# Chapters 9 & 10 – MBA504 Risk and Returns Return Basics –Holding-Period Returns –Return Statistics Risk Statistics Return and Risk for Individual Securities.

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Chapters 9 & 10 – MBA504 Risk and Returns Return Basics –Holding-Period Returns –Return Statistics Risk Statistics Return and Risk for Individual Securities Return and Risk for Portfolios –Efficient Set for Two Assets –Efficient Set for Many Securities Riskless Borrowing and Lending Capital Asset Pricing Model

Chapters 9 & 10 – MBA504 Dollar Return = Dividend + Change in Market Value Returns

Chapters 9 & 10 – MBA5043 Example Suppose you bought 100 shares of Wal-Mart (WMT) 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?

Chapters 9 & 10 – MBA5044 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 r i :

Chapters 9 & 10 – MBA5045 Example Suppose your investment provides the following returns over a four-year period:

Chapters 9 & 10 – MBA5046 Holding Period Returns Year-by-year historical rates of return starting in 1926 for the following five important types of financial instruments in the United States: –Large-Company Common Stocks –Small-company Common Stocks –Long-Term Corporate Bonds –Long-Term U.S. Government Bonds –U.S. Treasury Bills

Chapters 9 & 10 – MBA5047 Future Value of an Investment of \$1 in 1925 \$59.70 \$17.48 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. \$1,775.34

Chapters 9 & 10 – MBA5048 Return Statistics The history of capital market returns can be summarized by describing the –average return –the standard deviation of those returns –the frequency distribution of the returns.

Chapters 9 & 10 – MBA5049 Historical Returns, 1926-2002 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 Stocks16.933.2 Long-Term Corporate Bonds6.28.7 Long-Term Government Bonds5.89.4 U.S. Treasury Bills3.83.2 Inflation3.14.4

Chapters 9 & 10 – MBA50410 Average Stock Returns and Risk-Free Returns Risk Premium is the additional return (in excess of risk- free rate) resulting from bearing risk. One of the most significant observations of stock market data is this long-run excess of stock return over the risk- free return. –The average excess return from large company common stocks for the period 1926 through 1999 was 8.4% = 12.2% – 3.8% –The average excess return from small company common stocks for the period 1926 through 1999 was 13.2% = 16.9% – 3.8% –The average excess return from long-term corporate bonds for the period 1926 through 1999 was 2.4% = 6.2% – 3.8%

Chapters 9 & 10 – MBA50411 Risk Premia Suppose that The Wall Street Journal announced that the current rate for 1-year Treasury bills is 5%. What is the expected return on the market of small-company stocks? Recall that the average excess return from small company common stocks for the period 1926 through 1999 was 13.2% Given a risk-free rate of 5%, we have an expected return on the market of small-company stocks of 18.2% = 13.2% + 5%

Chapters 9 & 10 – MBA50412 The Risk-Return Tradeoff

Chapters 9 & 10 – MBA50413 Risk Premiums Rate of return on T-bills is essentially risk-free. Investing in stocks is risky, but there are compensations. The difference between the return on T-bills and stocks is the risk premium for investing in stocks.

Chapters 9 & 10 – MBA50414 You can either sleep well or eat well. -- An old saying on Wall Street

Chapters 9 & 10 – MBA50415 Risk Statistics There is no universally agreed-upon definition of risk. The measures of risk that we discuss are variance and standard deviation. –The standard deviation is the standard statistical measure of the spread of a sample –In terms of normal distribution

Chapters 9 & 10 – MBA50416 Normal Distribution A large enough sample drawn from a normal distribution looks like a bell-shaped curve. Probability Return on large company common stocks 99.74% – 3  – 49.3% – 2  – 28.8% – 1  – 8.3% 0 12.2% + 1  32.7% + 2  53.2% + 3  73.7% The probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3. 68.26% 95.44%

Chapters 9 & 10 – MBA50417 Risk and Return: Individual Securities The characteristics of individual securities that are of interest are the: –Expected Return –Variance and Standard Deviation –Covariance and Correlation

Chapters 9 & 10 – MBA50418 Expected Return and Variance Consider the following two risky asset world. There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund.

Chapters 9 & 10 – MBA50419

Chapters 9 & 10 – MBA50420 Consider a portfolio that is 50% invested in bonds and 50% invested in stocks.

Chapters 9 & 10 – MBA50421 The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: Risk and Return for a Portfolio

Chapters 9 & 10 – MBA50422 The Efficient Set for Two Assets We can consider other portfolio weights besides 50% in stocks and 50% in bonds … 100% bonds 100% stocks

Chapters 9 & 10 – MBA50423 100% stocks 100% bonds Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less. These compromise the efficient frontier.

Chapters 9 & 10 – MBA50424 Portfolio Risk as a Function of the Number of Stocks in the Portfolio Nondiversifiable risk; Systematic Risk; Market Risk Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk n  In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Thus diversification can eliminate some, but not all of the risk of individual securities. Portfolio risk

Chapters 9 & 10 – MBA50425 Efficient Set for Many Securities Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios. return PP Individual Assets

Chapters 9 & 10 – MBA50426 The section of the opportunity set above the minimum variance portfolio is the efficient frontier. return PP minimum variance portfolio efficient frontier Individual Assets

Chapters 9 & 10 – MBA50427 Optimal Risky Portfolio with a Risk- Free Asset In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills 100% bonds 100% stocks rfrf return 

Chapters 9 & 10 – MBA50428 Riskless Borrowing and Lending Now investors can allocate their money across the T-bills and a balanced mutual fund Investor risk aversion is revealed in their choice of where to stay along the capital allocation line. 100% bonds 100% stocks rfrf return  Balanced fund CML

Chapters 9 & 10 – MBA50429 Market Equilibrium All investors have the same CML because they all have the same optimal risky portfolio given the risk-free rate. 100% bonds 100% stocks rfrf return  Optimal Risky Portfolio CML

Chapters 9 & 10 – MBA50430 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 (  )of the security. Beta measures the responsiveness of a security to movements in the market portfolio.

Chapters 9 & 10 – MBA50431 Estimating  with regression Security Returns Return on market % R i =  i +  i R m + e i Slope =  i Characteristic Line

Chapters 9 & 10 – MBA50432 Relationship between Risk and Expected Return (CAPM) Expected Return on the Market: Expected return on an individual security: Market Risk Premium This applies to individual securities held within well- diversified portfolios.

Chapters 9 & 10 – MBA50433 This formula is called the Capital Asset Pricing Model (CAPM) Assume  i = 0, then the expected return is R F. Assume  i = 1, then Expected return on a security = Risk- free rate + Beta of the security × Market risk premium

Chapters 9 & 10 – MBA50434 Relationship Between Risk & Expected Return Expected return  1.5

Chapters 9 & 10 – MBA50435 Empirical Approaches to Asset Pricing Empirical methods are based less on theory and more on looking for some regularities in the historical record. –E(R) = R f + k 1 (beta) + k 2 (B/M) + k 3 (size) –k 1, k 2 >0, and k 3 <0

Chapters 9 & 10 – MBA50436 Style Portfolios Related to empirical methods is the practice of classifying portfolios by style e.g. –Value portfolio –Growth portfolio

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