# Introduction to Risk and Return

## Presentation on theme: "Introduction to Risk and Return"— Presentation transcript:

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

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

The Value of an Investment of \$1 in 1900
13

The Value of an Investment of \$1 in 1900
Real Returns 13

Average Market Risk Premia (by country)

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

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

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

Measuring Risk Variance - Average of squared deviations from mean.
Standard Deviation – Square root of the variance. A measure of volatility.

Measuring Risk Coin Toss Game-calculating variance and standard deviation

Measuring Risk 19

Equity Market Risk (by country)
Average Risk ( ) Standard Deviation of Annual Returns, %

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

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

Comparing Returns

Measuring Risk 20

Measuring Risk 21

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

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

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

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

Portfolio Risk 19

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%

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

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

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

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.

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.

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.

Portfolio Risk

Portfolio Risk Covariance with the market Variance of the market

Beta