Portfolio Return and Risk
State of Economy Prob. Return on A Return on B Portfolio Return
1 0.20 19% 4.6% ?5% 2 0.60 10% 10% 10% 3 0.20 35% 19.4% ?4% ~ 12% 9% 10.8% ER
??~E?RP??0.2?4.6%?0.6?10%?0.2?19.4%?10.8%
~~?AE?RA???BE?RB??0.6*12%+0.4*9%=10.8%
Portfolio return is a weighted average of security returns
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Portfolio Return and Risk
State of Probability Deviation Squared Probability ? Economy from mean Deviation Squared Deviation
1 0.20 0.0007688 ?6.2% 0.003844 2 0.60 0.0000384 ?0.8% 0.000064 3 0.20 8.6% 0.007396 0.0014792
~~??RP??0.0022864 and ??RP??4.78%
2
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Portfolio Return and Risk
~~??RA??0.0166 and ??RA??12.88%2
~~??RB??0.00544 and ??RB??7.38%2~~?A??RA???B??RB??0.6*12.88%+0.4*7.38%=10.68%
The standard deviation of returns on a portfolio is less than a weighted average of constituent security standard deviation!
~~(If RA and RB are less than perfectly positively correlated)
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Covariance and Correlation Coefficient
? Covariance: A measure of how two securities’ returns move together and the size of those co-movements
~~~~ covRA,RB?ERAi?ERARBi?ERB
State of Economy Prob.
1 2 3
Deviation Deviation from mean: A from mean: B 0.20 10% ?17% 0.60 1% ?2% 0.20 23% ?13%
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??????????~~???iRAi?ERARBi?ERBn?????i?1???
Covariance term ?0.00340 ?0.00012 ?0.00598 ?0.00950
~~cov?RA,RB?
