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# 08 Chapter model - 08 Chapter model 9:05 Chapter 8 Risk and...

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08 Chapter model 10/7/2009 9:05 2/14/2006 Chapter 8. Risk and Rates of Return Demand for Probability Rate of return on stock, the firms of this if this demand occurs Martin U.S. Water products occurring Martin Prod. U.S. Water Prob x Ret. Prob x Ret. Strong 30% 100% 20% 30.0% 6.0% Normal 40% 15% 15% 6.0% 6.0% Weak 30% -70% 10% -21.0% 3.0% 100% Expected return = 15.0% 15.0% MARTIN PRODUCTS Demand for Probability (1) (2) (3) the firms of this Return in Deviation Squared Prob. X products occurring this outcome from mean Deviation Sq Deviation Strong 30% 100% 85% 72.3% 21.7% Normal 40% 15% 0% 0.0% 0.0% Weak 30% -70% -85% 72.3% 21.7% Sum of squared deviations (Variance) = 43.4% (4) Standard deviation = 65.8% (5) U.S. WATER Demand for Probability (1) (2) (3) the firms of this Return in Deviation Squared Prob. X products occurring this outcome from mean Deviation Sq Deviation Strong 30% 20% 5% 0.3% 0.1% Normal 40% 15% 0% 0.0% 0.0% The relationship between risk and return is a fundamental axiom in finance. Generally speaking, it is totally logical to assume that investors are only willing to assume additional risk if they are adequately compensated with additional return. This idea is rather fundamental, but the difficulty in finance arises from interpreting the exact nature of this relationship (accepting that risk aversion differs from investor to investor). Risk and return interact to determine security prices, hence its paramount importance in finance. Stand-alone risk (Section 8.1) In explaining stand-alone risk, this model introduces probablity distributions and the calculation of expected retuns, standard deviations, and coefficients of variation. PROBABILITY DISTRIBUTIONS: CALCULATING EXPECTED RETURN The probability distribution is a listing of all possible outcomes and the corresponding probability. The expected return is calculated by multiplying the possible returns by their corresponding probabilities. PROBABILITY DISTRIBUTIONS: CALCULATING STANDARD DEVIATION Standard deviation measures the variability of a set of observations and is calculated by finding the square root of a sum of squared deviations. Sound confusing? The charts below calculate standard deviation for Martin and U.S. Water.

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Weak 30% 10% -5% 0.2% 0.1% Sum of squared deviations (Variance) = 0.2% (4) Standard deviation = 3.9% (5) SD for Martin 65.8% SD for U.S. Water 3.9% SAMPLE STANDARD DEVIATION CALCULATION Realized Deviation Squared Year return from mean Deviation 2003 15% 5% 0.2% 2004 -5% -15% 2.3% 2005 20% 10% 1.0% Avg return = 10.0% 3.5% Sum of squared deviations 1.75% Divide by n, where n = 2 13.23% Std deviation (take a square root) Sample SD (Excel) 13.23% COEFFICIENT OF VARIATION CV for Martin 4.39 CV for U.S. Water 0.26 PORTFOLIO EXPECTED RETURN
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08 Chapter model - 08 Chapter model 9:05 Chapter 8 Risk and...

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