CORPORATE FINANCIAL THEORY Lecture 2. Risk /Return Return = r = Discount rate = Cost of Capital...
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Transcript of CORPORATE FINANCIAL THEORY Lecture 2. Risk /Return Return = r = Discount rate = Cost of Capital...
CORPORATE FINANCIALTHEORY
Lecture 2
Risk /Return
Return = r = Discount rate = Cost of Capital (COC)
r is determined by risk
Two Extremes
Treasury Notes are risk free = Return is low
Junk Bonds are high risk = Return is high
Risk
Variance & Standard Deviation yard sticks that measures risk
2
1
)(
n
rrVariance
2Deviation Standard
The Value of an Investment of $1 in 1900
1900
1908
1916
1924
1932
1940
1948
1956
1964
1972
1980
1988
1996
2004
2012
$1
$10
$100
$1,000
$10,000
$100,000
Common Stock
US Govt Bonds
T-Bills
Start of Year
Dolla
rs (l
og sc
ale)
24,551
344
75
2013
Source: Ibbotson Associates
Year
Per
cent
age
Ret
urn
Stock Market Index Returns
-60%
-40%
-20%
0%
20%
40%
60%
80%
2012
Rates of Return 1900-2012
Risk premium, %
Country
4.29 4.69 5.05 5.43 5.5 5.61 5.67 6.04 6.29 6.94 7.137.94 8.34 8.4 8.74 9.1 9.61 10.21
0123456789
1011
Den
mar
k
Bel
giu
m
Sw
itze
rlan
d
Irel
and
Sp
ain
Nor
way
Can
ada
U.K
.
Net
her
lan
ds
Ave
rage
U.S
.
Sw
eden
Au
stra
lia
Sou
th A
fric
a
Ger
man
y
Fra
nce
Jap
an
Ital
y
Average Market Risk Premia (by country)
Diversification
Diversification is the combining of assets. In financial theory, diversification can reduce risk.
The risk of the combined assets is lower than the risk of the assets held separately.
Efficient Frontier
Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6%
Standard Deviation = Portfolio = 28.1 %
Return = weighted avg = Portfolio = 17.4%
Additive Standard Deviation (common sense):= .28 (60%) + .42 (40%) = 33.6%
WRONG
Real Standard Deviation:
CORRECT 28.1%or 281.
)42)(.28)(.4)(.4)(.6(.2.42.40.28.60
)σσρxx(2σxσx
2222
21122122
22
21
21
Efficient Frontier
Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6%
Standard Deviation = Portfolio = 28.1 %
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio
Efficient Frontier
Previous Example Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%
NEW Standard Deviation = weighted avg = 31.80%
NEW Standard Deviation = Portfolio = 23.43 %
NEW Return = weighted avg = Portfolio = 18.20%
Efficient Frontier
Previous Example Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%
NEW Standard Deviation = weighted avg = 31.80 %
NEW Standard Deviation = Portfolio = 23.43 %
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
Portfolio Risk / Return
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
Variance Deviation Standard Portfolio
Efficient Frontier
A
B
Return
Risk (measured as s)
Efficient Frontier
A
B
Return
Risk
AB
Efficient Frontier
A
BN
Return
Risk
AB
Efficient Frontier
A
BN
Return
Risk
ABABN
Efficient Frontier
A
BN
Return
Risk
AB
Goal is to move up and left.
WHY?
ABN
Efficient Frontier
Goal is to move up and left.
WHY?
The ratio of the risk premium to the standard deviation is called the Sharpe ratio:
p
fp rr
Ratio Sharpe
Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Efficient Frontier
Return
Risk
A
BNABABN
Markowitz Portfolio Theory
Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation.
Correlation coefficients make this possible.
The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.
Efficient Frontier
Standard Deviation
Expected Return (%)
•Each half egg shell represents the possible weighted combinations for two stocks.
•The composite of all stock sets constitutes the efficient frontier
Efficient Frontier
4 Efficient Portfolios all from the same 10 stocks
Measuring Risk
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
Measuring Risk
Diversification
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.”
Security Market Line
Return
Risk
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return =
rm
$1 Invested Growth (variable debt)
Leverage Varies toMatch Growth Fund
$1 Invested Growth (constant debt)
Leverage set at 20%
Security Market Line
Return
Risk
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return =
rm
Security Market Line
Return
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return =
rm
BETA1.0
Beta and Unique 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.
Beta and Unique Risk
2m
imiB
Beta and Unique Risk
2m
imiB
Covariance with the market
Variance of the market
Beta
(1) (2) (3) (4) (5) (6) (7)Product of
Deviation Squared deviationsDeviation from average deviation from average
Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)
1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24
Average 2 2 Total 304 456
Variance = σm2 = 304/6 = 50.67
Covariance = σim = 736/6 = 76
Beta (β) = σim/σm2 = 76/50.67 = 1.5
Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of
the variance to the covariance (i.e., β = σim/σm2)
Security Market Line
Return
.
rf
Risk Free
Return =
BETA
Security Market Line (SML)
Security Market LineReturn
BETA
rf
1.0
SML
SML Equation = rf + B ( rm - rf )
Capital Asset Pricing Model
R = rf + B ( rm - rf )
CAPM
Company Cost of Capital
A company’s cost of capital can be compared to the CAPM required return
Required
return
Project Beta1.13
Company Cost of Capital
12.9
5.0
0
SML
Arbitrage Pricing Theory
Alternative to CAPM
noise....)()()(Return 332211 factorfactorfactor rbrbrba
...)()(
premiumrisk Expected
2211
ffactorffactor
f
rrbrrb
rr
Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
6.36Market
.83-Inflation
.49GNP Real
.59-rate Exchange
.61-rateInterest
5.10%spread Yield)(r
PremiumRisk EstimatedFactor
factor fr
Three Factor Model
Steps
1. Identify macroeconomic factors that could affect stock returns
2. Estimate expected risk premium on each factor
( rfactor1 − rf, etc.)
3. Measure sensitivity of each stock to factors( b1, b2, etc.)
Three Factor Model
Three-Factor Model. Factor Sensitivities .
CAPM
bmarket bsize
bbook-to-
market
Expected return*
Expected return**
Autos 1.51 .07 0.91 15.7 7.9Banks 1.16 -.25 .7 11.1 6.2Chemicals 1.02 -.07 .61 10.2 5.5Computers 1.43 .22 -.87 6.5 12.8Construction 1.40 .46 .98 16.6 7.6Food .53 -.15 .47 5.8 2.7Oil and gas 0.85 -.13 0.54 8.5 4.3Pharmaceuticals 0.50 -.32 -.13 1.9 4.3Telecoms 1.05 -.29 -.16 5.7 7.3Utilities 0.61 -.01 .77 8.4 2.4
The expected return equals the risk-free interest rate plus the factor sensitivities multiplied by the factor risk premia, that is, rf + (bmarket x 7) + (bsize x 3.6) + (bbook-to-market x 5.2)** Estimated as rf + β(rm – rf), that is rf + β x 7.
Testing the CAPM
Average Risk Premium 1931-
2008
Portfolio Beta
1.0
SML20
12
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
Testing the CAPM
Portfolio Beta
1.0
SML
12
8
4
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
Average Risk Premium 1966-
2008
Measuring Betas
Measuring Betas
Measuring Betas
Estimated Betas
Beta Standard Error
Canadian Pacific 1.27 .10
CSX 1.41 .08
Kansas City Southern 1.68 .12
Genesee & Wyoming 1.25 .08
Norfolk Southern 1.42 .09
Rail America 1.15 .14
Union Pacific 1.21 .07
Industry portfolio 1.34 .06
Beta Stability
% IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER
10 (High betas) 35 69
9 18 54
8 16 45
7 13 41
6 14 39
5 14 42
4 13 40
3 16 45
2 21 61
1 (Low betas) 40 62
Source: Sharpe and Cooper (1972)
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Search for Alpha
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Asset Category 2005 2012 2005 2012
US Equity 40% 24% 61% 50%
Global Equity 20% 26%
Marketable Alternatives 0% 2% 11% 26%
Real Assets 6% 10%
Private Equity/ VC 5% 14%
Fixed Income 26% 20% 28% 24%
Cash 2% 4%
CalPERS Asset Allocation
Asset Category 2005 2012 2005 2012
US Equity 40% 24% 61% 50%
Global Equity 20% 26%
Marketable Alternatives 0% 2% 11% 26%
Real Assets 6% 10%
Private Equity/ VC 5% 14%
Fixed Income 26% 20% 28% 24%
Cash 2% 4%
Source: CalPERS 2005 Annual Investment Report, http://www.calpers.ca.gov/index.jsp?bc=/investments/assets/assetallocation.xml
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Asset Category 2005 2012 2005 2012
US Equity 45% 18% 67% 36%
Global Equity 22% 19%
Marketable Alternatives 4% 21% 8% 46%
Real Assets 3% 14%
Private Equity/ VC 2% 11%
Fixed Income 16% 13% 24% 18%
Cash 8% 5%
CICF Asset Allocation
Asset Category 2005 2012 2005 2012
US Equity 45% 18% 67% 36%
Global Equity 22% 19%
Marketable Alternatives 4% 21% 8% 46%
Real Assets 3% 14%
Private Equity/ VC 2% 11%
Fixed Income 16% 13% 24% 18%
Cash 8% 5%
Source: CICF 2006 Audit Report, CICF Portfolio Review, June 30, 2012
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Dow Jones C.S. Core HF Index
© Dow Jones Credit Suisse
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Risk Profile (HF vs Public Cos.)
US PUBLIC EQUITIES
Standard deviation = 17.1%
Return = 7.5%
Sharpe ratio = .43
S&P 500 Index
Note: Assumes a treasury yield of 0.20%
HEDGE FUNDS
Standard deviation = 7.0%
Return = 8.4%
Sharpe ratio = .81
HFR Fund of Funds Composite Index
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Private Equity Returns
Copyright © 2012 by Dr. Matthew Will. All rights reserved
Private Equity Risk / Return
Cambridge Associates LLC U.S. Private Equity Index®S&P (1986 – 2012)
Since Inception IRR & Multiples By Fund Vintage Year, Net to Limited Partners as of March 31, 2012, starting with vintage year 1986
Pooled Arithmetic Weighted
Pooled Upper Lower S&P 500 Return Mean Median Return Quartile Quartile
Sharpe 0.635 2.027 2.178 1.677 2.231 2.464 0.940
St. Dev. 18.23 7.72 6.44 7.68 6.55 8.51 5.93