Chapters 8, 9, 10

Financial Analysis and

DecisionsSCH-MGMT

640Risk and Return

Mila Getmansky Sherman

Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

9- 2

Capital Asset Pricing Model

R = rf + B ( rm - rf )

CAPM

9- 3

Beta and Unique Risk

beta

Expected

return

Expectedmarketreturn

10%10%- +

-10%+10%

stock

-10%

1. Total risk = diversifiable risk + market risk2. Market risk is measured by beta, the sensitivity to market changes

9- 4

Beta and Unique Risk

Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.

Beta - Sensitivity of a stock’s return to the return on the market portfolio.

9- 5

Beta and Unique Risk

2m

imiB

9- 6

Beta and Unique Risk

2m

imiB

Covariance with the market

Variance of the market

9- 7

Beta

(1) (2) (3) (4) (5) (6) (7)Product of

Deviation Squared deviationsDeviation from average deviation from average

Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)

1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24

Average 2 2 Total 304 456

Variance = σm2 = 304/6 = 50.67

Covariance = σim = 736/6 = 76

Beta (β) = σim/σm2 = 76/50.67 = 1.5

Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of

the variance to the covariance (i.e., β = σim/σm2)

9- 8

Testing the CAPM

Avg Risk Premium 1931-2005

Portfolio Beta1.0

Security Market Line

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

9- 9

Testing the CAPM

Avg Risk Premium 1931-65

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

9- 10

Testing the CAPM

Avg Risk Premium 1966-2005

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

9- 11

CAPM Assumptions

Two benchmarks: Treasury bills and market portfolio

U.S. Treasury bills are risk-free (risk = 0)Investors can borrow money at the same

rate at which they lend

9- 12

Arbitrage Pricing Theory

Alternative to CAPMAlternative to CAPM

Expected Risk

Premium = r - rf

= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …

Return = a + bfactor1(rfactor1) + bf2(rf2) + …

9- 13

Arbitrage Pricing Theory

Estimated risk premiums for taking on risk factors

(1978-1990)

6.36Mrket

.83-Inflation

.49GNP Real

.59-rate Exchange

.61-rateInterest

5.10%spread Yield)(r

ium Risk PremEstimatedFactor

factor fr

9- 14

Three Factor Model

Steps to Identify Factors

1. Identify a reasonably short list of macroeconomic factors that could affect stock returns

2. Estimate the expected risk premium on each of these factors ( r factor 1 − r f , etc.);

3. Measure the sensitivity of each stock to the factors ( b 1 , b 2 , etc.).

9- 15

Testing the CAPM

0.1

1

10

10019

26

1936

1946

1956

1966

1976

1986

1996

2006

High-minus low book-to-market

Return vs. Book-to-MarketDollars(log scale)

Small minus big

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

9- 16

Three Factor Model

9- 17

Topics Covered

Company and Project Costs of CapitalMeasuring the Cost of EquityWACC (Weighted Average Cost of Capital)

9- 18

Company Cost of Capital

A company’s cost of capital can be compared to the CAPM required return

Required

return

Project Beta1.13

Company Cost of Capital

12.9

5.0

0

SML

9- 19

Company Cost of Capital

10%nologyknown tech t,improvemenCost

COC)(Company 15%business existing ofExpansion

20%products New

30% ventureseSpeculativ

RateDiscount Category

9- 20

Debt and WACC

rassets = WACC = rdebt D/V + requity E/V

After tax WACC = (1-Tc)rdebt D/V + requity E/V

IMPORTANT

E, D, and V are all market values of Equity, Debt and Total Firm

Value

requity = rf + Bequity ( rm - rf )

V= D + E

9- 21

0

20

0 0.2 0.8 1.2

Capital Structure & COC

Expected return (%)

Bdebt Bassets Bequity

Rrdebt=8

Rassets=12.2

Requity=15

Expected Returns and Betas prior to refinancing

9- 22

Measuring Betas

The SML shows the relationship between return and risk

CAPM uses Beta as a proxy for riskOther methods can be employed to

determine the slope of the SML and thus Beta

Regression analysis can be used to find Beta

9- 23

Measuring Betas

Intel Computer

Slope determined from plotting the line of best fit.

Price data: July 1996 – June 2001

R2 = .29

B = 1.54

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

-20.00 -10.00 0.00 10.00 20.00

Market return, %

Inte

l re

turn

, %

9- 24

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

-20.00 -10.00 0.00 10.00 20.00

Market return, %

Inte

l re

turn

, %

Measuring Betas

Intel Computer

Slope determined from plotting the line of best fit.

Price data: July 2001 – June 2006

R2 = .30

B = 2.22

9- 25

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00

Market return, %

Hei

nz

retu

rn, %

Measuring Betas

Heinz

Slope determined from plotting the line of best fit.

Price data: July 1996 – June 2001

R2 = .18

B = .47

9- 26

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

-20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00

Market return, %H

ein

z re

turn

, %

Measuring Betas

Heinz

Slope determined from plotting the line of best fit.

Price data: July 2001 – June 2006

R2 = .15

B = .36

9- 27

Estimated Betas

Beta equity

Standard Error

Burlington Northern Santa Fe 0.83 0.19

Canadian Pacific 0.9 0.31CSX 0.99 0.2

Kansas City Southern 1.02 0.24Norfolk Southern 0.78 0.26

Union Pacific 0.69 0.18Industry portfolio 0.87 0.16