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Unformatted text preview: Chapter 10 Risk and Return Expected Return, Variance and Covariance • In Chapter 9 we used historical data to estimate the relationship governing security returns • Ultimately we are interested in the probability distribution governing these returns looking forward • The key components of this distribution are 1. Expected return – a measure of the “average” return 2. Variance – a measure of variability in returns 3. Covariance – a measure of how much two returns move together Example Definition of expected return: Definition of variance: Note: When calculating variance, better to use decimals rather than percentages Rate of Return Scenario Probability Stock fund Bond fund Recession 33.3%7% 14% Normal 33.3% 12% 1% Boom 33.3% 28% 3% p(s)r(s) N 1 = s = E(r) ∑ ] 2 E(r) s [r s p N 1 = s = 2 ) ( ) ( ∑ σ We will derive the following table Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession7% 0.0324 14% 0.0064 Normal 12% 0.0001 1% 0.0025 Boom 28% 0.0289 3% 0.0009 Expected return 11.00% 6.00% Variance 0.0205 0.0033 Standard Deviation 14.3% 5.7% Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession7% 0.0324 14% 0.0064 Normal 12% 0.0001 1% 0.0025 Boom 28% 0.0289 3% 0.0009 Expected return 11.00% 6.00% Variance 0.0205 0.0033 Standard Deviation 14.3% 5.7% % 11 ) ( %) 28 ( 3 1 %) 12 ( 3 1 %) 7 ( 3 1 ) ( = × + × + × = S S r E r E Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession7% 0.0324 14% 0.0064 Normal 12% 0.0001 1% 0.0025 Boom 28% 0.0289 3% 0.0009 Expected return 11.00% 6.00% Variance 0.0205 0.0033 Standard Deviation 14.3% 5.7% % 00 . 6 ) ( %) 3 ( 3 1 %) 1 ( 3 1 %) 14 ( 3 1 ) ( = × + × + × = B B r E r E Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession7% 0.0324 14% 0.0064 Normal 12% 0.0001 1% 0.0025 Boom 28% 0.0289 3% 0.0009 Expected return 11.00% 6.00% Variance 0.0205 0.0033 Standard Deviation 14.3% 5.7% 0324 . ) 11 . 07 . ( 2 = Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession7% 0.0324 14% 0.0064 Normal 12% 0.0001 1% 0.0025 Boom 28% 0.0289 3% 0.0009 Expected return 11.00% 6.00% Variance 0.0205 0.0033 Standard Deviation 14.3% 5.7% .0205 = (1/3 x .0324) + (1/3 x .0001) + (1/3 x .0289) Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession7% 0.0324 14% 0.0064 Normal 12% 0.0001 1% 0.0025 Boom 28% 0.0289 3% 0.0009 Expected return 11.00% 6.00% Variance 0.0205 0.0033 Standard Deviation 14.3% 5.7% 0205 . 143 . % 3 . 14 = = Covariance Would like to measure how much assets move together Consider the following product: [rstock(s)E(rstock)][rbonds(s)E(rbonds)] When both returns above or below expected value, product is positive....
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This note was uploaded on 10/17/2011 for the course ECON 101 taught by Professor Thompson during the Spring '11 term at Michigan State University.
 Spring '11
 Thompson

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