6%20-%20Models%20of%20Equilibrium

6%20-%20Models%20of%20Equilibrium - BANK 3004 Portfolio and...

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BANK 3004 Portfolio and Fund Management Page 1 of 5 Topic 6 – Models of Equilibrium © H. Bassan, 2009 Topic Overview In Topic 5, we discussed modern portfolio theory (MPT), which is normative: the theory describes how investors should best select the composition of a risky portfolio. Now, we consider theories of asset pricing: models that explain security prices under conditions of market equilibrium. We learn about capital market theory which hypothesises how the aggregate of investors will behave (and how prices/returns at which markets will clear are set) rather than how they should behave in MPT. These capital market models provide the relevant measures of risk for any asset and the relationship between expected return and risk of any asset when markets are in equilibrium. Even though these models are derived from the theory about how portfolios should be constructed, they provide major implications for the characteristics of optimum portfolios. The models were developed to simplify and predict the correlation structure of returns to perform portfolio analysis, but they are also used for other purposes which are viewed to be as important. We first consider the single-index model (SIM) which specifies the process by which security returns are generated. SIM assumes that there is a common factor, F (a systematic risk component), that affects the returns of a risky asset. We assume that a broad index of securities acts as a proxy for the common macro factor that affects security returns. The SIM provides significant insights into the nature of systematic risk versus firm-specific risk. In addition, the model eases the computational burden for implementing the Markowitz process – but under simplifying assumptions. The capital asset pricing model (CAPM), developed independently by William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966), was the first standard form of general equilibrium for asset returns and is based on a stringent set of assumptions. This important model gives us a prediction of the relationship between the risk of an asset and its expected return. CAPM provides an evaluation of the prices of assets in the markets and serves as a benchmark against which to determine fair return performance. We proceed to extend the analysis of the index model to develop multifactor models and the arbitrage-pricing framework. Multifactor models of security returns measure the exposure to many economy wide factors such as business cycles and interest rates. The multifactor model gives a richer understanding about risk and its compensation than the SIM or CAPM. Stephen Ross (1976) proposed another approach to explaining security prices. The arbitrage-pricing theory (APT) rules out the possibility of arbitrage (riskless) profits; that is, the exploitation of mis-priced securities is ruled out. Arbitrage pricing theory (APT) uses a “no-arbitrage argument” to derive a simple expected return/risk relationship: it implies a multifactor security market line. APT is the derivation of equilibrium conditions given a pre-specified process for returns.
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This note was uploaded on 10/19/2011 for the course BANK 3004 taught by Professor Hb during the Three '10 term at South Australia.

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6%20-%20Models%20of%20Equilibrium - BANK 3004 Portfolio and...

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