McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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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: ExampleExample – 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)

.4% ( .4%) .8%.4

1% ( 1%) 2%

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.

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Measuring Beta GraphicallyF

ost

erh

ou

se C

orp

ora

tio

n R

etu

rns

(%)

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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: ExampleExample – 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 .31Portfolio 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

Market Risk Premium =

f

m

m f

r

r

r r

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Market Risk Premium: Example

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Beta

Exp

ecte

d R

etu

rn (

%)

Let,

4%

12%

Market Risk Premium = 8%

f

m

r

r

Example:

4%fr

8%market risk premium Market Portfolio (market return = 12%)

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Capital Asset Pricing Model (CAPM)

Market risk premium -

Risk premium on any asset -

( )

or,*

( )

m f

f

f m f

f m f

r r

r r

r r r r

r r r r

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

According to CAPM, the expected return on the asset is

( ) 4% 1.2 (8%) 13.6%f m fr r r r

Let:

4%

12%

Thus, the Market Risk Premium = 8%

f

m

r

r

Suppose 1.2

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Graphic Representation of CAPM

Security Market Line - The relationship between expected return and beta.

fr

mr

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CAPM TestedBeta 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 theSecurity Market Line

Which should be used to assess the value of a proposed project?

• 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.

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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 theSecurity Market Line

Should this project be accepted? Why?

What does this imply, if anything, about this project’s NPV?