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 ID: 793803
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Slide1
Corporate FinancialTheory
Lecture 2
Slide2Risk /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
Slide3Risk
Variance & Standard Deviation
yard sticks that measures risk
Slide4The Value of an Investment of $1 in 1900
2017
Slide5Source: Princeton University
Rates of Return 1900-2016
Slide6Average Market Risk Premia (by country)
Slide7Diversification
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.
Slide8Efficient 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:
Slide9Efficient 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
Slide10Efficient 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%
Slide11Efficient 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
Slide12Portfolio Risk / Return
Slide13Efficient Frontier
A
B
Return
Risk (measured as
s
)
Slide14Efficient Frontier
A
B
Return
Risk
AB
Slide15Efficient Frontier
A
B
N
Return
Risk
AB
Slide16Efficient Frontier
A
B
N
Return
Risk
AB
ABN
Slide17Efficient Frontier
A
B
N
Return
Risk
AB
Goal is to move up and left.
WHY?
ABN
Slide18Efficient Frontier
Goal is to move up and left.
WHY?
The ratio of the risk premium to the standard deviation is called the Sharpe ratio:
Slide19Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Slide20Efficient Frontier
Return
Risk
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low Return
Slide21Efficient Frontier
Return
Risk
A
B
N
AB
ABN
Slide22Markowitz 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
.
Slide23Efficient 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
Slide24Efficient Frontier
4 Efficient Portfolios all from the same 10 stocks
Slide25Measuring Risk
Slide26Measuring Risk
Slide27Diversification
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.”
Slide28Security Market Line
Return
Risk
.
r
f
Risk Free
Return =
Efficient Portfolio
Market Return =
r
m
Slide29$1 Invested Growth
(variable debt)
Leverage Varies to
Match Growth Fund
Slide30$1 Invested Growth (constant debt)
Leverage set at 20%
Slide31Security Market Line
Return
Risk
.
r
f
Risk Free
Return =
Efficient Portfolio
Market Return =
r
m
Slide32Security Market Line
Return
.
r
f
Risk Free
Return =
Efficient Portfolio
Market Return =
r
m
BETA
1.0
Slide33Beta 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.
Slide34Beta and Unique Risk
Slide35Beta and Unique Risk
Covariance with the market
Variance of the market
Slide36Beta
Slide37Security Market Line
Return
.
r
f
Risk Free
Return =
BETA
Security Market Line (SML)
Slide38Security Market Line
Return
BETA
r
f
1.0
SML
SML Equation = r
f
+ B ( r
m
- r
f
)
Slide39Capital Asset Pricing Model
R =
r
f
+ B (
r
m
-
rf )
CAPM
Slide40Company Cost of Capital
A company’s cost of capital can be compared to the CAPM required return
Required
return
Project Beta
1.13
Company Cost of Capital
12.9
5.0
0
SML
Slide41Arbitrage Pricing Theory
Alternative to CAPM
Slide42Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
Slide43Three Factor Model
Steps
Identify macroeconomic factors that could affect stock returns
Estimate expected risk premium on each factor
(
r
factor1
− rf, etc.)Measure sensitivity of each stock to factors
( b1, b2, etc.)
Slide44Three Factor Model
Three-Factor Model
. Factor Sensitivities .
CAPM
b
market
b
size
b
book-to-market
Expected return*
Expected return**
Autos
1.51
.07
0.91
15.7
7.9
Banks
1.16
-.25
.7
11.1
6.2
Chemicals
1.02
-.07
.61
10.2
5.5
Computers
1.43
.22
-.87
6.5
12.8
Construction
1.40
.46
.98
16.6
7.6
Food
.53
-.15
.47
5.8
2.7
Oil and gas
0.85
-.13
0.54
8.5
4.3
Pharmaceuticals
0.50
-.32
-.13
1.9
4.3
Telecoms
1.05
-.29
-.16
5.7
7.3
Utilities
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 + (b
market
x 7) + (b
size
x 3.6) + (b
book-to-market
x 5.2)
** Estimated as
r
f
+ β(
r
m
–
r
f
), that is
rf
+ β x 7.
Slide45Testing the CAPM
Beta vs. Average Risk Premium
Slide46Testing the CAPM
Beta vs. Average Risk Premium
Slide47Measuring Betas
Slide48Measuring Betas
Slide49Measuring Betas
Slide50Estimated Betas
Slide51Beta 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)
Slide52Search for Alpha
Slide53Diversification
What is true diversification?
Slide54Harvard Endowment
Slide55CICF Asset Allocation
March 2015
Slide56CalPERS Asset Allocation
Source: CalPERS 2005 & March 2015
reportsd
http://www.calpers.ca.gov/index.jsp?bc=/investments/assets/assetallocation.xml
Slide57CICF Asset Allocation
Source: CICF 2006 Audit Report, CICF Portfolio Review, June 30, 2015
Slide58Dow Jones C.S. Core HF Index
© Dow Jones Credit Suisse
Slide59Risk 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
Slide60Private Equity Returns
U.S. Private Equity Fund
Index Summary: End-to-End Pooled Return Net to Limited Partners
Slide61Private 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