Risk and Capital Budgeting Chapter 13

Chapter 13 - Outline What is Risk? Risk Related Measurements Coefficient of Correlation The Efficient Frontier CAPM and Beta

What is Risk? Risk means uncertainty about a future outcome Risk varies greatly depending on the investment: –A T-Bill has zero or no risk – A gold-mining expedition in Africa has high risk Most investors and financial managers are risk averse, meaning they don’t like risk - Preference: relative certainty as opposed to uncertainty - Expectation: higher value or return for risky investments

Stocks, Bonds, Bills, and Inflation Hypothetical value of $1 invested at year-end Assumes reinvestment of income and no transaction costs or taxes This is for illustrative purposes only and not indicative of any investment. Past performance is no guarantee of future results. 3/1/2008. Copyright © 2008 Ibbotson Associates, Inc Average Return Ending Wealth $12,130 $2,526 $99.17 $20.51 $12.14

Rates of Return Source: Ibbotson Associates Year Percentage Return

Stocks, Bonds, Bills, and Inflation Compound Annual Return Arithmetic Annual Return Risk (Standard Deviation) *The 1933 Small Company Stock total return was 142.9%. This is for illustrative purposes only and not indicative of any investment. Past performance is no guarantee of future results. 3/1/2008. Copyright © 2008 Ibbotson Associates, Inc. Summary Statistics Distribution of Annual Returns Large Company Stocks 9.66%11.8%20.5% Small Company Stocks * 11.7%16.5%33.0% Government Bonds 5.7%6.1%9.4% Inflation 2.9%3.1%4.2% Treasury Bills 3.7%3.8%3.1%

Some Risk Related Statistical Measurements Expected Value: – equal to weighted average of outcomes x probabilities Standard Deviation: – measure of dispersion or variability around the expected value – the larger the standard deviation  the greater the risk Coefficient of Variation: – equal to standard deviation / expected value – the larger the coefficient of variation  the greater the risk

Variability and risk

Probability distribution with differing degrees of risk

Calculating mean (or expected) return Probability Probability Return x return % -2% Total 12% Mean or expected return

Calculating variance and standard deviation of Merck returns from past monthly data Deviation from mean Squared Month Return return deviation 1 5.4% 2.6% Total Mean: 16.8/6 = 2.8% Variance: /6 = Std dev: Sq root of = 5.85% per month

Calculating variance and standard deviation Deviation Probability from mean x squared Probability Return return deviation % -22% Total Variance Standard deviation = square root of variance = 14%

Mean and standard deviation mean measures average (or expected return) l standard deviation (or variance) measures the spread or variability of returns l risk averse investors prefer high mean & low standard deviation 20 standard deviation expected return better HOWEVER, INVESTOR FOCUS IS ON PORTFOLIO RISK & RETURN

Expected portfolio return Portfolio Expected Proportion x proportion (x) return (r) return (xr) Merck.40 10% 4% McDonald Total % Expected portfolio return

Risk and 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.”

Diversification eliminates unique risk deviation standard Portfolio Unique risk Market risk Number of securities 510

Stock Diversification Number of Stocks in Portfolio Risk Market Risk Diversifiable Risk This is for illustrative purposes only and not indicative of any investment. Past performance is no guarantee of future results. 3/1/2000. Copyright © 2000 Ibbotson Associates, Inc.

Where do Diversification Benefits Come from? Concepts of Correlation and Covariance Expected Return on portfolio Standard Deviation of Portfolio Returns

Coefficient of Correlation Shows the extent of correlation among projects Has a numerical value of between -1 and +1 Its value shows the risk reduction between projects: Negative correlation (-1)  Large risk reduction No correlation (0)  Some risk reduction Positive correlation (+1)  No risk reduction Coefficient of Correlation  Coefficient of Variation

The Efficient Frontier Combinations of projects with the best trade-off between risk and return 2 objectives: – Achieve the highest possible return at a given risk level – Provide the lowest possible risk at a given return level The Efficient Frontier is the best risk-return line or combination of possibilities

Mean & standard deviation: Portfolio of Merck & McDonald

Calculating covariance and correlation between Merck and McDonald from past monthly data Deviation Product Return: from mean: of Month Merck McD Merck McD deviations 1 5.4% 10.7% 2.6% 8.9% Total Mean Covariance: 106.1/6 = 17.7 Std dev Merck: 5.9% Std dev McD: 7.7% Corr. co-effic: Cov/(sd Me. sd McD ) = 17.7/(5.9 x 7.7) =.39

Calculating covariance and correlation Deviation from Probability Return on: mean return: x product of Prob. A B A B deviations % -10% -22% -22% Mean Total 136 Std dev Covariance Correlation = = =.6944 coefficient (sd A) x (sd B) 14 x 14 covariance136

Effect of changing correlations: Portfolio of Merck & McDonald

With a correlation of one, same as a weighted average. Portfolio Risk Example Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The standard deviation of their annualized daily returns are 19.8% for Wal-Mart and 29.7% for IBM. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.

Portfolio Risk with lower correlation: Example Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The standard deviation of their annualized daily returns are 19.8% for Wal-Mart and 29.7% for IBM. Assume a correlation coefficient of 0.70 and calculate the portfolio variance. With a correlation less than one, less than a weighted average.

The set of portfolios Expected return Risk x x x x x x x x x x x x x x x x x x x x x x A B The set of portfolios between A and B are efficient portfolios

Adding a riskless asset to the efficient frontier riskless rate tangency portfolio

Capital asset pricing model Expected return Expected market return Risk free rate Beta r = r f + (r m - r f )

Beta Beta is a statistical measure of volatility It measures how responsive or sensitive a stock is to market movements in general An individual stock’s beta shows how it compares to the market as a whole: beta = 1 means equal risk with the market beta > 1 means more risky than the market beta < 1 means less risky than the market

Beta Computation Covariance with the market Variance of the market

Beta

Market risk (beta) for common stocks 1994 Stock Beta AT&T.92 Exxon.51 Biogen 2.20 Ford Motor Co Bristol Myers Squibb.97 General Electric 1.22 Coca Cola 1.12 McDonald’s 1.07 Compaq 1.18 Microsoft 1.23

Market risk (beta) for common stocks 2010* Stock Beta AT&T.63 Exxon.39 Biogen.68 Ford Motor Co Bristol Myers Squibb.59 General Electric 1.72 Coca Cola.51 McDonald’s.52 Hewlett-Packard 1.03 Microsoft 1.06 * Source: Finance.yahoo.com, which is based on 36 months of data and S&P500 as market index.