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**Today Risk and Return Reading Portfolio Theory**

Capital Asset Pricing Model Reading Brealey, Myers, and Allen, Chapters 7 and 8

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Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation - Average value of squared deviations from mean. A measure of volatility. Variance measures ‘Total Risk’

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Measuring Risk 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.” Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. 18

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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 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 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 Return and Risk**

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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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**Copyright 1996 by The McGraw-Hill Companies, Inc**

Beta and Unique Risk 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes beta Expected return market 10% - + +10% stock Copyright 1996 by The McGraw-Hill Companies, Inc -10%

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Beta and Unique 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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Beta and Unique Risk Covariance with the market Variance of the market

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**Markowitz Portfolio Theory**

Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation. Correlation coefficients make this possible. The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

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**Markowitz Portfolio Theory**

Price changes vs. Normal distribution Coca Cola - Daily % change Proportion of Days Daily % Change

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**Markowitz Portfolio Theory**

Standard Deviation VS. Expected Return Investment A % probability % return

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**Markowitz Portfolio Theory**

Standard Deviation VS. Expected Return Investment B % probability % return

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**Markowitz Portfolio Theory**

Expected Returns and Standard Deviations vary given different weighted combinations of the stocks Expected Return (%) Coca Cola 40% in Coca Cola Exxon Mobil Standard Deviation

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Efficient Frontier Each half egg shell represents the possible weighted combinations for two stocks. The composite of all stock sets constitutes the efficient frontier Expected Return (%) Standard Deviation

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**Efficient Frontier T rf S**

Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier. Expected Return (%) T Lending Borrowing rf S Standard Deviation

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**Efficient Frontier Example Correlation Coefficient = .4**

Stocks s % of Portfolio Avg Return ABC Corp % % Big Corp % % Standard Deviation = weighted avg = Standard Deviation = Portfolio = Return = weighted avg = Portfolio =

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**Efficient Frontier 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 = Standard Deviation = Portfolio = Return = weighted avg = Portfolio = Let’s Add stock New Corp to the portfolio

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**Efficient Frontier NOTE: Higher return & Lower risk**

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

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Efficient Frontier Return B A Risk (measured as s)

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Efficient Frontier Return B AB A Risk

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Efficient Frontier Return B N AB A Risk

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Efficient Frontier Return B ABN N AB A Risk

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**Efficient Frontier Goal is to move up and left. Return WHY? B ABN N AB**

Risk

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**Efficient Frontier Return Low Risk High Return High Risk High Return**

Low Return High Risk Low Return Risk

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**Efficient Frontier Return Low Risk High Return High Risk High Return**

Low Return High Risk Low Return Risk

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Efficient Frontier Return B ABN N AB A Risk

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**. Security Market Line rf Return Market Return = rm**

Efficient Portfolio Risk Free Return = rf Risk

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**. Security Market Line rf Return Market Return = rm**

Efficient Portfolio Risk Free Return = rf 1.0 BETA

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**. Security Market Line rf Return Risk Free Return =**

Security Market Line (SML) rf BETA

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**Security Market Line rf SML Equation = rf + β ( rm - rf ) Return SML**

BETA 1.0 SML Equation = rf + β ( rm - rf )

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**Capital Asset Pricing Model**

R = rf + β ( rm - rf ) CAPM

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**Beta vs. Average Risk Premium**

Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0

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**Beta vs. Average Risk Premium**

Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium SML 30 20 10 Investors Market Portfolio Portfolio Beta 1.0

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**Beta vs. Average Risk Premium**

Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0

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**Arbitrage Pricing Theory**

Alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + … Return = a + bfactor1(rfactor1) + bf2(rf2) + …

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**Arbitrage Pricing Theory**

Estimated risk premiums for taking on risk factors ( )

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