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Unformatted text preview: General Properties of Asset Pricing Models We are interested in pricing assets. Assets are either &nancial securities or actual means of production (e.g. land, machines) that people buy in order to earn a pro&t. The form of pro&t that we will analyze is called a return, and is generally de&ned as the pro&t earned on an asset divided by the original price of the asset. We want to explain the fact that some assets earn high returns and others earn negative returns. We want to be able to write down an equation that says E ( r j ) = f ( x j ) , where E ( & ) is the expectations operator, r j is the return on asset j , and x j is a vector of characteristics of asset j . To &gure out which asset characteristics should matter and which function of characteristics makes the most sense, we make up asset pricing models. In this section we describe a generic asset pricing model. It turns out that all asset pricing models can be described as special cases of one single equation. In general, we want a way to describe the expected return for any asset. The equation we discuss in this section describes expected returns. Y. F. Chow (CUHK) Financial Economics 2009¡10 First Term 1 / 56 Stochastic Discount Factor (SDF) Model: E( RM ) = 1 The stochastic discount factor (SDF) model is rapidly emerging as the most general and convenient way to price assets. Most existing asset pricing methods can be shown to be particular versions of the SDF model. This includes the capital asset pricing model (CAPM) of Sharpe (1964), Lintner (1965) and Black (1972), the general equilibrium consumptionbased intertemporal capital asset pricing model (CCAPM) of Rubinstein (1976) and Lucas (1978), and even the Black&Scholes theorem for pricing options. A detailed analysis of the SDF model may be found in the book by Cochrane (2000), and in the surveys by Ferson (1995) and Campbell (1999). Y. F. Chow (CUHK) Financial Economics 2009&10 First Term 2 / 56 The SDF model is based on a very simple proposition. The price of an asset is the expected discounted value of the asset&s payo/ in the end of the period: P j = E ( X j M ) where P j = the price of the asset j at the beginning of the period, X j = the payo/ of the asset j at the end of the period, M = the discount factor for the period (0 & M & 1), and E ( ¡ ) = the expectation operator. The discount factor is sometimes called the pricing kernel and will be a stochastic variable. This equation can also be written in terms of the asset&s gross return R j = X j / P j = 1 + r j : 1 = E ( R j M ) (1) for j = 1 , 2 , . . . , N . Gross returns can be de¡ned either in nominal or real terms; correspondingly, the discount factor must then also be expressed in nominal or real terms. Notice that while R j is an assetspeci¡c quantity, a single pricing kernel works for all assets....
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 Spring '09
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 Capital Asset Pricing Model, The Land, F. Chow, Y. F. Chow

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