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# AG RISK ANALYDEC MAK AEB 6182

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This 4 page Class Notes was uploaded by Weldon Rau I on Friday September 18, 2015. The Class Notes belongs to AEB 6182 at University of Florida taught by Charles Moss in Fall. Since its upload, it has received 22 views. For similar materials see /class/206591/aeb-6182-university-of-florida in Agricultural Economics And Business at University of Florida.

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Date Created: 09/18/15

AEB 6182 Lecture XII Professor Charles Moss The Capital Asset Pricing Model Lecture XII Literature A Most of today s materials comes from Eugene F Fama and Merton H Miller The Theory of F inance Hinsdale Illinois Dryden Press 1972 Chapter 7 The primary literature is 1 Lintner John Security Prices Risk and Maximal Gain from Diversification Journal ofFiriance 20Dec 1965 587615 2 Lintner John The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets Review of Economics and Statistics 47Feb 1965 1337 3 Mossin Jan Equilibrium in a Capital Asset Market Econometrica 34Oct 1966 76883 4 Sharpe W F Capital Asset Prices A Theory of Market Equilibrium under Conditions of Risk Journal ofFinance 19Sept 1964 42542 Setting Up the Market A Perfect Markets We assume that all markets are competitive for goods and p31 0 investments 1 All goods and investments are infinitely divisible 2 Information is costless 3 There are no transaction costs 4 No individual is large enough to effect the price Firms All goods are produced by firms These firms purchase the factors of production in the rst period produce output and market their goods in the second period In addition these firms do not have any capital of their own and must raise this capital by issuing stock Consumers Consumers begin with an endowment w The consumer s choice problem initially is twofold 1 First the consumer must decide how much to consume in this period c1 and how much to invest h This investment will earn a rate of return h11Ri which will be consumed in the second period c2 2 Second the consumer must decide how to invest h1 that is how to divide it up between a wide array of assets In general this implies two decision dimensions The rst is intertemporal across time In this decision the consumer has a time preference the preference between consuming now and consuming later AEB 6182 Lecture XII Professor Charles Moss 02 U c c lt11r 1 2 cl The second is the risk or uncertainty on the investment Both of these questions can be represented in the utility function U Market Equilibrium Assuming that rms supply investment and consumers demand investment opportunities we hypothesize that there exists an equilibrium where the supply of stocks equals the demand of stocks 111 Risk Equilibrium From the Consumer s Point of View A At the outset we assume that consumers are risk averse and that risk can be characterized using the normal distribution function 1 N Given these assumptions we can use the Expected ValueVariance or in this case the Expected ValueStandard Deviation approach to expected utilityrisk efficiency N M 2M 11 where up is the expected retum from the portfolio M is the expected return on a specific asset and xi is the level of asset I held in a specific portfolio Similarly the standard deviation of the portfolio can be written as a 11 11 4 where SP is the standard deviation of a particular portfolio and 61139 is the covariance between asset i and asset j In addition we impose a portfolio balance condition N Z 9 11 We can reformulate the risk measure standard deviation of the portfolio to analyze the contribution of each asset to the overall risk of the portfolio AEB 6182 Lecture XII Professor Charles Moss The risk of a particular asset Xj is then dependent on weighted covariances between asset j and the returns in the rest of the portfolio Remember that the X18 are weights in the general portfolio This raises two points a First note that the risk of an individual asset depends on the portfolio weights and the risk of the portfolio b Second the risk of a particular asset depends both on its own variance and the variance of the remaining assets in the portfolio Thus as the number of assets becomes large and the portfolio becomes well diversified the risk of a particular asset is more dependent on the covariance with other assets in the portfolio than on its own risk B Following our previous discussions of Expected ValueVariance frontier we assume that consumers choose the portfolio that minimizes risk for any given level of expected income However in this case risk is parameterized by the standard deviation instead of the variance 1 Mathematically N N min a 22am u L In Lagrange form this becomes Lopau uihzl 2 11 3L 60p 1 1 0 16 16 llle 2 6L N 0 all up gm aL N 1 0 ax

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