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In mathematical finance, multiple factor models are asset pricing models that can be used to estimate the discount rate for the valuation of financial assets; they may in turn be used to manage portfolio risk.
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data. In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
Mean-variance efficiency of the market portfolio is equivalent to the CAPM equation holding. This statement is a mathematical fact, requiring no model assumptions. Given a proxy for the market portfolio, testing the CAPM equation is equivalent to testing mean-variance efficiency of the portfolio.
The Fama–MacBeth regression is a method used to estimate parameters for asset pricing models such as the capital asset pricing model (CAPM). The method estimates the betas and risk premia for any risk factors that are expected to determine asset prices.
The security could be any asset, such as stocks, bonds, or derivatives. The theoretical return is predicted by a market model, most commonly the capital asset pricing model (CAPM). The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses beta as a multiplier.
[10] [11] The CAPM, for example, can be derived by linking risk aversion to overall market return, and restating for price. [9] Black-Scholes can be derived by attaching a binomial probability to each of numerous possible spot-prices (i.e. states) and then rearranging for the terms in its formula. See Financial economics § Uncertainty.
The CAPM can be derived from the following special cases of the CCAPM: (1) a two-period model with quadratic utility, (2) two-periods, exponential utility, and normally-distributed returns, (3) infinite-periods, quadratic utility, and stochastic independence across time, (4) infinite periods and log utility, and (5) a first-order approximation ...
In practice, a linear combination of observed factors included in a linear asset pricing model (for example, the Fama–French three-factor model) proxy for a linear combination of unobserved risk factors if financial market efficiency is assumed. In the Intertemporal CAPM, non-market factors proxy for changes in the investment opportunity set. [3]