Beta measures the sensitivity of a stock's returns to changes in the market and is used to estimate the expected return under CAPM.
2) CAPM holds that the expected return is equal to the risk-free rate plus the product of beta and the market risk premium.
3) Empirical tests have found mixed support for CAPM and alternative models like the Fama-French three-factor model may better explain returns.
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Risk, Return and the Capital
Budget
This chapter introduces the quantitative techniques
used to estimate the required returns on equity.
It also establishes the relationship between market
risk and the relative riskiness of the firm.
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Measuring Market Risk
Market Portfolio - Portfolio of all assets in the
economy.
Beta - Sensitivity of a stock’s return to the return on
the market portfolio.
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Measuring Beta: Example
Example – The Fosterhouse Gourmet Foods corporation has the following %
returns on its stock, relative to the listed changes in the % return on the
market portfolio. Its beta (β) can be derived from this information.
Month * Market Return % Fosterhouse Return %
1 +1 +1.8
2 -1 +1.6
3 +1 +0.2
4 +1 -0.8
5 -1 +0.0
6 -1 -2.8
* The returns are expressed as percentages, though the results
will be identical if expressed as decimals.
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Measuring Beta: Example (ctd)
When the market was up 1%, Fosterhouse Corporation’s
average percent change was +.4%.
When the market was down 1%, Fosterhouse Corporation’s
average percent change was -.4%.
The change of .8% (-.4% to .4%) divided by the 2% (-1.0%
to 1.0%) change in the market produces a beta of .4.
b = - - = =
.4% ( .4%) .8% .4
1% - ( -
1%) 2%
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Stock Betas for Common Stocks
(May 2005 - April 2010)
What factors contribute
to the variation in these
betas?
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Total Risk and Market Risk
Recall that total risk is a combination of unique
risk and market risk.
What are the effects of diversification on unique
risk and market risk?
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Portfolio Beta
The beta of your portfolio will be an average of the betas of
the securities in the portfolio.
What would be the average beta if you owned all of the S&P
Composite Index stocks?
What is the beta of the risk-free return, U.S. Treasury Bills?
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Portfolio Beta: Example
Example – Calculate the beta of a portfolio that consists of 25%
Ford, 25% Boeing, and 50% McDonald’s.
Company Beta Weight Beta×Weight
Ford 2.53 .25 .63
Boeing 1.28 .25 .32
McDonald's .62 .50 .31
Portfolio Beta = 1.26
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Measuring Market Risk:
The Market Risk Premium
Market Risk Premium - Risk premium of market portfolio; the
difference between the market return and the return on risk-free Treasury
bills.
Let,
Risk-free rate of return
Market Return
f
m
Market Risk Premium =
m f
r
r
r r
=
=
-
12. Market Risk Premium: Example
12
-
12
14
12
10
8
6
4
2
0
market risk premium = 8%
0 0.2 0.4 0.6 0.8 1
Beta
Expected Return (%)
Let,
4%
12%
f
r
r
m
=
=
Market Risk Premium = 8%
Example:
4% f r =
Market Portfolio
(market return = 12%)
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Capital Asset Pricing Model
(CAPM)
r r
r r
Market risk premium -
Risk premium on any asset -
r r r r
( )
b
or,*
r r r r
( )
m f
f
f m f
b
f m f
=
=
- = ´ -
= + ´ -
Let r = expected return on any asset
* Note: These are identical, the risk-free rate has just been moved to the right hand side.
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CAPM: Example
f
r
r
m
=
=
According to CAPM, the expected return on the asset is
( ) 4% r = rf +b ´ rm - rf = +1.2´(8%) =13.6%
Let:
4%
12%
Thus, the Market Risk Premium = 8%
Suppose b =1.2
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Graphic Representation of
CAPM
Security Market Line - The relationship between expected
return and beta.
m r
f r
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CAPM Tested
Beta vs. Average Risk Premium
What do these results imply?
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Alternative Explanations to
CAPM
Small minus big
High minus low book-to-market
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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Alternative Explanations Tested
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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CAPM and Expected Returns
Is CAPM useful?
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Project Risk and the
Security Market Line
• Company Cost of Capital: Expected rate of return demanded
by investors in a company, determined by the average risk of
the company’s securities
• Project Cost of Capital: Minimum acceptable expected rate
of return on a project given its risk.
Which should be used to assess the value of a proposed project?
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Determinants of Project Risk
Consider:
1.Operating Leverage and Project Risk
2.The presence of non-diversifiable risk
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Project Risk and the
Security Market Line
Should this project be accepted? Why?
What does this imply, if anything, about this project’s NPV?
Hinweis der Redaktion
Chapter 12 Learning Objectives
1. Measure and interpret the market risk, or beta, of a security.
2. Relate the market risk of a security to the rate of return that investors demand.
3. Calculate the opportunity cost of capital for a project.
Chapter 12 Outline
Measuring Market Risk
Beta
Portfolio Beta
CAPM
Capital Budgeting and Project Risk
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio. Also known as market risk.
Note: In practice, estimates based on just 6 months would be very unreliable. Most estimates of standard deviation and beta use something like 5 years of monthly data.
Beta(β) - Sensitivity of a stock’s return to the return on the market portfolio. Also known as market risk.
Note: In practice, estimates based on just 6 months would be very unreliable. Most estimates of standard deviation and beta use something like 5 years of monthly data.
Steps to this graph:
1. Observe rates of return, usually monthly, for the stock and the market.
2. Plot the observations.
3. Fit a line showing the average return to the stock at different market returns.
Note: These estimates of beta used 5 years of monthly data.
Note: The beta of a portfolio is just the weighted sum of the betas of the individual stocks.
Market Risk Premium - Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.
Market Risk Premium - Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.
CAPM (Capital Asset Pricing Model) - Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.
Beta(β) - Sensitivity of a stock’s return to the return on the market portfolio. Also known as market risk.
CAPM (Capital Asset Pricing Model) - Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.
Beta(β) - Sensitivity of a stock’s return to the return on the market portfolio. Also known as market risk.
Security Market Line – The relationship between expected return and beta; a graphic representation of the CAPM.
Note: The “ten investors” represent the ten beta deciles with, “10” as the most aggressive (highest beta).
Book-to-market ratio -- Ratio of book value of equity to market value of equity
Book-to-market ratio -- Ratio of book value of equity to market value of equity
Company Cost of Capital – Expected rate of return demanded by investors in a company, determined by the average risk of the company’s securities.
Project Cost of Capital – Minimum acceptable expected rate of return on a project given its risk.
Project Cost of Capital – Minimum acceptable expected rate of return on a project given its risk.
Security Market Line – The relationship between expected return and beta; a graphic representation of the CAPM.
