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

Variance & Standard Deviation yard sticks that measures risk

rrVariance

2Deviation Standard

The Value of an Investment of $1 in 1900

$1,000

$10,000

$100,000

Common Stock

US Govt Bonds

T-Bills

Start of Year

24,551

Source: Ibbotson Associates

Stock Market Index Returns

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

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%

Real Standard Deviation:

CORRECT 28.1%or 281.

)42)(.28)(.4)(.4)(.6(.2.42.40.28.60

)σσρxx(2σxσx

21122122

Efficient Frontier

Example Correlation Coefficient = .4

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

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

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

Variance Deviation Standard Portfolio

Efficient Frontier

Return

Risk (measured as s)

Efficient Frontier

Return

Efficient Frontier

Return

Efficient Frontier

Return

Efficient Frontier

Return

Goal is to move up and left.

Efficient Frontier

Goal is to move up and left.

The ratio of the risk premium to the standard deviation is called the Sharpe ratio:

Ratio Sharpe

Efficient Frontier

Return

Low Risk

High Return

High Risk

High Return

Low Risk

Low Return

High Risk

Low Return

Efficient Frontier

Return

Low Risk

High Return

High Risk

High Return

Low Risk

Low Return

High Risk

Low Return

Efficient Frontier

Return

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

05 10 15

Number of Securities

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 Free

Return =

Efficient Portfolio

Market Return =

$1 Invested Growth (variable debt)

Leverage Varies toMatch Growth Fund

$1 Invested Growth (constant debt)

Leverage set at 20%

Return

Risk Free

Return =

Efficient Portfolio

Market Return =

Return

Risk Free

Return =

Efficient Portfolio

Market Return =

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

Covariance with the market

Variance of the market

(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)

Return

Risk Free

Return =

Security Market Line (SML)

Security Market LineReturn

SML Equation = rf + B ( rm - rf )

Capital Asset Pricing Model

R = rf + B ( rm - rf )

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

Arbitrage Pricing Theory

Alternative to CAPM

noise....)()()(Return 332211 factorfactorfactor rbrbrba

...)()(

premiumrisk Expected

ffactorffactor

rrbrrb

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

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 .

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-

Portfolio Beta

Investors

Market Portfolio

Beta vs. Average Risk Premium

Testing the CAPM

Portfolio Beta

Investors

Market Portfolio

Beta vs. Average Risk Premium

Average Risk Premium 1966-

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)

Search for Alpha

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%

Real Assets 6% 10%

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

Asset Category 2005 2012 2005 2012

US Equity 45% 18% 67% 36%

Real Assets 3% 14%

Fixed Income 16% 13% 24% 18%

Cash 8% 5%

CICF Asset Allocation

Asset Category 2005 2012 2005 2012

US Equity 45% 18% 67% 36%

Real Assets 3% 14%

Fixed Income 16% 13% 24% 18%

Cash 8% 5%

Source: CICF 2006 Audit Report, CICF Portfolio Review, June 30, 2012

Dow Jones C.S. Core HF Index

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

Private Equity Returns

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

CORPORATE FINANCIAL THEORY Lecture 2. Risk /Return Return = r = Discount rate = Cost of Capital...

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