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 1900 2017 13

Rates of Return 1900-2016 Source: Princeton University 14

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:

Efficient Frontier Let’s Add stock New Corp to the portfolio 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 NOTE: Higher return & Lower risk 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 19

Efficient Frontier Return B A Risk (measured as s)

Efficient Frontier Return B AB A Risk

Efficient Frontier Return B N AB A Risk

Efficient Frontier Return B ABN N AB A Risk

Efficient Frontier Return Goal is to move up and left. WHY? B ABN N AB Risk

Efficient Frontier The ratio of the risk premium to the standard deviation is called the Sharpe ratio: Goal is to move up and left. WHY?

Efficient Frontier Return Low Risk High Return High Risk High Return Low Return High Risk Low Return Risk

Efficient Frontier Return Low Risk High Return High Risk High Return Low Return High Risk Low Return Risk

Efficient Frontier Return B ABN N AB A Risk

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 Each half egg shell represents the possible weighted combinations for two stocks. The composite of all stock sets constitutes the efficient frontier Expected Return (%) Standard Deviation

4 Efficient Portfolios all from the same 10 stocks Efficient Frontier 4 Efficient Portfolios all from the same 10 stocks

Measuring Risk 20

Measuring Risk 21

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.” 18

. Security Market Line rf Return Market Return = rm Efficient Portfolio Risk Free Return = rf Risk

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

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

. Security Market Line rf Return Market Return = rm Efficient Portfolio Risk Free Return = rf Risk

. Security Market Line rf Return Market Return = rm Efficient Portfolio Risk Free Return = rf 1.0 BETA

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

Beta and Unique Risk Covariance with the market Variance of the market

Beta

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

Security Market Line rf SML Equation = rf + B ( rm - rf ) Return SML BETA 1.0 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 12.9 5.0 SML Required return Company Cost of Capital Project Beta 1.13

Arbitrage Pricing Theory Alternative to CAPM

Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990)

Three Factor Model Steps Identify macroeconomic factors that could affect stock returns Estimate expected risk premium on each factor ( rfactor1 − rf, etc.) 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 7.9 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 1.9 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 + (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.

Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium

Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium

Measuring Betas

Measuring Betas

Measuring Betas

Estimated Betas

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

Diversification What is true diversification?

Harvard Endowment

CICF Asset Allocation March 2015

CalPERS Asset Allocation Source: CalPERS 2005 & March 2015 reportsd http://www.calpers.ca.gov/index.jsp?bc=/investments/assets/assetallocation.xml

CICF Asset Allocation Source: CICF 2006 Audit Report, CICF Portfolio Review, June 30, 2015

Dow Jones C.S. Core HF Index © Dow Jones Credit Suisse

Risk Profile (HF vs Public Cos.) US Public equities Hedge Funds Standard deviation = 17.1% Return = 7.5% Sharpe ratio = .43 S&P 500 Index Note: Assumes a treasury yield of 0.20% Standard deviation = 7.0% Return = 8.4% Sharpe ratio = .81 HFR Fund of Funds Composite Index

Private Equity Returns U.S. Private Equity Fund Index Summary: End-to-End Pooled Return Net to Limited Partners

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