# SEC07 - UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL FNCE...

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UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL FNCE 601 FINANCIAL ANALYSIS LECTURE NOTES Franklin Allen Fall 2003 QUARTER 1 - WEEK 5 Tu: 9/30/03 and Th: 10/2/03 Copyright 2003 by Franklin Allen

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FNCE 601 - Section 7(i) - Page 1 Section 7: Measuring Risk Motivation In this section and the next we’re going to talk about risk. We’ve got a lot of work before we get results, so I’ll give two motivation examples to start with. Motivation Example 1 Consider the following two investments. (i) A lone prospector intends to search for gold in the Rockies and is issuing 100 shares to finance his expenses. The evidence suggests that if he strikes gold he will hit it big and the payoff on the project will be \$100. However, the probability of this is only 10 percent. There is a 90 percent chance he will find no gold in which case the payoff on the project will be \$0. Hence the expected payoff is \$10. (ii) Another investment is 100 shares of an electric utility. If the economy does well a lot of electricity will be used, the utility’s profits will be high and its stock will yield a gross payoff of \$15. The probability of this happening is 50 percent. The other possibility is that the economy does badly and not much electricity is used. In this case the payoff on the firm’s stock is \$5. The probability of this happening is 50 percent so the expected payoff is again \$10. Both of these investments have the same expected return. Which of them is more risky in a financial sense?
FNCE 601 - Section 7(i) - Page 2 Motivation Example 2 Suppose T-bills are yielding 4%. Is it ever worthwhile investing in a risky stock yielding a total return (i.e. including dividends and capital gains) of 3%? What we’re going to do over the next two weeks or so is derive a formula for risk adjusted discount rates of the form r = r F + β (r M - r F ) where r F - risk free rate (e.g., T-bill rate) r M - return on market portfolio (e.g., a value-weighted portfolio of all stocks on the NYSE) β = Measure of risk = Cov (Stock, Market portfolio) Var (Market portfolio) Notice that what’s important in the measure of risk is covariance with the market portfolio. You can see from this why we get the results that we do in the motivation examples. Understanding why covariances matter is the core concept in understanding risk. It is not a simple idea and we have a lot of ground to cover before you have a full intuitive understanding of the CAPM and these examples. Section 7(i): Historical and Statistical Review Before we go on to deal with risk and asset pricing risk we should start with a brief historical and statistical review. The appendix at the end of the section starts with historical data for the US. The first figure (from the Stocks, Bonds, Bills and Inflation Yearbook for 2003 published by Ibbotson

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FNCE 601 - Section 7(i) - Page 3 Associates) shows that there is a vast difference between the returns on different investments. The second thing to notice is the amount you would have had at the end of 2002 if you had
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## SEC07 - UNIVERSITY OF PENNSYLVANIA THE WHARTON SCHOOL FNCE...

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