Unformatted text preview: d returns are based on the probabilities of possible outcomes
In this context, “expected” means average if the process is repeated many times
E(R) = Σ Pi Ri Expected Returns
Expected Returns Individual risky asset Expected returns are based on the probabilities of possible outcomes
In this context, “expected” means average if the process is repeated many times
The “expected” return does not even have to be a possible return n
E ( R ) = ∑ pi Ri
i =1 Example: Expected Returns
Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?
State Boom > Normal
0.20 Recession > Probability
0.3 > 0.5 C
0.15 0.2 0.02 0.10 T
0.25
0.01 RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.9%
RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7% Variance and Standard Deviation
Variance and Standard Deviation Variance and standard deviation still measure the volatility of returns
Using unequal probabilities for the entire range of possibilities
Weighted average of squared deviations
n σ 2 = ∑ pi ( Ri − E ( R)) 2
i =1 Example: Variance and Standard Example: Variance and Standard Deviation Consider the previous example. What are the variance and standard deviation for each stock?
Stock C σ2 = .3(.15.099)2 + .5(.1.099)2 + .2(.02.099)2 = .002029 σ = .045 Stock T ...
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 Winter '14
 Standard Deviation, Capital Asset Pricing Model, Modern portfolio theory, KEi, DCLK

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