CORPORATE FINANCIAL THEORY 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

The Value of an Investment of $1 in

Source: Ibbotson Associates Year Percentage Return Stock Market Index Returns 2012 Rates of Return

Risk premium, % Country 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  % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 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:

Efficient Frontier Example Correlation Coefficient =.4 Stocks  % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 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  % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Standard Deviation = weighted avg = 31.80% NEW Standard Deviation = Portfolio = % NEW Return = weighted avg = Portfolio = 18.20%

Efficient Frontier Previous Example Correlation Coefficient =.3 Stocks  % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Standard Deviation = weighted avg = % NEW Standard Deviation = Portfolio = % NEW Return = weighted avg = Portfolio = 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION

Portfolio Risk / Return

Efficient Frontier A B Return Risk (measured as  )

Efficient Frontier A B Return Risk AB

Efficient Frontier A B N Return Risk AB

Efficient Frontier A B N Return Risk AB ABN

Efficient Frontier A B N 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:

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 B N AB ABN

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. efficient portfolios  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

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. rfrf Risk Free Return = Efficient Portfolio Market Return = r m

$1 Invested Growth (variable debt) Leverage Varies to Match Growth Fund

$1 Invested Growth (constant debt) Leverage set at 20%

Security Market Line Return Risk. rfrf Risk Free Return = Efficient Portfolio Market Return = r m

Security Market Line Return. rfrf Risk Free Return = Efficient Portfolio Market Return = r m 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

Beta

Security Market Line Return. rfrf Risk Free Return = BETA Security Market Line (SML)

Security Market Line Return BETA rfrf 1.0 SML SML Equation = r f + B ( r m - r f )

Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM

Company 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 SML

Arbitrage Pricing Theory Alternative to CAPM

Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors ( )

Three Factor Model Steps 1. Identify macroeconomic factors that could affect stock returns 2. Estimate expected risk premium on each factor ( r factor1 − r f, etc.) 3. Measure sensitivity of each stock to factors ( b 1, b 2, etc.)

Three Factor Model Three-Factor Model. Factor Sensitivities.CAPM b market b size b book-to- market Expected return* Expected return** Autos Banks Chemicals Computers Construction Food Oil and gas Pharmaceuticals Telecoms Utilities 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.

Testing the CAPM Average Risk Premium Portfolio Beta 1.0 SML Investors Market Portfolio Beta vs. Average Risk Premium

Testing the CAPM Portfolio Beta 1.0 SML Investors Market Portfolio Beta vs. Average Risk Premium Average Risk Premium

Measuring Betas

Estimated Betas Beta Standard Error Canadian Pacific CSX Kansas City Southern Genesee & Wyoming Norfolk Southern Rail America Union Pacific Industry portfolio

Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER 10 (High betas) (Low betas) Source: Sharpe and Cooper (1972)

Copyright © 2012 by Dr. Matthew Will. All rights reserved

Source: CalPERS 2005 Annual Investment Report,

Copyright © 2012 by Dr. Matthew Will. All rights reserved Source: CICF 2006 Audit Report, CICF Portfolio Review, June 30, 2012

Copyright © 2012 by Dr. Matthew Will. All rights reserved © Dow Jones Credit Suisse

Copyright © 2012 by Dr. Matthew Will. All rights reserved 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

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