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Topic 10 lecture 1.docx

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Business Studies
Helen Lu

Topic 10- Risk, Return, Portfolios, Diversification and the CAPM Forward looking expected returns - Expected returns depend upon possible outcomes weighted by their probabilities Elements of the equation E(R A=Expected Return pi=probability of i RAirate of return This equation appears complicated but it is actually relatively straightforward In simple terms it is: EAR )= Probabili1y x Retur1 + Probability2x Return 2… Example to show this State Probability of state of Rate of return economy Boom 0.14 0.18 Normal 0.75 0.11 Recession 0.11 -0.06 What is the future expected rate of return? E(R A=Probability 1 Return +1Probability x 2eturn + P2obability x Re3urn 3 0.14 x 0.18 + 0.75 x 0.11 + 0.11 x -0.06 = 0.1011 0.1011 x 100 = 10.11 Another example to reinforce the point Suppose there are three possible future states of the world, and you have predicted the following returns for stocks BDA and CEC in these states. What are the expected returns on the stocks? State Probability BDA return CEC Return Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession 0.2 0.02 0.01 E(R BDA)=0.3 x 0.15 + 0.5 x 0.10 + 0.2 x 0.02 = 0.099 0.099 x 100 = 9.9% E(R CEC)=0.3 x 0.25 + 0.5 x 0.20 + 0.2 x 0.01 = 0.177 0.177 x 100 = 17.7% Variance and standard deviation in a simple model of states of the world Standard deviation=spread of returns about the expected return Standard deviation = square root of variance Remember variance is large Standard deviation squared = variance Again this formula looks difficult but when it is broken down it is actually quite straightforward 2 2 Var(R)  P 1
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