Chapter 06
Risk and Return
Determinants of Intrinsic Value:
The Cost of Equity
Net operating
profit after taxes
Free cash flow
(FCF)
Value =
Required investments
in operating capital
−
FCF1
+
(1 + WACC)1
FCF2
+
(1 + WACC)2
=
+...
FCF∞
(1 + WACC)∞
Weighted average
cost of capital
(WACC)
Market interest rates
Cost of debt
Firm’s debt/equity mix
Market risk aversion
Cost of equity
Firm’s business risk
Important Notes
1. Risk of financial asset is judged by the risk of
its cash flow
2. Asset risk: Stand Alone basis vs. Portfolio
Context
3. Portfolio context: Diversifiable Risk vs. Market
Risk.
4. Investors in general are Risk Averse
STAND ALONE RISK
Stand alone risk: the risk an
investor would face if she or he held
only one particular asset.
Investment risk pertains to the
probability of actually earning a low
or negative return. The greater the
chance of low or negative returns,
the riskier the investment.
Probability Distribution &
Expected Rate of Return
Dollar Return
rate of return 
Amount invested
Amount received - Amount invested
=
Amount invested
^
r = expected rate of return.
n
r̂ =  Pi ri .
i =1
Probability Distribution &
Expected Rate of Return
Probability Distributions
Demand for the
Probability of this
Company's Products Demand Occurring
Strong
Normal
Weak
0,30
0,40
0,30
1,00
Rate of Return on Stock
if this Demand Occurs
Sale.com
Basic Foods
90%
45%
15%
15%
−60%
−15%
Calculation of Expected Rates of Return: Payoff Matrix
Demand for the
Probability of this
Company's Products Demand Occurring
(1)
(2)
Strong
Normal
Weak
0,3
0,4
0,3
1,0
Expected Rate of Return =
Sum of Products =
Sale.com
Rate of Return
(3)
Basic Foods
Product
Rate of Return
(2) x (3) = (4)
(5)
90%
15%
−60%
27,0%
6,0%
−18,0%
r̂ 
15,0%
45%
15%
−15%
r̂ 
Product
(2) x (5) = (6)
13,5%
6,0%
−4,5%
15,0%
Stand Alone Risk: Measurements
•
Standard Deviation: a measure of the tightness of
the probability distribution. The tighter the probability
distribution, the smaller the Standard Deviation and
the less risky the asset.
•
Coefficient of Variation: Standard Deviation divided
by return. It measures risk per unit of return, thus
provides more standardized basis for risk profile
comparison between assets with different return.
Standard Deviation
Variance
2 
n
2
(r
- r̂)
Pi
 i
i =1
Standard Deviation


n
2
(r
- r̂)
Pi
 i
i =1
Standard Deviation
Calculating Standard Deviations
Sale.com
Panel a.
Probability of
Occurring
(1)
0,3
0,4
0,3
Rate of Return on
Stock
(2)
90%
15%
−60%
1,0
Deviation from
Expected
Expected Return
Return
(3)
(2) − (3) = (4)
15%
75,0%
15%
0,0%
15%
−75,0%
Squared
Deviation
2
(4) = (5)
56,25%
0,00%
56,25%
Sq. Dev. × Prob.
(5) x (1) = (6)
16,88%
0,00%
16,88%
Sum = Variance =
33,75%
Std. Dev. = Square root of variance =
58,09%
Basic Foods
Panel b.
Probability of
Occurring
(1)
0,3
0,4
0,3
1,0
Rate of Return on
Stock
(2)
45%
15%
−15%
Deviation from
Expected
Expected Return
Return
(3)
(2) − (3) = (4)
15%
30,0%
15%
0,0%
15%
−30,0%
Squared
Deviation
2
(4) = (5)
9,00%
0,00%
9,00%
Sum = Variance =
Std. Dev. = Square root of variance =
Sq. Dev. × Prob.
(5) x (1) = (6)
2,70%
0,00%
2,70%
5,40%
23,24%
Probability distribution
Basic Foods
The larger the Standard
Deviation:
• the lower the probability
that actual returns will be
close to the expected
return
• hence the larger the risk
Sale.com
Rate of
return (%)
-60
-15 0 15
45
Expected Rate of Return
90
Historical Data to Measure
Standard Deviation
Standard Deviation
n
Estimated   S 
2
(
r
t - r Avg )

t =1
n 1
Coefficient of Variation (CV)
Standardized measure of dispersion
about the expected value:

CV = ^
r
Shows risk per unit of return.
B
A
0
A = B , but A is riskier because larger
probability of losses.

r
^
= CVA > CVB.
Risk & Return
in Portfolio Context
Return
^
rp is a weighted average:
n
rp = S w i ri .
^
^
i=1
Risk
Correlation Coefficient to measure the tendency
of two variables moving together
Portfolio Return
Stock
Microsoft
General Electric
Pfizer
Coca-Cola
Portfolio weight
0,25
0,25
0,25
0,25
Portfolio's Expected Return
Expected Return
12,0%
11,5%
10,0%
9,5%
10,75%
Portfolio Risk:
Standard Deviation of 2-Asset-Portfolio
Variance
 p  w1  1  w2  2  2( w1w2 1 2 12 )
2
2
2
2
Covariance
2
Cov12  12  1 2 12
Correlatio n Coeficient  12
Standard Deviation
p 
 p2
Portfolio Risk:
Standard Deviation of 2-Asset-Portfolio
•
The standard deviation of a portfolio is generally not a
weighted average of individual standard deviations (SD).
•
The portfolio's SD is a weighted average only if all the
securities in it are perfectly positively correlated. Risk is not
reduced at all if the two stocks have r = +1.0.
•
Where the stocks in a portfolio are perfectly negatively
correlated, we can create a portfolio with absolutely no risk,
or Portfolio’s SD equal to 0. Two stocks can be combined
to form a riskless portfolio if r = -1.0.
Portfolio Risk:
Perfectly Negative Correlation
Year
Stock W returns
2000
40%
2001
-10%
2002
35%
2003
-5%
2004
15%
Average return
15%
Standard deviation
22.64%
Correlation Coefficient
Stock M returns
-10%
40%
-5%
35%
15%
15%
22.64%
Portfolio WM
(Equally weighted avg.)
15%
15%
15%
15%
15%
15%
0.00%
-1.00
Returns Distribution for Two Perfectly
Negatively Correlated Stocks (ρ = -1.0) and
for Portfolio WM
Stock W
Stock M
40 .
40
.
15
0
-10
.
.
.
.
40
. 15 . . . . .
15
0
0
-10
Portfolio WM
.
.
-10
Portfolio Risk:
Perfectly Positive Correlation
Year
Stock M returns
2000
-10%
2001
40%
2002
-5%
2003
35%
2004
15%
Average return
15%
Standard deviation
22,64%
Correlation Coefficient
Stock M' returns
-10%
40%
-5%
35%
15%
15%
22,64%
Portfolio MM'
-10%
40%
-5%
35%
15%
15%
22,64%
1,00
Returns Distributions for Two Perfectly
Positively Correlated Stocks (ρ= +1.0) and
for Portfolio MM’
Stock M’
Stock M
Portfolio MM’
40
40
40
15
15
15
0
0
0
-10
-10
-10
Portfolio Risk:
Partial Correlation
Year
Stock W returns
2000
40%
2001
-10%
2002
35%
2003
-5%
2004
15%
Average return
15%
Standard deviation
22,64%
Correlation coefficient
Stock Y returns
28%
20%
41%
-17%
3%
15%
22,57%
Portfolio WY
34%
5%
38%
-11%
9%
15%
20,63%
0,67
Adding Stocks to a Portfolio


What would happen to the risk of an average
1-stock portfolio as more randomly selected
stocks were added?
p would decrease because the added stocks
would not be perfectly correlated, but the
expected portfolio return would remain
relatively constant.
23
1 stock ≈ 35%
Many stocks ≈ 20%
1 stock
2 stocks
Many stocks
-75 -60 -45 -30 -15 0
15 30 45 60 75 90 10
5
Returns (%)
24
Effects of Portfolio Size on
Portfolio Risk
p (%)
Company Specific Risk
35
Stand-Alone Risk,
M

p
20
Market Risk
0
10
20
30
40
2,000+
# Stocks in Portfolio
Market risk is that part of a security’s
stand-alone risk that cannot be eliminated
by diversification, and is measured by
beta.
Firm-specific risk is that part of a security’s
stand-alone risk that can be eliminated by
proper diversification.
Capital Asset Pricing Model &
The Concept of Beta







Capital Asset Pricing Model (CAPM): relevant risk of individual stock is
the amount of risk that the stock contributes to well-diversified stock
portfolio, or the market portfolio.
Market risk, which is relevant for stocks held in well-diversified
portfolios, is defined as the contribution of a security to the overall
riskiness of the portfolio. It is measured by a stock’s beta coefficient.
Beta measures a stock’s market risk. It shows a stock’s volatility
relative to the market.
Beta shows how risky a stock is if the stock is held in a well-diversified
portfolio.
Beta can be calculated by running a regression of past returns on Stock
i versus returns on the market. The slope of the regression line is
defined as the beta coefficient.
If beta > 1.0, stock is riskier than the market.
If beta < 1.0, stock less risky than the market.


i
bi  
 
 i , M
 M 
Using a Regression to
Estimate Beta


Run a regression with returns on the stock in
question plotted on the Y axis and returns on
the market portfolio plotted on the X axis.
The slope of the regression line, which
measures relative volatility, is defined as the
stock’s beta coefficient, or b.
28
Beta - Illustration
Beta Graph
Stocks returns
30%
Stock L
Stock A
0%
-10%
0%
10%
-30%
Market returns
20%
Stock H
Calculating Beta in Practice



Many analysts use the S&P 500 to find the
market return.
Analysts typically use four or five years’ of
monthly returns to establish the regression
line.
Some analysts use 52 weeks of weekly
returns.
30
Beta - Calculation
CALCULATING THE BETA COEFFICIENT FOR AN ACTUAL COMPANY
Now we show how to calculate beta for an actual company, General Electric.
Step 1. Acquire Data
Step 2. Calculate Returns
Date
Maret 2003
Februari 2003
Maret 1999
Market Level
(S&P 500 Index)
848,18
841,15
1.286,37
Average return
(annual)
Standard deviation
(annual)
Correlation between GE and the market.
Beta (using the SLOPE function)
GE Adjusted Stock
Market Return
Price
0,8%
25,50
-1,7%
24,05
NA
34,42
GE Return
6,0%
4,7%
NA
-8,8%
-3,4%
17,6%
66,0%
1,09
29,2%
How is beta interpreted?




If b = 1.0, stock has average risk.
If b > 1.0, stock is riskier than average.
If b < 1.0, stock is less risky than average.
Most stocks have betas in the range of 0.5 to
1.5.
32
Security Market Line (SML)
Relationship between required rate of return and risk
ri = rRF + RPMbi .
ri = rRF + (rM – rRF)bi .




ri = Required return^on Stock i
rRF = Risk-free return
(rM-rRF) = Market risk premium
bi = Beta of Stock i
Use the SML to calculate each
alternative’s required return.




The Security Market Line (SML) is part of the
Capital Asset Pricing Model (CAPM).
SML: ri = rRF + (RPM)bi .
Assume rRF = 8%; rM = rM = 15%.
RPM = (rM - rRF) = 15% - 8% = 7%.
34
Impact of Inflation Change on
SML
r (%)
New SML
 I = 3%
SML2
SML1
18
15
11
8
Original situation
0
0.5
1.0
1.5
Risk, b35i
Impact of Risk Aversion
Change
r (%)
SML2
After change
SML1
18
 RPM = 3%
15
Original situation
8
1.0
Risk, bi
36