Introduction • Corporate Finance – how decision making affects “value”. • Corporate finance is not a number “game”. • Focus: (a) practical issues that arise in valuation, (b) taxes, (c) incentives of different stakeholders.
Chapter 7 Risk, Return and the Cost of Capital Final objective: Estimating the opportunity cost of capital. Explain and calculate • Expected return • Security risk • Diversification • Portfolio risk • beta.
-$400,000 0 1 2 Capital Budgeting Example • Capital Budgeting Decision • Suppose you had the opportunity to buy a tbill which would be worth $400,000 one year from today. • Interest rates on tbills are a risk free 7%. • What would you be willing to pay for this investment? PV today: $400,000 / (1.07) = $373,832
Cost of Capital • Capital Budgeting Decision • Suppose you are offered a construction deal with similar cost and payoff. • An important concept in finance is that a risky dollar is worth less than a safe dollar. • You are told that the risk is quantified by the cost of capital, which is 12%. NPV= -350,000+400,000/1.12 = $7,142
Calculating Returns Suppose you bought 100 shares of BCE one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do?
Holding Period Returns The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri:
Common Stocks Long Bonds T-Bills The Future Value of an Investment of $1 in 1957: Evidence from Canada $42.91 $20.69
An Investment of $1 in 1900: US evidence Real Returns
How does this relate to cost of capital? • Suppose there is an investment project which you know has the same risk as Standard and Poor’s Composite Index. • What rate should you use?
Rates of Return 1900-2003 Stock Market Index Returns Percentage Return Year • Source: Ibbotson Associates
Measuring Risk Histogram of Annual Stock Market Returns # of Years Return %
Average Stock Returns and Risk-Free Returns • The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk. • One of the most significant observations of stock (and bond) market data is this long-run excess of security return over the risk-free return. • The historical risk premium was 7.6% for the US.
Average Market Risk Premia (by country) Risk premium, % Country
Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation – Square root of variance. A measure of volatility.
Return Statistics • The history of capital market returns can be summarized by describing the • average return • the standard deviation of those returns
– 60% 0% + 60% Canada Returns, 1957-2003 Average StandardInvestment Annual Return Deviation Distribution Canadian common stocks 10.64% 16.41% Long Bonds 8.96 10.36 Treasury Bills 6.80 4.11 Inflation 4.29 3.63
Risk Statistics There is no universally agreed-upon definition of risk. A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
Expected Return, Variance, and covariance Consider the following two risky asset worlds. There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund.
The Return for Portfolios The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.
1 2 3 4 5 6 N 1 2 3 4 5 6 N Portfolio Risk To calculate portfolio variance add up the boxes STOCK STOCK
Diversification • The variance (risk) of the security’s return can be broken down into: • Systematic (Market) Risk • Unsystematic (diversifiable) Risk The Effect of Diversification: • unsystematic risk will significantly diminish in large portfolios • systematic risk is not affected by diversification since it affects all securities in any large portfolio
Portfolio Risk as a Function of the Number of Stocks in the Portfolio In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Nondiversifiable risk; Systematic Risk; Market Risk n Thus diversification can eliminate some, but not all of the risk of individual securities.
Expected stock return beta +10% • 10% Expected - 10% + 10% market return -10% Copyright 1996 by The McGraw-Hill Companies, Ic Beta and Unique Risk 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes
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.
Definition of Risk When Investors Hold the Market Portfolio • Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security. • Beta measures the responsiveness of a security to movements in the market portfolio.
Chapter 8Risk and Return • Markowitz Portfolio Theory • Risk and Return Relationship • Validity and the Role of the CAPM
Markowitz Portfolio Theory • Given a certain level of risk, investors prefer stocks with higher returns. • Given a certain level of return, investors prefer less risk. • By combining stocks into a portfolio, one can achieve different combinations of return & standard deviation. • Correlation coefficients are crucial for ability to reduce risk in portfolio.
Markowitz Portfolio Theory Expected Returns and Standard Deviations vary given different weighted combinations of the stocks Expected Return (%) Coca Cola 40% in Coca Cola Exxon Mobil Standard Deviation
Efficient Frontier Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 40% 21%
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
Efficient Frontier Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 40% 21% Portfolio 28.117.4% Let’s Add stock New Corp to the portfolio
Efficient Frontier Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio 28.1 50% 17.4% New Corp 30 50% 19% New Portfolio 23.43 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION
Efficient Frontier Return B AB A Risk
Efficient Frontier Return B N AB A Risk
Efficient Frontier Return B N ABN AB A Risk
2-Security Portfolios - Various Correlations return 100% stocks = -1.0 = 1.0 = 0.2 100% bonds
Efficient Frontier return efficient frontier minimum variance portfolio Individual Assets P
Riskless Borrowing and Lending return Now investors can allocate their money across the T-bills and a balanced mutual fund CML 100% stocks Balanced fund rf 100% bonds
Market Equilibrium: CAPM return CML efficient frontier M rf P
return Changes in Riskfree Rate CML1 CML0 100% stocks Second Optimal Risky Portfolio First Optimal Risky Portfolio 100% bonds
Market Return = rm Security Market Line Return . Efficient Portfolio Risk Free Return = rf 1.0 BETA
Security Market Line Return SML rf BETA 1.0 SML Equation = rf + B ( rm - rf )
Risk & Expected Return Expected return b 1.5
Characteristic Line Slope = bi Estimating b with regression Security Returns Return on market % Ri = ai + biRm + ei
CAPM versus Reality • Do investors care about mean and variance? • Is there a security that is risk-free? • Short selling? • Transaction costs? • Most important: homogeneous expectations?