Chapter 7-8-9 Principles of Corporate Finance Tenth Edition Ch
7-9 Slides by Matthew Will and Bo Sj 2012 McGraw-Hill/Irwin
Copyright 2011 by the McGraw-Hill Companies, Inc. All rights
reserved.
Slide 2
7-2 Risk and Return 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.
Slide 3
7-3 Risk and Return The investor looks at the expected (E)
return: E(r) = r f + 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
Slide 4
7-4 Please forget: All (stupid) stock recomendatuions and
trading tips from DI, DN, E24, Affrsvrlden, Privata affrer, 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?
Slide 5
7-5 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
Slide 6
7-6 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
Slide 7
7-7 A little varning If you dont 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 dont observe that many jumps historically!
Thus, - two moments (mean and variance) are ok to understand how
things work and how to invest!
Slide 8
7-8 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
Slide 9
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.
Slide 10
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.
Slide 11
7-11 Scenario mean 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%
Slide 12
7-12 Example Scenario Mean E(r) = p 1 *E(r 1 ) + p 2 *E(r 2 ) +
p 3 *E(r 3 ) = 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?
Slide 13
7-13 Variance = risk The variance, and the standard deviation,
around the mean measures risk.
Slide 14
7-14 Scenario Variance 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.
Slide 15
7-15 The Value of an Investment of $1 in 1900
Slide 16
7-16 Real Returns The Value of an Investment of $1 in 1900
Slide 17
7-17 The Pattern... 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.
Slide 18
7-18 The Conclusion 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.
Slide 19
7-19 Average Market Risk Premia (by country) Risk premium, %
Country
Slide 20
7-20 Rates of Return 1900-2008 Source: Ibbotson Associates Year
Percentage Return Stock Market Index Returns
Slide 21
7-21 Measuring Risk Return % # of Years Histogram of Annual
Stock Market Returns (1900-2008)
Slide 22
7-22 Equity Market Risk (by country) Standard Deviation of
Annual Returns, % Average Risk (1900-2008)
Slide 23
7-23 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.
Slide 24
7-24 Outcome of diversification. Notice that the figure has the
wrong scale. Most diversification is reached around 15-20 assets.
Not 5 assets.
Slide 25
7-25 Outcome of Diversification: Risk reduction: only market
risk remain in portfolio
Slide 26
7-26 Diversification 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
Slide 27
7-27 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.
Slide 28
7-28 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:
Slide 29
7-29 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)
Slide 30
7-30 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.
Slide 31
7-31 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:
Slide 32
7-32 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.
Slide 33
7-33 The Risk Averse Invesstor 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.
Slide 34
7-34 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: r 1 = 12, =15 r 2 = 8, = 10 Correlation
= +1: A straigth line Correlation
7-36 Portfolio Risk two-asset example Example Correlation
Coefficient =.4 Stocks % of PortfolioAvg Return ABC Corp2860% 15%
Big Corp42 40% 21% Standard Deviation of Portfolio = 28.1:
Portfolio variance= (28 2) (.6 2 ) + (42 2 )(.4 2 ) +
2(.4)(.6)(28)(42)(.4) = > St. dev: 28.1 Return : r = (15%)(.60)
+ (21%)(.4) = 17.4%
Slide 37
7-37 More Portfolio Risk Example Correlation Coefficient =.4
Stocks % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 40%
21% Standard Deviation = Portfolio = 28.1 Return = weighted avg. =
Portfolio = 17.4% Next, add the stock New Corp to the
portfolio
Slide 38
7-38 Portfolio Risk Example Correlation Coefficient =.3 Stocks
% of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 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.
Slide 39
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 4 5 6 N 123456N STOCK
To calculate portfolio variance add up the boxes
Slide 40
7-40 Markowitz Mean-Variance theory 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).
Slide 41
7-41 Graph: An intuitive algorthim for an efficient portfolio
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.
Slide 42
7-42 Be smart - Extent your choices 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 r f 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 w 1 to risk-free and w 2 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)
Slide 43
7-43 The Individual Investor 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 individuals choice.
Slide 44
7-44 Suppose we all are the same: Equilibrium on the markets 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.
Slide 45
7-45 CAPM 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.
Slide 46
7-46 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 r i on asset (i) is E(r
i ) = risk-free rate + compensation for asset i:s non-diversifiable
risk, E(r i ) = r f + i [E(r m ) r f ].
Slide 47
7-47 And Beta is Beta measures the risk of the individual
asset. We can use it calculate the required return on a stock, or a
firms 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(r i, r m )/Var(r m )
Or a linear regression r i = a i + i r m + e i Think of r m in
terms of the business cycle, as the economy moves up and down, so
will the return on individual assets, but to different
degrees.
Slide 48
7-48 Estimate Beta 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 r m 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.
Slide 49
7-49 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
Slide 50
7-50 Sharpe Ratio You need compensation for non-diversifiable
risk, CAPM allows us to measure this risk and If you compare over
time: E(r i ) r f = + i [E(r m )-r f ] You can never earn
systematic returns over what CAPM predicts, that means = 0.
(Jensens alpha) Another investment performance measure is Sharpes
ratio = (r r f )/ Return per unit of risk
Slide 51
7-51 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.
Slide 52
7-52 Company Cost of Capital A companys cost of capital can be
compared to the CAPM required return Required return Project Beta
0.5 Company Cost of Capital 3.8 0.2 0 SML
Slide 53
7-53 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 stocks return to the return on the market
portfolio.
Slide 54
7-54 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.
Slide 55
7-55 Dells 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.
Slide 56
7-56 Market Risk Beta Covariance with the market Variance of
the market
Slide 57
7-57 Cost of Capital 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 companys debt. (Given from ratings and
peers in practice) Beta gives us a companys 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
Slide 58
7-58 WACC Assume a mix of debt and equity in a firm. Required
return on debt and equity together. Use YTM on new debt to set r D
and CAPM (and BETA) to set r E Use market value of debt and equity,
not book values. Only amatures refers to return on book value of
equity, yes even if they are CEO:s for big companies.
Slide 59
7-59 Estimate Beta 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
http://www.wikiwealth.com/wacc-analysis:azn
Slide 60
7-60 Beta is affected by 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.
Slide 61
7-61 What Beta to use? 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.
Slide 62
7-62 After CAPM I The APT model Arbitrage Pricing Theory : Ross
(1976) basically breaks down one single risk premium (r m r f )
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.
Slide 63
7-63 After CAPM II 3 Factor Model 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 r i = B 1 * Market factor (return on market r
m ) B 2 * Size factor (small firms are special) B 3 *
Book-to-market factor (growth opportunities)
Slide 64
7-64 CAPM or Not? CAPM is heavily critized. Bad at predicting
returns, not good for investments. But for understanding it is very
good. If you dont 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).
Slide 65
7-65 Web Resources Click to access web sites Internet
connection required www.globalfindata.com
http://www.gacetafinanciera.com/TEORIARIESGO/MPS.pdf