Risk & Return
Return is what makes you eat well
Risk is what makes you sleep well
Our goal is to understand...
Recall that ’r’ has many names....
• Interest rate
• Rate of return / Required rate of return
– stocks
• Yield / Yield to maturity
– Bonds
• (Opportunity) cost of capital
– Capital budgeting
‘r’ compensates investors for..
• Impatience! Time Value of Money
– people rather have things now than later
• Risk!
– investors dislike uncertainty
Expected vs. Realized returns
• 60 - 40 chance that return on Microsoft next
year will be +25% OR -10%.
• Expected return is _____%
• The actual return will be either ____ or ____
Surprises....
• Surprise, after the fact, in return is either
+14% = (25% - 11%)
-21% = (-10% - 11%)
or
Actual return = E(r) + unexpected return
e.g. -10% = 11% - 21%
• Investors don’t like surprises
What is the expected surprise?
• multiply probability times each surprise
• Answer = _____
• Expected surprise is always ____ !!!
• Trick: take expected squared surprises
Variance
• Expectation of squared surprises is called
Variance
• Square root of variance is called
Standard deviation
– Easier to understand
• Calculate variance and std. dev. of Microsoft
returns
Microsoft...
• Variance:
.6 (.25 - .11)2 + .4 (-.1 - .11)2 = _____
• Standard Deviation:
SQRT(____) = ____
• Standard deviation is easier to interpret
– Has the same units as return (%)
Variance / Std. Dev. Formulae
   p j   rj  r 
N
2
2
j 1
Std . dev.   
2
Another example..
pi
Probability
of state
ri
Return in
state
+1% change in GNP
.25
-5%
+2% change in GNP
.50
15%
+3% change in GNP
.25
35%
State of Economy
Expected Return
i
(pi x ri)
i=1
-0.0125
i=2
0.075
i=3
0.0875
Expected return = (-0.0125 + 0.0750 +
0.0875)
=
0.15 or 15%
Variance
i
pi
(ri - r)2
pi x (ri - r )2
i=1
.25
.04
.01
i=2
.5
0
.00
i=3
.25
.04
.01
Var(R) =
Std. Dev. = ___
Std. Dev. of selected stocks
Company
AT & T
Digital Equip.
Ford Motor
Genentech
McGraw Hill
Tandem Comp.
MARKET PORTFOLIO

24.2%
38.4
28.7
51.8
29.3
50.7
20.8
Total Risk
• Standard Deviation (or variance) is a measure
of total risk
• It gives us an idea of how likely one is likely
to get ‘burned’ if he/she invests in any single
stock or portfolio of stocks
The Normal Distribution
Historical Returns and Standard Deviations
Value of a $1 investment
What do you notice?
• From the previous two graphs, we notice
that...
• The _________ the standard deviation, the
___________ is the value of a $1 investment
in the long run
• In general, the _______ the risk, the
_______ the return!
Five Largest One-Day Percentage Declines in the DowJones Industrial Average
Date
The Five Worst Days
Point Loss
October 19, 1987
October 28, 1929
October 29, 1929
November 6, 1929
December 18, 1899
508.00
38.88
30.57
25.55
5.57
% Loss
22.6%
12.8
11.7
9.9
8.7
Why do returns fluctuate?
New Information!
• Market-wide info.
–
–
–
–
War
Oil shock
Rise in interest rate
Exchange rate changes
• Asset-specific info
–
–
–
–
Strikes
Lawsuit
Death of CEO
FDA approval of a
drug
Hence...

Total Risk
Market Risk
a.k.a
Systematic Risk
Non-diversifiable Risk
+
Asset-specific Risk
a.k.a
Unsystematic risk
Diversifiable Risk
Unique Risk
Portfolio Expected Returns and Variances
• Portfolio weights: put 50% in Asset A and 50% in
Asset B:
State of the Probability
economy of state
Return
on A
Return
on B
Return on
portfolio
Boom
Bust
30%
-10%
-5%
25%
12.5%
7.5%
0.40
0.60
1.00
Portfolio Expected Returns and Variances
(continued)
• E(RP)
=
• Var(RP) =
0.40 x (.125) + 0.60 x (.075) = .095 = 9.5%
0.40 x (.125 - .095)2 + 0.60 x (.075 - .095)2
= .0006
• SD(RP) = .0006 = .0245 = 2.45%
• Note:
E(RP) =
• BUT:
Var (RP)
.50 x E(RA) + .50 x E(RB) = 9.5%

.50 x Var(RA) + .50 x Var(RB)
Portfolios....
Portfolio returns:
50% A and 50% B
Stock B returns
Stock A returns
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0
0
0
-
-
-0.01
0.01
0.01
-0.02
-
-
-0.03
0.02
0.02
-
-
0.03
0.03
Portfolio Expected Returns and Variances (continued)
• New portfolio weights: put 3/7 in A and 4/7 in B:
State of the Probability
economy
of state
Return
on A
Return
on B
Return on
portfolio
Boom
Bust
30%
-10%
-5%
25%
10%
10%
0.40
0.60
1.00
Portfolio Expected Returns and
Variances (concluded)
• A.
E(RP)
=
10%
• B.
SD(RP)
=
0%
Amazing, eh?
E(R) of Portfolio
• Weighted average of E(R) of stocks in portfolio
For 2-stock portfolio,
• E(Rp) = W1 x E(R1) + W2 x E(R2)
In general....
• E(Rp) = weighted average of expected
return on individual stocks
BUT!!
• SD(Rp) < weighted average of SD(Ri) on
individual stocks
• This is the essence of diversification benefits
How Diversification Works...
• Asset-specific risk is reduced
• Adding more assets reduces this risk further
• good news and bad news ‘cancel’ out..
– with less than perfect correlation among stock
returns
Portfolio Diversification
Average annual
standard deviation (%)
49.2
Diversifiable risk
23.9
19.2
Non-diversifiable
Risk
1
10
20
30
40
1000
Number of stocks
in portfolio
Diversification continued..
• In the limit, ALL asset-specific risk can be
eliminated by holding a slice of the MARKET
portfolio
• Market portfolio is a portfolio of all assets in an
economy
– In practice, S&P 500 is a reasonable approximation
of market portfolio
Believe me no, I thank my fortune for it
My ventures are not in one bottom trusted
Nor to one place; nor is my whole estate
Upon the fortune of this present year.
Therefore, my merchandise makes me not sad.
- Antonio, in The Merchant of Venice
Captial Asset Pricing Model
• Is…one of the most important ideas in finance
in this century
• Is…based on the idea that all investors will
diversify because it makes sense to do so
• Says…hence investors only care about
systematic risk
• Says…systematic risk is measured by BETA
CAPM says..
• If investors can get rid of asset-specific risk
(without sacrificing returns) they will do so
• Corollary 1: Market rewards investors (in
terms of higher return) only for bearing risk
they cannot avoid - i.e. systematic risk (or
beta)
• Corollary 2: All investors (should??) hold
market portfolio
CAPM Equation


E ( Ri )  R f  E  Rm   R f   i
• E(Ri)
• E(Rm)
portfolio
• Rf
• [E(Rm) - Rf]
=
=
Expected return on asset i
Expected return on market
=
=
Risk-free rate
Market risk premium
In general...
• Beta can be any number, but typically it is
between 0.4 to 3.0
Company
T U Electric
Genentech
AT&T
Microsoft
USX
Intel
Gaming Corp. of Amer.
Beta
0.39
0.56
0.71
1.21
1.35
1.73
4.10
By Definition...
• Beta of risk-free asset is always ZERO
– Risk-free assets have no risk!
– not even systematic risk
• Beta of the market portfolio is always ONE
– Market risk is ‘average’ risk
– S&P 500 is often taken as an approximation of
market portfolio
The Security Market Line (SML)
Asset expected
return E (Ri)
= E (RM ) – Rf
E (RM)
Rf
Asset
beta
0
M
= 1.0
Using CAPM
• The formula can be used to estimate
– ‘r’ for projects in DCF methods
– ‘r’ for expected / required return in valuing stocks
• CAPM equation is one of the most widely used
equations in finance
Example
• Beta of Intel = 1.73
• T-bills rate = Rf = 5%
• E(Rm) = 12%
– (estimated from past average of market return)
Hence,
• Market risk premium = [E(Rm) - Rf] = 7%
• E(R) = .05 + [.12 - .05] x 1.73 = _____
Estimating Beta
• Slope of regression line of Ri on Rm
Ri
0.2
0.15
95.000%
0.1
0.05
0
-0.15
-0.1
-0.05
0
-0.05
-0.1
-0.15
-0.2
0.05
0.1
0.15
Rm
Beta on calculator
Rm
.08
.21
-.05
.12
.10
Ri
.11
.33
.03
.11
.17
• Clear Statistical Memory:
• Enter (x,y) pair: xi INPUT
• Get slope: 0
y-hat, m
Intercept
CL
yi

+

SWAP
Slope
Beta of Portfolios
• Weighted average of beta of individual stocks
• For 2-stock portfolio:
p = W1 x 1 + W2 x 2
Example
1. Compaq Beta:
2. Nordstrom Beta:
1.60
1.20
• W1 = 7000/28000
• W2 = 21000/28000
Invest: $ 7,000
Invest: $21,000
= 0.25
= 0.75
• Portfolio Beta =
.25(1.6) + .75(1.2) = ______
Another use of CAPM
• Used to identify undervalued or overvalued
securities
• If your estimate of expected return is greater
than CAPM-based required return --> asset is
undervalued
• If your estimate of expected return is less
than CAPM-based required return --> asset is
overvalued
SML: Undervalued vs. Overvalued
Asset expected
return E (Ri)
Undervalued
E (RM)
Overvalued
Rf
Asset
beta
0
M
= 1.0
SML Continued...
• If an asset plots above SML, it is
UNDERVALUED
– E(R) is higher than justified by risk
• If an asset plots below SML, it is
OVERVALUED
– E(R) is lower than justified by risk
Market Equilibrium & SML
• In equilibrium, buying and selling pressure
forces all assets to plot exactly on SML
– mispricing does not last for very long
• Hence, in equilibrium, the Reward-to-Risk
ratio for all assets is the same:
(Re ward  to  Risk ) i 
E ( Ri )  R f
Betai
In Equilibrium...
E ( Ri )  R f
Betai

E(Rj )  Rf
Beta j

E ( Rm )  R f
1(  Betam )
Which gives us


E ( Ri )  R f  E  Rm   R f   i
Recap
• Measure of total risk is variance or standard
deviation
• The essence of diversification is reducing total
risk of a portfolio
• Total risk of a portfolio is always reduced when
security returns are less than perfectly correlated
Recap
• Market portfolio is the portfolio of ALL risky
securities
• Market portfolio has no unsystematic risk
• Market portfolio only has systematic risk
• CAPM says all investors hold market portfolio
Recap
• The contribution an individual security makes to
the risk of the market portfolio is measured by
beta
• Hence for individual securities risk is measured
by beta
• For diversified portfolios, risk is measured by
standard deviation (or variance)
One final point…
• Corporations finance their activities by a mix of
debt, preferred, and common stock
• Hence for a corporation’s activities as a whole,
the required rate of return is measured by
Weighted Average Cost of Capital
• WACC