9-5b.- Risk and CAPM

# 9-5b.- Risk and CAPM - Risk and CAPM Ramesh Rao 1...

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Ramesh Rao 1 Risk and CAPM

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Ramesh Rao 2 Organization A. Measuring Returns and Risk for Individual Securities B. Risk and Return for Collections of Securities C. Diversification and “Relevant Risk” D. The Capital Asset Pricing Model E. Other Pricing Frameworks
Ramesh Rao 3 A. Measuring Returns and Risk for Individual Securities How do you measure Risk ? How do you evaluate the Risk- Return Tradeoff? How does this lead to a theory of prices? What is the “relevant” risk of an investment?

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Ramesh Rao 4 Preliminaries Risk v. Uncertainty General Risk v. Financial Risks Ex-ante v. Ex-post Returns What can statistics and finance teach us? What they do not teach us Who is a good decision-maker?
Ramesh Rao 5 A Motivating Example An individual purchases a share of stock which will be held for one year. The stock costs \$50 per share. What are the one period ex-ante returns if the investor estimates that at the end of the year the stock will pay \$5 and can be sold for \$60? What are the one period ex-post returns if at the end of the year the investor actually receives a dividend of \$6 and is able to sell the stock for \$55?

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Ramesh Rao 6 Example-Cont. Ex-Ante Returns 3 . 0 1 50 \$ 60 \$ 5 \$ 1 Investment Initial Price Period of End Forcasted Dividend Forecasted ~ = - + = - + = R 22 . 0 1 50 \$ 55 \$ 6 \$ 1 Investment Initial Price Period of End Actual Dividend Actual = - + = - + = R Main Lesson? Ex-Post Returns
Ramesh Rao 7 Probability Distributions Probability distributions Discrete Continuous Probability distributions allow us to quantify uncertainty, allowing risk analysis. We can use risk measures to assist in making decisions. Definition? Significance?

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Ramesh Rao 8 Discrete Distribution Boom 12% \$141 41% High growth 15 \$131 31% Normal 25 \$116 16% Low growth 30 \$106 6% Recession 18 \$ 81 -19% 100% Economy Prob. Stock Stock Price Return General Dynamics stock Current price = \$100 Criticism
Ramesh Rao 9 Need to simplify Information Expected return: Level of benefits Variance: Variability of benefits How is this simplification justified?

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Ramesh Rao 10
Ramesh Rao 11 Price changes vs. Normal distribution Microsoft - Daily % change 1986-1997 0 100 200 300 400 500 600 -10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10% # of Days (frequency) Daily % Change

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Ramesh Rao 12 Level of Benefits: Expected Return Expected Return: The probability weighted sum of all possible returns. = (0.12)(0.41) + (0.15)(0.31) + (0.25)(0.16) + (0.30)(0.06) + (0.18)(-0.19) = 0.1195 or 11.95% ( 29 ( 29 Return return of y probabilit = R Dangers?
Ramesh Rao 13 Variability of Returns: Variance Risk: the potential for variability in returns high risk low risk Riskless The standard deviation Variance: Probability-weighted squared deviations of returns from the mean. ( 29 [ ] 2 2 R ~ return of Prob. R - = σ = 2 Caveats?

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Ramesh Rao 14 Calculating Variance σ 2 = (0.12)(0.41 - 0.1195) 2 + (0.15)(0.31 - 0.1195) 2 + (0.25)(0.16 - 0.1195) 2 + (0.30)(0.06 - 0.1195) 2 + (0.18)(-0.19 - 0.1195) 2 = 0.0342 1848 . 0 0342 . 0 2 = = = σ σ Interpretation?
Ramesh Rao 15 Example Boom 0.30 0.16 0.18 Moderate 0.50 0.12 0.14 Recession 0.20 0.08 0.04 Expected Return 0.124 0.132 Variance 0.000784 0.002416 Economy Prob. Return A Return B

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