Transcript The Firm and The Financial Manager

Chapter
7-8-9
Principles of
Corporate Finance
Tenth Edition
Ch 7-9
Slides by
Matthew Will and Bo Sjö 2012
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Risk and Return
7-2
 Asset pricing:
– Investors predict future cash flows, and then set the price
(today) to get at least an expected required return. (HPR)
– Stocks. Bonds, etc. whatever ...
– Since there are both buyers and sellers, and everything is
voluntary, we expect returns to be = ”required returns”,
meaning prices are in equilibrium over time.
 Risk and Return
– Investors are risk averse
– Investors require higher (expected) returns for higher risk, or
they pay less for a risky asset compared to a not-so risky, or
a risk-free asset.
Risk and Return
7-3
The investor looks at the expected (E) return:
– E(r) = rf + E(risk premium)
– Asset pricing theories explain how this is done,
CAPM, APT etc.
Since investors are risk averse they control risk
in two steps
– Diversification in portfolios (Explain how it works)
– Split their portfolios between a risk free asset and
their risky-portfolio (Explain)
• In the process they find optimal combinations of returns
per unit of risk, and the optimum portfolio
Please forget:
All (stupid) stock recomendatuions and trading
tips from DI, DN, E24, Affärsvärlden, Privata
affärer, etc.
Serious investments is about maximizing the
return on saving given the risk the investor is
willing to take.
So, what is risk and return?
How should it be measured?
7-4
Look at Historical Returns
Holding period Returns
A clear pattern between risk and return
historically
–
–
–
–
–
Goods/Inflation
Government short-term bonds
Corporate bonds
Stocks
Small firm stocks
7-5
Return and Risk?
Historical return
– Arithemtic mean
– Geometric mean
Expected Future return
– Arthimetic return (or mean)
– Scenario return (or mean)
Risk?
– Is the variance (or standard deviation) around the
mean. The bigger the variance the bigger the risk
7-6
A little varning
 If you don’t know so much about statistics, people will try to
fool you. 2 examples
– Risk will not go away over time; your stock portfolio does not get less
risky over time.
– Asset returns (and prices) are random variables.
– Random variables are described by their moments; the mean, the
variance, kurtosis, skewness etc.
– For asset you normally only need the mean and the variance. It is not
woorth exploring higher moments (Samuelson 1966)
– If stock prices ’jumps’ now and then, you need more moments. =>
Predict the jumps by using poission distribution. This is difficult since
you don’t observe that many jumps historically!
– Thus, - two moments (mean and variance) are ok to understand how
things work and how to invest!
7-7
Measuring Returns
Mean, variances (Stand. Deviation), covariances
(correlation)
Correlation creates the diversification effect
Mean can be measured as
– Arithmetic or geometric mean
– Mean based on historical values or scenario mean
7-8
7-9
Return
 HPR, for historical
analysis/evaluation.
 Also, think in terms of
Expected return: The
price today is set on
E(P + Div) to give
E(r) = expected
(required) return.
r1 
P1  P0  Div t P1  P0 Div t


P0
P0
P0
Can also be rewritten as :
P1  Div1
P0 
(1  r )
7-10
Mean Return
 Artithmetic mean or
Geometric mean
 Rule of thumb: The
geometric mean is
somewhat better for
historical evaluations.
The arithmetic mean is
somewhat better for
predictions.
T
Arithmetic : r  
t 1
HPRt
T
Geometric : (1  rg )T  (1  r1 )(1  r2 )...(1  rT )
rg  (1  r1 )(1  r2 )...(1  rT )
1/ T
1
Scenario mean
7-11
The future has a fixed number of possible
outcomes (or states), ex 3 outcomes, and each
outcome have a probability:
– Economy goes up (boom = 30% probability)
– Economy remains the same (no change = 30%)
– Economy goes down (recession = 40%)
Each outcome can begiven a probability, so that
all probabilities sum to unity. Set a a return for
each scenario outcome, example:
– Boom r=15%, The same = 5%, Recession = -2%
Example Scenario Mean
7-12
E(r) = p1*E(r1) + p2*E(r2) + p3 *E(r3) =
0.3*0.15 + 0.3*0.05 + 0.4*(-0.02) = 0.052 or
5.2%
When do we use this?
When the future is not like the past.
And, write down expectations about the future,
in trems if risk, as well. Example, I predict that
next quarters GDP growt is 4.5%, but what do I
think about up and down and the risk of my
estimate?
7-13
Variance = risk
 The variance, and the
standard deviation,
around the mean
measures risk.

T
rt  r 
t 1
T
 
2
2
T
Sample :  2  
t 1
rt  r 
2
T 1
Standard dev.    2
7-14
Scenario Variance
k
Var( r )   p( s )r ( s )  E ( r )
2
s 1
Scenario variance: there are k possible outcomes (s), all
probabilities p(s) sum to 1.0.
E(r) is the scenario mean for these k outcomes.
7-15
The Value of an Investment of $1 in 1900
$100,000
Common Stock
14,276
US Govt Bonds
T-Bills
$1,000
241
71
$100
$10
Start of Year
2008
$1
19
00
19
10
19
20
19
30
19
40
19
50
19
60
19
70
19
80
19
90
20
00
Dollars (log scale)
$10,000
7-16
The Value of an Investment of $1 in 1900
Real Returns
$1,000
581
Equities
$100
Bills
$10
9.85
2.87
Start of Year
2008
$1
19
00
19
09
19
19
19
29
19
39
19
49
19
59
19
69
19
79
19
89
19
99
Dollars (log scale)
Bonds
The Pattern ...
7-17
Over history we see
High return <-> High volatily
Low return <–> low volatility
Stocks – high return, high volatility, high risk
Tbill: low return, low volatlity, low risk
Gov. Bonds and corporate bonds - in between
And, portfolios of small firms displays higer
returns and hiher variance than the average
market portfolio.
The Conclusion
7-18
 People are risk-averse, this explains the pattern
 When they invest in risky things (high variance around
the expected value) they demand higher return to
compensate for the risk.
 The higher the risk - the higher the risk premium. To
volutarily hold risky assets (volatile returns) investors
demand higher expected returns.
 When looking at the returns on the market
portfolio of stocks over the return on Tbills we see
the risk premium investors demand for holding
these risky assets.
7-19
Average Market Risk Premia (by country)
Risk premium, %
Country
Italy
Japan
France
Germany
South Africa
Australia
9.61 10.21
8.74 9.1
8.34
8.4
7.94
Sweden
U.S.
6.94 7.13
Average
Netherlands
U.K.
Canada
Norway
Spain
Ireland
Switzerland
Belgium
6.04 6.29
5.05 5.43 5.5 5.61 5.67
4.69
4.29
Denmark
11
10
9
8
7
6
5
4
3
2
1
0
7-20
Rates of Return 1900-2008
Stock Market Index Returns
Percentage Return
80.0
60.0
40.0
20.0
0.0
-20.0
-40.0
-60.0
Source: Ibbotson Associates
Year
7-21
Measuring Risk
Histogram of Annual Stock Market Returns
(1900-2008)
# of Years
24
24
21
20
17
16
11 11
12
8
1
2
-40 to -30
3
2
50 to 60
40 to 50
30 to 40
20 to 30
10 to 20
0 to 10
-10 to 0
-20 to -10
Return %
-30 to -20
0
4
-50 to -40
4
13
7-22
Average Risk (1900-2008)
40
35
30
25
20
15
Germany
Italy
Japan
28.32 29.57
Norway
France
Belgium
Sweden
Ireland
South Africa
Netherlands
Spain
Denmark
U.K.
U.S.
Switzerland
17.02
23.98 24.09 25.28
21.83 22.05 22.99 23.23 23.42 23.51
20.16
18.45 19.22
Australia
10
5
0
33.93 34.3
Canada
Standard Deviation of Annual Returns, %
Equity Market Risk (by country)
Understanding Risk
Risk aversion leads to diversification
Spread your investment among many
different assets, => huge reduction in risk in
relation to reduction in return
Diversification - Strategy designed to reduce risk
by spreading the portfolio across many
investments.
Unique Risk - Risk factors affecting only that
firm. Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that affect
the overall stock market. Also called “systematic risk.”
7-23
Portfolio standard deviation
Outcome of diversification. Notice that the figure has the wrong scale.
Most diversification is reached around 15-20 assets. Not 5 assets.
0
5
10
Number of Securities
15
7-24
Portfolio standard deviation
Outcome of Diversification:
Risk reduction: only market risk remain in portfolio
Unique
risk
Market risk
0
5
10
Number of Securities
15
7-25
Diversification
7-26
 Diversification works through the covariance
(correlation) between assets.
 Since assets are not perfectly correlated, combination
of risky assets gives a bigger reduction in risk
compared to reduction in return.
 To max return: invest all in asset with higest expected
return
 To min risk: invest all in risk free asset
 Risk averse seeks to max return per risk =>
diversification
Adding two random returns
 Covariance and
correlation:
 Correlation is a number
between -1 and +1.
Where +1 indicate
perfect correlation. (-1)
indicate perfect negative
correlation.
T
 12  
t 1
r
1,t
 r1 r2,t  r2 
T 1
 12
Correlatio n 12 
 1 2
and  12  12 1 2
7-27
The return on a 2-asset portfolio
 Two assets: 1 and 2
 The expected return on
2-asset portfolio:
 Portfolio weights must
sum so unity.
 The expected return on
an N-asset portfolio:
7-28
rp  w1r1  w2 r2
w1  w2  1 and w2  (1  w1 )
N
For N assets : rp   wi ri
i 1
Variance of 2-asset portfolio
 When adding two (or
more) returns beware of
the covariance
(correlation), which will
affect the outcome
 Variance or st. dev is
measuring risk.
 Let the correlation
coeffcient go from +1
over 0 to -1 and study
the outcome (graph)
 p2  w12 12  w22 22  2 w1w2 cov( r1 , r2 )
 w12 12  w22 22  2 w1w2 1 2 12
What happens as p12 goes
from  1, to 0 and - 1?
The diversific ation effect is
that the portfolio variance and
becomes is reduced whenever
assets are not perfectly correlated ( 1).
7-29
The N-asset portfolio
The N-asset portfolio involves a large number
of covariances (correlations). However, there
are short-cuts for people doing this in practice.
Use monthly data for the last 5 (or up 10 say a
business cycle) years to estimate, means,
variances and covariances.

7-30
Two asset: Portfolio Risk
Example
Suppose you invest 60% of your portfolio in
Campbell Soup and 40% in Boeing. The expected
dollar return on your Campbell Soup stock is 3.1%
and on Boeing is 9.5%. The expected return on
your portfolio is:
Expected Return  (0.60  3.1)  (0.40  9.5)  5.7%
7-31
Portfolio Risk- Two Assets
Suppose you invest 60% of your portfolio in Campbell Soup and 40%
in Boeing. The expected annual return on your Campbell Soup stock is
3.1% and on Boeing is 9.5%.
The standard deviation of their annualized daily returns are 15.8% and
23.7%, respectively. Assume a correlation coefficient of 1.0 and
calculate the portfolio variance.
Portfolio Variance  [(0.60) 2  (15.8) 2 ]
 [(0.40) 2  (23.7) 2 ]
 2  0.40  0.60  15.8  23.7  1.0  359.5
Standard Deviation  359.5  19.0 %
7-32
The Risk Averse Invesstor
7-33
To get higher return an investor must accept
higher risk
The choice between risk and return is the
investors own (individual) decision
For each choice of risk, the investor wants the
highest possible return.
 When constructing a well diversified portfolio
to reduce risk, the correlations among assets are
essential.
Figure
 Draw a figur that shows expected returns E(r) on the
vertical line and risks () on the horizontal line.
 Illustrate the effects of different possible correlations
in a two asset portfolio:
 Example values:
 r1 = 12,  =15
 r2= 8,  = 10
 Correlation = +1: A straigth line
 Correlation <+1: A curve that bends inwards in the
graph.
 Correlation = -1: Perfect hedge no risk is left.
7-34
Important Formulas
7-35
Expected Portfolio Return  (w1 r1 )  ( w 2 r2 )
w1  w2  1.0
Portfolio Variance  w12σ12  w 22σ 22  2( w1w 2σ1σ 2 12 )
Portfolio Risk two-asset example
Example
Stocks
ABC Corp
Big Corp

28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation of Portfolio = 28.1:
Portfolio variance= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= > St. dev: 28.1
Return : r = (15%)(.60) + (21%)(.4) = 17.4%
7-36
More Portfolio Risk
Example
Stocks
ABC Corp
Big Corp

28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation = Portfolio = 28.1
Return = weighted avg. = Portfolio = 17.4%
Next, add the stock New Corp to the portfolio
7-37
7-38
Portfolio Risk
Example
Stocks
Portfolio
New Corp
Correlation Coefficient = .3

% of Portfolio
28.1
50%
30
50%
Avg Return
17.4%
19%
NEW Standard Deviation of Portfolio = 23.43
NEW Return of Portfolio = 18.20%
NOTE: A little higher return and much lower risk
How did we do that? Mainly through diversification, the
correlation between portfolio and New asset is quite low.
Actually 0.3 is the correlation of gold.
7-39
Portfolio Risk
Example of a covariance matrix for N-asset portfolio construction. The shaded
boxes contain variance terms; the remainder contain covariance terms.
1
2
3
STOCK
To calculate
portfolio
variance add
up the boxes
4
5
6
N
1
2
3
4
5 6
STOCK
N
Markowitz Mean-Variance theory
7-40
 Markowitz formalised the investment process of a
risk-averse investor. Recall that only two moments are
necessary to describe a risky asset: mean and variance
 All people are risk averse
 They build portfolios to diversify and reduce risk, in
order to find their desired combination of maximum
return for minimum risk.
 They are left with market risk in their portfolis which
they want compensation for by asking for higher return
on the portfolio (=> they bid down relative prices on
risky assets).
 The rational investor estimates construct an efficient
frontier of all well-diversified investment portfolios
(graph).
Graph: An intuitive algorthim for an efficient
portfolio
7-41
 Estimate expected returns, st,dev and correlations.
 Look at formula for the portfolio mean and the
portfolio variance.
 Fix a level of risk (st.dev) ask a computer to calculate
the weights that leads to the higest return for this level
of risk.
 Fix a new level of risk, find the weights that optimizes
the expected return for this risk level,
 Interpolate between the estimates to get a curve of
effecient (well diversified) portfolios.
 Markowitz: Make your individual choice between risk
and return along the line according to taste for risk.
Be smart - Extent your choices
7-42
 In the graph of the efficent (well-diversified) portfolios, mark
the risk free-rate on the vertical axis.
 Draw a line from the risk-free rate that is tangent to the effcient
portfolio. (Tobin 1958)
 Now, make your (smarter) choices between risk and return
along that straight line starting from rf and just touching the
effcient frontier portfolio. The tangent with the efficient
portfolio is the optimal risky portfolio. These portfolio weights
represent the best well diversified portfolio.
 Invest in the risk-free asset and in therisk portfolio. Thus,
allocate w1 to risk-free and w2 to risky portfolio.
 You can borrow money to invest more than 100% of your
assets in the risky portfolio, to maximize your utility from
returns and risk. (extend graph)
The Individual Investor
7-43
 From the graph: Investors can controll risk through:
– 1) Diversification and finding the optimal risky portfolio
– 2) Mix their investment between the optimal risky portfolio
and the risk-free asset. This portfolio is called the complete
portfolio = Risk-free + risky assets. (Risky assets = stocks
and corporate bonds etc.)
 Important, learn to be smart investors, think in terms
of portfolio returns.
 1) and 2) above is THE SEPARATION THEOREM.
Find the well-diversified portfolio is a technical
problem. Chosing the highest utility combination
between risk-free and risk portfolio is the individual’s
choice.
Suppose we all are the same:
Equilibrium on the markets
7-44
 If everyone behaves like the person Marowitz
described => Capital Asset Pricing Model
 CAPM
 The optimal risky portfolio is the market porfolio
 We approximate with stock market index
 Difference between the return on the market and the
risk-free rate is the risk premium people ask for to hold
the risky (well-diversified) portfolio.
 Individual stocks are priced with respect to their
contribution to the portfolio return and risk.
CAPM
7-45
 Notice that all assets, and the market portfolio, is
willingly held by the ”market”.
 It is a free market you can by and sell as you want.
 If the the expected return is too low, people will sell
risky assets. Prices on risky assets go down today and
expectd returns will go up.
 If the expected return is too high (returns give more
than compensation for risk), people buy more. Prices
go up and expected returns go down.
 Individual years are not important here, on average all
will be as in theory.
CAPM predicts:
That individual stocks are priced according to
their expected return, so that investors are
compensated for market risk only. Not total
risk, only the part that cannot be diversified
away needs to be compensated.
On average we have, according to CAPM that
the expected return ri on asset (i) is
E(ri) = risk-free rate + compensation for asset
i:s non-diversifiable risk,
E(ri) = rf + i [E(rm) – rf].
7-46
And Beta is
7-47
 Beta measures the risk of the individual asset. We can
use it calculate the required return on a stock, or a
firm’s equity.
 Beta is measured as the covariance between the
expected return on the asset and the market, divided
with the variance of the expected market return
 i = Cov(ri, rm)/Var(rm)
 Or a linear regression ri = ai + i rm + ei
 Think of rm in terms of the business cycle, as the
economy moves up and down, so will the return on
individual assets, but to different degrees.
Estimate Beta
7-48
 Beta for the market = 1.0 (of course), the average of all
assets. Individual assets have Betas that are either
lower, equal or higher than 1.0
 Estimate Beta, decide on the risk free rate and caculate
the required return for any risky asset.
 Risk premium on the market rm – r are typically
estimated in the range of 4.5 -5.5%. (Sometimes, in
historical times, down to 4% or up to 8%), see BMA
ch 7.
 See course web for references
 CAPM works quite well for corporate finance
investments. CAPM is standard.
CAPM
CAPM predicts that the market portfolio is the
optimal risky portfolio.
 Everyone holds a replica of the market
portfolio, because we all have the same
information.
All assets are priced with respect to beta, and
the CAPM formula. Any deviations will be
eliminated by market forces. (=>arbitrage
trading) and the security market Line. Figures
8.6-8.7
7-49
Sharpe Ratio
You need compensation for non-diversifiable
risk, CAPM allows us to measure this risk and
If you compare over time:
E(ri) – rf =  + i [E(rm)-rf]
You can never earn systematic returns over
what CAPM predicts, that means  = 0.
(Jensen’s alpha)
Another investment performance measure is
Sharpe’s ratio = (r – rf)/
Return per unit of risk
7-50
Security Market Line
Use the security market line to determine
(illustrate) if an asset is overpriced or
underprices, or corretly priced, at the moment.
 Discuss the required cost of capital.
7-51
Company Cost of Capital
A company’s cost of capital can be compared
to the CAPM required return
SML
Required
return
3.8
Company Cost of
Capital
0.2
0
0.5
Project Beta
7-52
Portfolio 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.
7-53
Portfolio Risk
The return on Dell stock
changes on average
by 1.41% for each
additional 1% change in
the market return. Beta
is therefore 1.41.
7-54
Dell’s Beta
The return on Dell stock
changes on average
by 1.41% for each
additional 1% change in
the market return. Beta
is therefore 1.41.
7-55
Market Risk – Beta
 im
Bi  2
m
Covariance with the
market
Variance of the market
7-56
Cost of Capital
7-57
CAPM gives us the cost of equity, the required
return (discount rate) for stocks.
The cost of debt is measured by the YTM on
the company’s debt. (Given from ratings and
peers in practice)
Beta gives us a company’s cost of equity, and
the required return on investments financed
with equity.
A company has both debt and equity =>
Weighted average cost of captal WACC
WACC
7-58
 Assume a mix of debt and
equity in a firm. Required
return on debt and equity
together.
 Use YTM on new debt to set
D
E
r 
r 
r
rD and CAPM (and BETA) to wacc D  E D D  E E
set rE
and with company ta xes tc
 Use market value of debt and
D
E
rwacc 
(1 t c ) rD 
rE
equity, not book values.
DE
DE
Only amatures refers to
return on book value of
equity, yes even if they are
CEO:s for big companies.
Estimate Beta
7-59
 Debt is YTM on new debt (not old), for this type of
firm and level of debt. Risk-free plus default risk
rating.
 Beta is estimated typically from monthly data five
years back. Industry standard.
 Adjusted Beta, adjust the estimate especially for younf
firms.
 Equity Beta and Asset Beta
 Equity Beta (=levered Beta) is what you estimate,
includes finaning risk from debt. Recalculate to
construct a Beta value as if the firm was all equity =
Asset Beta = Unlevered Beta.
 http://www.wikiwealth.com/wacc-analysis:azn
Beta is affected by
7-60
 If you estimate Beta from market returns it reflects
both the financial risk and the business risk of the firm
 An all-equity firm has only business risk
 With both debt and equity financing there is both
busines risk and financial risk in Beta.
 Thus, Beta must be unlevered if we want to compare
firms and if we want to calculate an average sector
beta.
 In addition ”Adjusted Beta” values - the estimate is
usually biased away from 1.0. Therefore ”Adjusted
Beta” values adjusts estimates of equity Betas to come
closer to 1.0.
What Beta to use?
7-61
 Adjusted Betas are especially important for young
firms.
 Equity Betas = Levered Betas vs Asset Betas =
Levered Betas
 For a correct estimation of WACC we look for
estimated future returns. For firm valuation in
particuar, and sometimes project valuation, use sector
YTM and sector Beta values.
 Sector Betas, are typically unlevered and then
relevered for the (Debt/equity ratio) of firm or the
project. Typically, analyse the effects of debt financing
by varying the debt/equity ratio.
After CAPM I – The APT model
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 Arbitrage Pricing Theory : Ross (1976) basically
breaks down one single risk premium (rm – rf) into
several macro economic risk factors; and different risk
premiums.
 Risk factors example: economic growth, inflation,
interest rates, energy prices.
 It does not tells us which these risks are, only that
investors compare portfolios and returns to create an
efficient market portfolio.
 In CAPM all risks are priced in the market risk
premium. APT splits into several risk premiums.
After CAPM II – 3 Factor Model
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Fama and French discovered that a three factor
version of the APT usually works better than
CAPM for predicting returns, and seem to work
all over the world.
The three factors are
ri =
B1* Market factor (return on market rm)
B2 * Size factor (small firms are special)
B3 * Book-to-market factor (growth
opportunities)
CAPM or Not?
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 CAPM is heavily critized.
 Bad at predicting returns, not good for investments.
 But for understanding it is very good. If you don’t
understand CAPM you understand nothing!
 It is a very robust theory. Change an underlying
assumption and the model still holds, perhaps with an
additional parameter in the equation. It does not break
down as other theories.
 Everyone who has tried to explain asset pricing has the
CAPM as a special case of their theory.
 Works for NPV and valuation in corporate finannce
because you can usually change things in the future
(with new information).
Web Resources
Click to access web sites
Internet connection required
www.globalfindata.com
http://www.gacetafinanciera.com/TEORIARIESGO/MPS.pdf
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