Slide+10+-+MV+Efficiency,+Capm,+SML,+Factor+Models...

Slide+10+-+MV+Efficiency,+Capm,+SML,+Factor+Models... - M...

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Mean Variance Efficiency, CAPM, the SML, Factor Model and CCAPM By Diep Duong
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Outline Returns Expected Returns and Variances Portfolios, Mean-Variance Efficiency Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line CAPM The SML and the Cost of Capital: A Preview Factor Model and Regression A quick tour on Consumption based Asset Pricing Model
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Some Motivations In previous topics, we mostly talk about Present Value Model Basically, PV is an Pricing Problem, how to price assets in the market We mention about risk and return but in a informal way. Can we set things up formally ? Secondly, in economics, rationality is important. People optimize their own benefits. If you invest, then what is your decision rule (Strategy) if you are economically rational ?
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Financial Asset Return Financial Assets could be stock, bonds, futures,… Financial assets generate income and are traded in the markets The same rule - return is composed of two parts - Return due to Income (gain) - Return due to Capital Gain Another simple but important rule, at today time, - We know everything in the past (Certain) - We do not know anything about future (Uncertain) When things are uncertain or random, we work with Random Variable
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Asset Returns as Random Variables So we want to think of asset return to be a Random Variable. It’s random because of the uncertain states of our world Things become more complicated - What do we mean when you say you know Return of stock A in this case ? - If we describe a RV, we only can tell about all possibilities, or a distribution of it. Actually, in finance, practitioners often care about EXPECTATION and VARIANCE (The first two moments) of Asset Return
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Expected Returns Expected returns are based on the probabilities of possible outcomes In this context, “expected” means “average” if the process is repeated many times “Average” here does not necessarily means with equal weights. The weights sum up to 1. For Discrete RV or Continuous RV R of density is where ) ( ) ( : Outcome Continuous ) ( : Outcome Discrete 1 f dr r rf R E R p R E n i i i = = = = μ
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Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. What are the expected returns? State Probability C T Boom 0.3 15 25 Normal 0.5 10 20 Recession ??? 2 1 R C = .3(15) + .5(10) + .2(2) = 9.9% R T = .3(25) + .5(20) + .2(1) = 17.7%
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Variance and Standard Deviation Variance and standard deviation (square root of variance) measure the volatility of returns Using unequal probabilities for the entire range of possibilities Weighted average of squared deviations - = - = = dr r f R E r R E R p n i i i ) ( )) ( ( σ Outcome Continuous )) ( ( σ Outcome Discrete 2 2 1 2 2
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This note was uploaded on 07/01/2010 for the course ECON 393 taught by Professor D during the Spring '10 term at Rutgers.

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Slide+10+-+MV+Efficiency,+Capm,+SML,+Factor+Models... - M...

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