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Reviewing Risk Measurement Concepts First Affirmative Financial Network, LLC R. Kevin OKeefe, CIMA

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What we will cover Beta Standard Deviation Sharpe Ratio R-squared Correlation Coefficient How they interrelate

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Limitations and Uses Limitations: Cannot predict specific events Are historical, backward-looking Uses: Can help improve portfolio construction Can help identify unwanted exposure Can help defend investment decisions

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Beta A measure of a securitys sensitivity to market movements It is a relative measure, not an absolute measure of volatility It does not tell you enough; you need to know the R-squared.

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Beta = 1.0

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Beta = 0.5

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Beta = 2.0

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Estimating Beta: Fund 1 R1Rm -15-20 30 40 What is the slope (rise / run)?

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Estimating Beta: Fund 1 45 60

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Estimating Beta: Fund 1 Rise / run = 45 / 60 =.75 This is easy! But … What happens when the data get more complex?

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Estimating Beta: Fund 2 R2Rm 3-30 15 20 20 10 -10-40

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Estimating Beta: Fund 2

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Regression line Beta =.42

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Beta : Example Fidelity Select Gold Fund Beta: 0.25 Std Dev: 31.28 R-squared: 2

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Beta: The Details The beta of a portfolio is the weighted average of the individual betas of the securities in the portfolio. Half the securities in the market have a beta > 1, and half have a beta < 1. You cannot diversify away beta.

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Standard Deviation Standard deviation defines a band around the mean within which an investments (or a portfolios) returns tend to fall. The higher the standard deviation, the wider the band.

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Standard Deviation Assumes normal distribution (bell-shaped curve)

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Standard Deviation

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68.3% 95.5% -1 SD+1SD-2 SD+2 SD Standard Deviation

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Q. What does it mean that a portfolios standard deviation is x%? A. It means that x = 1 standard deviation (which allows you, therefore, to say something statistically meaningful about the range of probable returns.)

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68.3% 95.5% -1 SD+1SD-2 SD+2 SD Standard Deviation

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Trick Question: Which portfolio is riskiest? A B C Mean return7% 20% 30% Standard dev.3% 6% 15%

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Standard Deviation Answer: It depends on your definition of risk! Does risk mean … Probability of loss? Magnitude of loss? Probability of underperforming target?

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Standard Deviation Trick Question: Which portfolio is riskiest? A B C Mean return7% 20% 30% Standard dev.3% 6% 15%

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Beta vs. Standard Deviation Two Funds: Same Slope Same Intersect Same Characteristic Line What statistical measure is identical for these two funds?

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Two funds

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Beta vs. Standard Deviation Two Funds: Which will exhibit greater variability (i.e., higher standard deviation)? Which has more securities? Which has the higher R 2 ?

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Beta vs. Standard Deviation Fund A Greater variability Higher standard deviation? Fewer securities Lower r-squared Fund B Less variability Lower standard deviation? More securities Higher r-squared

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R-Squared Tightness of fit around the characteristic line OR, if you prefer, the percentage of a portfolios fluctuations that can be explained by fluctuations in its benchmark index Relates to beta, not standard deviation Tells you how much significance there is to the beta: higher R 2 = greater significance

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Sharpe Ratio Sharpe Ratio = Excess Return* Standard Deviation *Above the risk-free rate 1.The number is meaningless except in a relative context. 2.Based on Standard Deviation, not Beta, thus more meaningful at the portfolio level rather than at the component level.

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Correlation Coefficient Meaningful at the component level The Myth of Negative Correlation Correlation coefficients are cyclical; they strengthen and weaken over time

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Correlation Coefficients (3 year)

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Correlation Coefficients (10 year)

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Risk Adjusted Measures Total risk = Market risk + non-market risk All measures must be contextualized Standard Deviation: 1. Dont forget to account for returns 2. Risk must be defined 3. Remember that standard deviation measures upside volatility as well as downside.

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Risk Adjusted Measures Beta: 1. Dont forget to account for R 2. 2. A useful measure, but insufficient in portfolio construction …

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Risk Adjusted Measures Sharpe ratio: 1. Meaningless number, except as a way of comparing different portfolios over an identical period. 2. Measures absolute risk (vs. relative risk).

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Risk Adjusted Measures Correlation Coefficients: 1. Fluctuate over time 2. Remember to factor in expected returns

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Limitations and Uses Limitations: Cannot predict specific events Are historical, backward-looking Uses: Can help improve portfolio construction Can help identify unwanted exposure Can help defend investment decisions

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Questions and Discussion ? ? ? ?

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© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Return, Risk, and the Security Market Line Chapter Thirteen.

© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Return, Risk, and the Security Market Line Chapter Thirteen.

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