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**Introduction to Risk and Return**

Principles of Corporate Finance Tenth Edition Chapter 7 Introduction to Risk and Return Slides by Matthew Will McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. 1 1 1 1 1 2

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**Topics Covered Over a Century of Capital Market History**

Measuring Portfolio Risk Calculating Portfolio Risk How Individual Securities Affect Portfolio Risk Diversification & Value Additivity 2 2 2 2 3 2

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**The Value of an Investment of $1 in 1900**

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**The Value of an Investment of $1 in 1900**

Real Returns 13

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**Average Market Risk Premia (by country)**

Risk premium, % Country

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Dividend Yield Dividend yields in the U.S.A. 1900–2008

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**Stock Market Index Returns**

Rates of Return Stock Market Index Returns Percentage Return Year Source: Ibbotson Associates 14

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**Histogram of Annual Stock Market Returns**

Measuring Risk Histogram of Annual Stock Market Returns ( ) # of Years Return %

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**Measuring Risk Variance - Average of squared deviations from mean.**

Standard Deviation – Square root of the variance. A measure of volatility.

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Measuring Risk Coin Toss Game-calculating variance and standard deviation

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Measuring Risk 19

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**Equity Market Risk (by country)**

Average Risk ( ) Standard Deviation of Annual Returns, %

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**Annualized Standard Deviation of the DJIA over the preceding 52 weeks**

Dow Jones Risk Annualized Standard Deviation of the DJIA over the preceding 52 weeks (1900 – 2008) Standard Deviation (%) Years

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Measuring Risk 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

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Comparing Returns

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Measuring Risk 20

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Measuring Risk 21

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Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes 19

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**Portfolio Risk Example**

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is: 19

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**Portfolio Risk Another Example**

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

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**Portfolio Risk Another Example**

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

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Portfolio Risk 19

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**Portfolio Risk Example Correlation Coefficient = .4**

Stocks s % of Portfolio Avg Return ABC Corp % % Big Corp % % Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Real Standard Deviation: = (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4) = CORRECT Return : r = (15%)(.60) + (21%)(.4) = 17.4%

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**Portfolio Risk Let’s Add stock New Corp to the portfolio**

Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp % % Big Corp % % 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

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**Portfolio Risk NOTE: Higher return & Lower risk**

Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio % % New Corp % % NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = NEW Return = weighted avg = Portfolio = 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION

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**Portfolio Risk To calculate portfolio variance add up the boxes**

The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N To calculate portfolio variance add up the boxes STOCK STOCK

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Portfolio 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.

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**Portfolio Risk The return on Dell stock changes on average**

by 1.41% for each additional 1% change in the market return. Beta is therefore 1.41.

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**Portfolio Risk The middle line shows that a well**

Diversified portfolio of randomly selected stocks ends up with 1 and a standard deviation equal to the market’s—in this case 20%. The upper line shows that a well-diversified portfolio with 1.5 has a standard deviation of about 30%—1.5 times that of the market. The lower line shows that a well-diversified portfolio with .5 10%—half that of the market.

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Portfolio Risk

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Portfolio Risk Covariance with the market Variance of the market

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Beta

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