Introduction to Risk The pricing of Risky Assets

Required return depends on the risk of the investment The Greater the risk the greater the return Do all risks result in higher return? Look at the history of Capital Market returns Returns from non-financial investments have to be comparable with returns from financial investments of similar risk What determines the required rate of return of an investment?

Market Indexes Summarize the performance of different classes of securities Most well known: Dow Jones Industrial Average Standard & Poor’s Composite Index Indexes are portfolios of various stocks DJIA: 30 stocks SP500: 500 stocks

Different types of Indexes Equally Weighted portfolios (DJIA)  Each asset is represented in the portfolio by 1 share, no matter what the price of the share and the total value of the firm  If you are using 30 firms in your index, you will include a stock of each in it Value weighted portfolios(SP500)  Stocks in the portfolio are weighted by their relative weight on the market. The bigger the company, the higher it’s weight

Market Capitalization Total number of stocks * price of stock This is the measure of size that is used when building value weighted portfolios.

The Value of an Investment of $1 in 1926 Source: Ibbotson Associates Index Year End

Source: Ibbotson Associates Index Year End Real returns The Value of an Investment of $1 in 1926

Value in 1994 of $1 invested in 1926 $7 in 1994 had the same purchasing power as $1 in NOMINALREAL SMALL CAP$2,843$6402$340$660 S&P500$811$2587$97$267 CORPORATE BONDS $38$64.1$4.5$6.6 TREASURY BONDS $26$48.9$3.1$5 T-BILLS$12$16.6$1.5$1.7 INFLATION$7

Risk of different Asset Classes SecurityRisk Treasury BillsInflation Risk Treasury Bonds+ Interest Risk Corporate Bonds+ Default Risk Common Stocks+ Market Risk + Unsystematic Risk

Average Return Average Nominal Return Average Real Return Average Risk Premium Treasury bills 3.7%0.6%0 % Government bonds Corporate bonds Common stocks Small-firm stocks

Rates of Return Source: Ibbotson Associates Year Percentage Return

US Stock Market

Return, percent Annual Market Returns in the US

Measuring Risk Variance (σ 2 ) and Standard Deviation (σ) Average value of squared deviations from mean. A measure of volatility.

Deviation from mean Squared Month Return return deviation 1 5.4% 2.6% Total Mean: 16.8/6 = 2.8% Variance: 205.4/6 = 34.2 Standard deviation: 34.2 = 5.9% per month Annualized standard deviation 5.9 x (12) = 20.3% Merck’s historical Mean and Standard Deviation

Average Return Average Nominal Return Average Risk Premium Standard Deviation Treasury bills 3.7%0 %3.3 % Government bonds Corporate bonds Common stocks Small-firm stocks

Brief periods of extremely high volatility October 19, 1987, market fell 23% in one day VARIABILITY IN STOCK MARKET RETURNS

Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. – 90%+ 90%0% Average Standard Series Annual Return DeviationDistribution Large Company Stocks12.2%20.5% Small Company Stocks Long-Term Corporate Bonds Long-Term Government Bonds U.S. Treasury Bills Inflation Historical returns 1926 to Today

Normal Distribution A large enough sample drawn from a normal distribution looks like a bell-shaped curve. Return on large company common stocks The probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3. Probability 99.74% – 3  – 49.3% – 2  – 28.8% – 1  – 8.3% % + 1  32.7% + 2  53.2% + 3  73.7% 68.26% 95.44%

Normal Distribution The 20.1-percent standard deviation we found for stock returns from 1926 through 1999 can now be interpreted in the following way: if stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3.

Source: © Stocks, Bonds, Bills, and Inflation 2002 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. Normal Distribution

Calculated over recent five-year period Firm faces changing business risks over 70-year period Calculate monthly variance and multiply by twelve, assuming successive monthly returns are independent Standard deviation increases with the square root of the length of time over which it is being measured Most stocks more variable than market Diversification reduces variability Changes in the price of different stocks are not perfectly correlated Tend to offset each other Variability In Returns Of Individual Stocks

Portfolio Standard Deviation UNIQUE RISK MARKET RISK Number of securities 510 Diversification Eliminates Unique Risk

MARKET RISK Or Systematic Risk Or Undiversifiable Risk Affects All Stocks UNIQUE RISK Or Unsystematic Risk Or Diversifiable Risk Or Specific Risk Or Residual Risk Affects Individual Stocks Or Small Groups Of Stocks Unique Risk Of Different Firms Unrelated Eliminated By Diversification Individual Stocks Have Two Kinds Of Risk

A drug trial showing that beta blockers increase risk of cancer in older people will affect Pfizer’s stock But has no effect on shares of GM or IBM A strike at a single GM plant will affect only GM and perhaps its suppliers and competitors A hot summer will increase demand for air conditioners But won’t affect the demand for computers Unique Or Unsystematic Risk

All firms affected by economy and exposed to market risk Example: surprise in rate of growth in GNP Market risk cannot be diversified away Market Or Systematic Risk

Risk of a well-diversified portfolio depends only on the market or systematic risk of the securities in the portfolio Risk of a non- diversified portfolio depends on the market risk and the unique risk of the securities in the portfolio Portfolio Risk

The market or an average stock has  =1 A stock with  =2 has twice as much systematic risk as the market An investor in a high beta stock will expect to earn a higher return than an investor in a low beta stock Systematic Risk Of A Stock Measured By Its Beta

The return on a portfolio, diversified or not, depends only on the market risk of the portfolio The market doesn’t reward us for taking unique risks we can avoid at very little cost by diversification otherwise mutual funds would always sell at a premium to the value of their underlying shares Major Investors Hold Diversified Portfolios, With Little Or No Diversifiable Or Unique Risk

Market risk (beta) for common stocks StockBetaStockBeta AT&T.92Exxon.51 Biogen2.2Ford Motor1.12 Bristol Myers.97General Electric1.22 Coca Cola1.12McDonald’s1.32 Compaq1.18Microsoft1.23

 = 2.2 Biogen has 2.2 times as much market risk as the market relation between  and actual returns not precise because of biogen’s unique risk actual returns scattered about fitted line BIOGEN

1. TOTAL RISK = DIVERSIFIABLE RISK + MARKET RISK 2. MARKET RISK IS MEASURED BY BETA, THE SENSITIVITY TO MARKET CHANGES beta EXPECTED RETURN EXPECTED MARKET RETURN STOCK Risk Of Individual Stocks

Diversification makes sense for investors Does it also make sense for a firm? If diversification makes sense for the firm, each new project has to be analyzed in the context of the firm’s portfolio of existing projects Value of the diversified portfolio of projects would be greater than the sum of the projects considered separately No. Investors can easily diversify by holding different securities; they will not pay more for firms that diversify In countries with efficient capital markets, diversification does not increase or decrease a firm’s value Total value of a firm is the sum of its parts Diversification And Value Additivity

r = r f +  (r m - r f ) EXPECTED RETURN Expected market return Risk free rate BETA MARKET PORTFOLIO Security market line

r m - r f Rate of return on market - t-bill rate Has averaged 8.4% over 69 years Market risk premium

f m X r r EXPECTED RETURN BETA 1.0 X SML and investments Investments lying below the security market line are dominated by a mixture of the market portfolio and the riskless asset

 = 0.92 Interest rate on t-bills r f = 6% Market risk premium r m - r f = 8.4% Expected return on AT&T r = r f +  (r m - r f ) = X 8.4 = 13.7% Expected Return On AT&T Stock At Beginning Of 1995