Download Fundamental Risk

Chapter 18
The Analysis of Equity Risk
and the Cost of Capital
The Analysis of Equity Risk and the
Cost of Capital
Link to Previous Chapters
Chapter 3 reviewed standard beta
technologies to measure the cost
of capital. Chapter 13
distinguished operating risk and
financing risk.
This Chapter
This chapter analyzes the
fundamental determinants of
operating and financing risk in
equity investing. It also
introduces price risk and outlines
ways to incorporate risk when
valuing firms and trading in their
shares.
Link to Next Chapter
Chapter 19 analyzes the risk of
firms’ debt.
Link to Web Page
The book’s web site has more
discussion of risk.
What are the
problems with
standard beta
technologies?
What are the
fundamental
determinants of
risk?
What is price
risk?
How is risk
incorporated in
valuation?
What you will learn from this
chapter
• That precise measures of the cost of capital are
difficult to calculate
• What risk is
• How business investment can yield extreme (high and
low) returns
• How diversification reduces risk
• Problems with using the standard Capital Asset Pricing
Model and other beta technologies
• The difference between fundamental risk and price risk
• The determinants of fundamental risk
• The determinants of price risk
What you will learn from this
chapter (cont.)
• How fundamental analysis protects against price
risk
• How pro forma analysis can be adapted to prepare
value-at-risk profiles
• How fundamentals help to measure betas
• How the investor finesses the problem of not
knowing the required return
• How to combine value-at-risk profiling and
screening analysis
The Nature of Risk
• Value is determined by expected payoffs
discounted for risk
• Risk is determined by the likelihood of
getting payoffs that are different from the
expected payoff
• Risk is characterized by the set of possible
outcomes that an investor faces and the
probabilities of these outcomes: a payoff (or
return) distribution
Models of the Distribution of Returns:
The Normal Distribution
Best and Worst Performers, 2004: Wall
Street Journal Shareholder Scorecard
The Best Performers
The Worst Performers
One Year
Company
Return, %
Taser International
361.1%
Kmart Holding
313.2%
Chicago Mercantile Exchange 218.5%
Autodesk
209.6%
Apple Computer
201.4%
American Eagle Outfitters
188.1%
TXU.
177.6%
Penn National Gaming
161.9%
Boyd Gaming
161.3%
First Marblehead
157.1%
Sepracor
148.1%
USG
143.0%
Sirius Satellite Radio
141.1%
Urban Outfitters
139.7%
Wynn Resorts
138.9%
OSI Pharmaceuticals
132.1%
Cree
126.6%
Tesoro
118.7%
Southwestern Energy
112.1%
VeriSign
106.1%
Cytyc
99.2%
Valero Energy
97.6%
Diamond Offshore Drilling
97.2%
Tibco Software
97.0%
Monsanto
96.1%
One Year
Company
Return, %
Agere System
-55.1%
Foundry Networks
-51.8%
Ciena
-49.1%
PMC-Sierra
-44.0%
Synopsys
-42.3%
Chiron
-41.5%
Level 3 Communications-40.5%
UTStarcom
-40.2%
Rite Aid
-39.4%
LSI Logic
-38.2%
Novell
-35.9%
Millennium Pharmaceuticals
-34.9%
Inc.
Fairchild Semiconductor-34.9%
Atmel
-34.8%
Vishay Intertechnology -34.4%
Novellus Systems
-33.7%
Allied Waste Industries -33.1%
Teradyne
-32.9%
Sanmina-Sci
-32.8%
Intersil CI A
-32.3%
Entercom Communications
-32.2%
CI A
Tenet Healthcare
-31.6%
Icos
-31.5%
Unisys
-31.4%
SPX
-30.2%
The Actual Distribution of
Annual Stock Returns
Probability
-2 sd
-100%
-47%
0 sd
13%
2 sd
73%
100%
Annual Return
Diversification and Risk: the Effect on
Standard Deviation from Adding More
Securities to a Portfolio
Portfolio
Standard Deviation
1
5
10
15
Number of
Securities
The Normal Distribution for the
S&P 500 Portfolio
Mean annual return = 13%
Standard deviation of returns = 20%
The Actual Distribution of S&P 500
Portfolio Annual Returns, 1926-98
Number of
Times
Observed
12
9
6
3
0
-50%
-40%
-30%
-20%
-10%
1%
10%
20%
30%
Source: Based on data from the Center for Research in Security Prices, University of Chicago
40%
50%
The Problems with “Asset Pricing
Models”
1. Risk factors are hard to identify
2. Risk premiums on risk factors are very
hard to measure
3. Often assume normal distributions of return
The CAPM is “Seductively
Precise”
• Normally distributed stock returns are assumed
• The market risk premium is a big guess
Is it 3½%, 4½%, 8%, or 9½%?
Has the market risk premium declined in the
1990s?
• Betas are estimated with error
• Estimates of the cost of capital are made from
market prices and assume that the market is
efficient
Fundamental Risk
• Risk is determined by a firm’s business
activities and so is understood by analyzing
those activities
• A basic distinction: operating and financing risk
Required Return for Equity  Required Return for Operations
 Market Leverage  Required Return Spread 
E 

F
Operating
Risk

V0D
 F   D 
V0E


Financing
Risk
A Framework for Analysis of
Fundamental Risk
V0E
RE 1 RE 2 RE 3
 CSE 0 
 2  3 
ρE
ρE
ρE
RE t  ROCE t  ρ E  1CSE t 1




Profitability
Risk
Growth
Risk
Risk is the chance of earning poor residual earnings
Profitability Risk: The Chance of
Getting Poor ROCE
Return on Common Equity  Return on Net Operating AssetsFinancial Leverage  Operating Spread 
NFO
ROCE  RNOA
  CSE RNOA  NBC 
Operating 
Risk
Financing
Risk
The Analysis of Fundamental
Risk
Fundamental Risk
ROCE Risk
FLEV x [ RNOA – NBC ]
ROCE = RNOA +
Operating Risk 1
Profit Margin
Risk
Asset Turnover
Risk
OI/Sales
Sales/NOA
Expense
Risk
Operating
Leverage Risk
Expense
Fixed Cost
Sales
Variable Cost
Growth Risk
(Operating Risk 2)
Growth in NOA =
Growth in Sales x
1/ATO
Financing Risk
Operating Liability
Leverage Risk
OL/NOA
Financial
Leverage Risk
Borrowing
Cost Risk
NFO/CSE
NFE/NFO
The Analysis of Operating Risk
RNOA = PM x ATO
The Drivers of Operating Risk
• PM Risk
Expense Risk
Operating Leverage Risk
• ATO Risk
• OLLEV Risk
The Analysis of Financing Risk
The drivers of the financing premium:
• Financial Leverage (FLEV) Risk
• Borrowing Cost Risk
The Analysis of Growth Risk
1
Growth in NOA  Growth in Sales 
ATO
Sales Risk
Sales risk is the primary business risk
Compounding Risk Factors
Produce Extreme Returns
A drop in sales is compounded by PM risk, ATO
risk, FLEV risk and NBC risk
• The effect of a drop in sales is magnified by
expense risk
• The effect of a drop in sales is magnified by
operating leverage risk
• The effect of a drop in sales is magnified by
asset turnover risk
• The effect of a drop in sales is magnified by
OLLEV risk
• The effect of a drop in sales is magnified by
FLEV risk
• The effect of a drop in sales is magnified by
borrowing cost risk
Value-at-Risk Profiles
•
Value-at-Risk profiles are prepared by developing
pro formas for different scenarios. The outcomes
in these pro formas are determined by the risk
factors.
•
Steps to prepare Value-at-Risk Profiles
1. Identify economic factors that affect the risk
drivers
2. Identify risk protection mechanisms in place
within the firm
3. Identify the effect of economic factors on the
fundamental risk drivers
4. Prepare pro forma financial statements under
alternative scenarios for the fundamental risk
drivers
5. Forecast residual operating income for each
scenario and, from these forecasts, calculate
the set of values from the scenarios
Value-at-Risk Profile: Firm A
Firm A
_____________________________________________________
Scenario
1
2
3
4
5
6
7
1%
0%
1%
2%
3%
4%
5%
0.1
0.1
0.2
0.2
0.2
0.1
0.1
Sales ($ million)
25
50
75
100
125
150
175
Operating expenses
($ million)
Fixed costs
20
20
20
20
20
20
20
Variable costs
18
36
54
72
90
108
126
Total expenses
38
56
74
92
110
128
146
6
1
8
15
22
29
52%
12%
1.3%
8.0%
12%
14.7%
16.6%
0.63
1.03
1.30
1.50
1.65
1.77
1.87
32.7%
12.3%
1.7%
12.0%
19.8%
26.0%
30.9%
39.7
48.7
57.7
66.7
75.7
84.7
93.7
15.4
8.9
2.5
4.0
10.5
16.9
23.4
40
49
16
133
251
366
484
Factor: GDP growth
Probability of scenario
Fundamentals affected
Operating income
($ million)
Profit margin
Asset turnover
RNOA
Beginning NOA
($ million)
ReOI (R=1.06)
Value with
limited liability
13
_____________________________________________________
PM risk driver:
ATO risk driver:
Operating expense = 20 + 72% of sales
Net operating assets = 30.7 + 36% of sales
Value-at-Risk Profile: Firm B
Firm B
___________________________________________________
Scenario
1
2
3
4
5
6
7
1%
0%
1%
2%
3%
4%
5%
0.1
0.1
0.2
0.2
0.2
0.1
0.1
25
50
75
100
125
150
175
4
4
4
4
4
4
4
Variable costs
22
44
66
88
110
132
154
Total expenses
26
48
70
92
114
136
158
Operating income
($ million)
Profit margin
1
2
5
8
11
14
17
4%
4%
6.7%
8.0%
8.8%
9.3%
9.7%
Asset turnover
0.81
1.17
1.37
1.50
1.59
1.65
1.70
12.0%
14.0%
15.4%
16.6%
Factor: GDP growth
Probability of scenario
Fundamentals affected
Sales ($ million)
Operating expenses
($ million)
Fixed costs
RNOA
Beginning NOA
($ million)
ReOI (R=1.06)
Value with
limited liability
3.3%
4.7%
9.1%
30.7
42.7
54.7
66.7
78.7
90.7
102.7
2.8
0.6
1.7
4.0
6.3
8.6
10.8
31
33
83
133
184
234
283
___________________________________________________
PM risk driver:
ATO risk driver:
Operating expense = 4 + 88% of sales
Net operating assets = 18.7 + 48% of sales
___________________________________________________________________
Value-at-Risk Profiles: Firm A and B
Historical Betas
Historical Betas are estimated from past
stock returns:
i   Return on the Market  ei 
Return i     Beta

Beta
estimate
Beta is a covariance with the return on
the market. This (standardized)
covariance is estimated from this timeseries regression.
Betas revert towards their
average of 1.0
Investors are interested in the future beta over the
period they hold the investment. High and low
historical betas tend to move closer to 1.0 over
time.
A rough rule for forecasting future betas from
historical betas:
Future Beta  0.35  0.65  Historical Beta 
This adjustment pulls betas towards 1.0.
Fundamental Betas: Forecasting
Future Betas from Fundamentals
Two steps:
1. Estimate relationship between historical betas
and fundamental attributes (say, FLEV and
OLLEV) in the cross section
Historical Beta i   b0  b1FLEVi   b2 OLEV i   ui 
2. Use estimates of b0, b1, and b2 to predict future
beta for a firm using the most recent measures
of the fundamentals for that firm:
Predicted Beta i   b̂0  b̂1FLEV i   b̂ 2 OLEV i 
Some Fundamental Measures that
have been Used to Predict Betas
• Earnings variability
• Cash flow variability
• Size
• Growth in earnings or sales
• Growth in assets
• P/E ratio
• P/B ratio
• Dividend yield
Scenario Planning and
Pro Forma Analysis
Pro forma analysis can be used to model
outcomes for different planning scenarios.
Investigate, for example,
• Adaptation Options
• Growth Options
• Strategic Risk Management Options
Different future paths can be articulated with pro
forma analysis. The value of each path calculated
can then be.
Price Risk and Fundamental Risk
• Fundamental Risk is the risk of value
not being realized because of
fundamental factors that affect the firm’s
activities
• Price Risk is the risk of value not being
realized in prices because of factors
other than fundamentals
Price Risk
Market Inefficiency Risk
The market price may not reflect the
“fundamental value”
• Scenario A risk
• Scenario B risk
Fundamental analysis reduces Scenario A
risk, but Scenario B risk can still affect a
diligent fundamental investor
Price Risk:
Scenario A and Scenario B
Scenario A: Price gravitates to fundamental value
Cum-dividend
Value
PTC = VTC
Normal return,
PTC  V0
Actual return,
PTC  P0
V0
Abnormal return,
V0  P0
P0
Time
0
1
2
3
4
T
Scenario B: Price deviates from fundamental value
Cum-dividend
Value
PTC
Abnormal return,
PTC  VTC
Actual return,
VTC
PTC  P0
Normal return,
VTC  V0
P 0 = V0
Time
0
1
2
3
4
T
Liquidity Risk
Liquidity Risk is the risk of not finding a buyer or
seller at the fundamental price
•Liquidity discounts
•Mechanisms to reduce liquidity risk
– Brokers
– Market makers
– Investment banks (“deal makers”)
The fees of these specialists are the costs of
reducing the liquidity discount
Inferring the Expected Return
from Market Prices
Reverse engineering to estimate the expected
reurn:
P0  CSE 0 
RE 1 RE 2
RE T  RE 
 2      T   T 1  /ρ TE
ρE
ρE
ρE
 ρ E  g 
Given an estimate of
growth (g), the expected
return can be estimated
from prices and
forecasts of earnings
P0 

AEG 2 AEG 3
AEG T 1 T 
Earn



...
ρE 

1
2
ρ

g
ρ
ρE
 E  1 

E
E
1
If market is efficient, expected return = cost of capital
Implied Expected Returns and Valueat-Risk Profiles
1. Group firms with similar Value-at-Risk profiles
2. Rank firms within each group on implied
expected returns
3. Buy those with high expected returns, sell those
with low expected returns
Holding risk constant
Relative Value Analysis: Evaluation
firms within a Risk Class
Relative value ratios for firms in same risk class:
Relative Value Ratio 
V0E 1/P0 1
V0E 2 /P0 2 
V0E 1 and V0E 2  are calculated by discounting expected
residual earnings (or capitalizi ng earnings and growth)
at the risk-free rate.
P0 1 and P0 2  are the market prices for the two investments.
A relative value ratio of 1.0 implies no arbitrage
Perceived Risk
Name of Stock
Perceived Risk
Mean
Asset Size
Financial Leverage
Variance
Variability
in Earnings
_____________________________________________________________________________________________
AT&T
1.89
1.22
11.83
0.165
1.09
Procter & Gamble
2.36
1.74
8.85
0.318
2.79
IBM
2.39
1.52
10.30
0.338
1.95
General Electric
2.69
1.64
9.95
0.468
1.29
Exxon
2.70
1.97
11.33
0.277
2.25
Commonwealth Edison
3.20
2.40
9.32
0.620
1.76
Dow Jones & Co.
3.57
2.38
6.28
0.477
2.96
McDonalds
3.87
2.36
7.97
0.413
2.32
Sears Roebuck
3.91
1.69
10.24
0.573
1.42
DuPont
4.11
1.91
10.08
0.508
1.64
Safeway
4.28
3.27
8.21
0.691
2.01
Citicorp
4.30
2.37
11.69
Dr. Pepper
4.32
2.03
5.11
0.215
General Motors
4.59
2.43
10.57
0.422
Xerox
4.69
2.45
8.95
0.397
1.04
American Broadcasting
4.86
1.83
7.37
0.370
0.47
Holiday Inns
5.13
1.86
7.43
0.536
1.34
Tandy
5.54
2.00
6.84
0.225
3.27
Litton Industries
5.66
1.78
8.21
0.552
2.52
RCA
5.67
2.02
8.97
0.855
Georgia Pacific
5.88
2.51
8.53
0.450
3.13
Emery Air Freight
5.92
2.58
5.62
0.697
2.28
E.F. Hutton
6.37
2.75
8.64
1.80
U.S. Homes
7.23
2.60
6.63
20.18
International Harvester
8.78
0.41
8.58
1.52
2.26
0.704
Source: G.E. Farrelly, K.R. Ferris and W.R. Reichenstein,” Perceived Risk, Market Risk, and Accounting Determined
Risk measures,” Accounting Review, April 1985, pp. 278-288.
Building in a Margin of Safety
1. Use a high discount rate in evaluating a
BUY; use a low discount rate in evaluating
a SELL
2. Be conservative (for a BUY) or optimistic
(for a SELL) in forecasting