Capital Asset Pricing Model and Arbitrage Pricing Essay

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Capital Asset Pricing Model and Arbitrage Pricing Theory:

Capital Asset Pricing Model (CAPM) is an arithmetical theory that describes the relationship between risk and return in a balanced market. The Capital Assets Pricing Model was autonomously and simultaneously developed by William Sharpe, Jan Mossin, and John Litner. The researches of these founders were published in three different and highly respected journal articles between 1964 and 1966. Since its inception, the model has been used in various applications that range from public utility rates to corporate capital budgeting. However, the initial introduction of the model was characterized by suspicious view from the investment community. This was largely because CAPM apparently indicated that professional investment management was hugely a waste of time. Due to its implementation problems and shortcomings associated with its relation to Arbitrage Pricing Theory, Capital Asset Pricing Model has continued to face constant academic attacks.

Overview of Capital Asset Pricing Model:

Since its introduction, the Capital Asset Pricing Model offers a huge portion of the justification for the tendency toward reactive investing in large index mutual funds (Cooper and Cousins, n.d.). After the initial suspicious view of CAPM, investment professionals changed their perspective nearly a decade later to view the model as a vital tool that assist investors to understand risk. Actually, the development of this model not only resulted in the birth of asset pricing theory but it has also been widely used in various applications like calculating capital costs for companies and analyzing the performance of managed portfolios.

This is because the Capital Asset Pricing Model consists of a key element that separates the risk affecting an asset's return into two main classifications i.e. company-specific or unsystematic risk and systematic or general economic risk. Unlike the systematic risk that occurs because of the general economic uncertainty, the long-term average returns for company-specific or unsystematic risk should be zero. According to this model, the return on assets should averagely equal the yield on a risk-free bond within a given period of time. This should also include a premium that is proportional to the amount of systemic risk that the stock contains. Generally, the Capital Assets Pricing Model refines the concepts of systematic and unsystematic risks that were developed in 1950s by Harry M. Markowitz.

In Markowitz model that is commonly known as the mean-variance model, an investor chooses a portfolio at a time (t -- 1) that results in a stochastic return at t. This is based on the assumption that investors are risk reluctant and only care about the mean and variance of their investment return when selecting their portfolio. Consequently, these investors select portfolios that are mean-variance efficient on the basis that the portfolios lessen the variance of their return, given the probable return and lessen this return, given variance (Fama & French, 2004).

The Capital Asset Pricing Model refines the algebraic statement in Markowitz's mean-variance model into a testable prediction regarding the link between risk and probable return. The model turns the initial approach through identifying a portfolio that must be effective for asset prices to clear each asset market.

Consequently, the model states that the risk associated with an asset is calculated in relationships to the risk of the entire market, which is expressed either as correlation to the market average or as the stock's beta. The concept of the Capital Asset Pricing Model is that it hypothesizes a simple linear relationship between the anticipated return and the market risk of a security (Banz, 1981). Since this model provides powerful and spontaneously enjoyable predictions on how to calculate risk and its relationship with expected return, it's an attractive concept, which is the core of investment courses.

Analysis of the Capital Asset Pricing Model:

In order to achieve the equilibrium of the Capital Asset Pricing Model, there are various assumptions that must be defined including the need for investors to capitalize on the expected utility of wealth. The other assumptions are the existence of many investors who behave competitively, lack of taxes and commissions, investors' equal access to all securities, frictionless markets, and investors' use of similar input lists because of uniform expectations. Based on these assumptions, the Capital Asset Pricing Model can be developed and the prevailing equilibrium achieved. Furthermore, the achievement of the CAPM equilibrium based on the defined assumptions results in other elements.

First, all investors will select an optimal market portfolio, M, that incorporates every asset in the economy because all assets are evaluated in the portfolio in proportion to their weight in the economy. Given that all investors use similar input lists and have the same expectations, they are likely to select an identical risky portfolio i.e. The one on the efficient frontier within the tangency line drawn from the risk-free asset (Taylor, 2005). Consequently, the demand of any asset left outside the portfolio would be zero and its price would also approach zero. Once investors note this, they will adjust their portfolios to include this asset until its price reflects its amount or level of risk resulting in inclusion of all assets in M.

Secondly, as the market portfolio, M, is within the efficient frontier and is the tangent to the risk-free asset, it includes all information regarding assets in the market that makes it an efficient portfolio. As a result, every investor will select to distribute his/her wealth between the efficient portfolio, M, and the risk-free asset.

The third element regarding the achievement of CAPM equilibrium is that the market portfolio's risk premium will be relative to its own risk and the risk aversion degree of the average investor. Therefore, every investor selects a proportion, b to invest in the efficient portfolio, M and another fraction 1-b to spend in the risk-free asset. This leads to the next element with which the risk premium on each asset is proportional market portfolio's risk premium and the beta coefficient of the market portfolio's asset.

Arbitrage Pricing Theory:

As a single-period model, Arbitrage Pricing Theory is a model where all investors believes that stochastic returns of capital assets are steady with a factor structure (Huberman & Wang, 2005). The theory is based on the concept that the returns of an asset can be predicted through the relationship between that asset and other common risk factors. Generally, the Arbitrage Pricing Theory was developed as an alternative tool of computing the expected returns on stock. Ross, who primarily developed this theory, states that the probable returns on assets are almost linearly associated with factor loadings if the equilibrium prices don't provide arbitrage opportunities beyond the static portfolios of the assets.

Based on this argument, the Arbitrage Pricing Theory is based on the anticipation of arbitrage. According to Ross' formal proof, the linear pricing relation is an essential condition for equilibrium in a market with which agents maximize specific types of utility. The linear relation between the expected returns and the betas is identical to the determination of the stochastic discount factor.

As an alternative to the Capital Asset Pricing Model, the Arbitrage Pricing Theory emphasizes on the linear relation between the expected returns of assets and their covariance with several random variables. In this case, the covariance is understood as the amount of risk which investors cannot avoid through diversification. Moreover, the slope coefficient in this linear relationship and the covariance are understood as risk premiums.

Overview and Analysis of Arbitrage Pricing Theory:

As previously mentioned, the Arbitrage Pricing Theory is a substitute model that is used to measure equilibrium expected returns on financial assets. As suggested by its name, this theory rests on the concept that financial markets that are operating effectively should be arbitrage-free. Through the use of a factor model of returns of an asset, the concept implies limitations on the relations between the asset returns while generating an equilibrium pricing relationship. Since every stock is sensitive to all factors, the determination of expected returns through the notion of returns on stock requires the common set of factors to be mutually consistent.

An arbitrage strategy that can occur in two major ways is used to help in understanding the need for the factors to be mutually consistent. First, the arbitrage strategy may involve investment in both the buying and selling assets that generate an instant positive cash inflow and a guaranteed profit in the future. An investor who could pay more or less wealth may attempt investing on an infinite scale when faced by an investment strategy that is based on this pay-off structure. Secondly, an arbitrage strategy may be an investment plan that is currently costless though it guarantees positive returns in the future. Sensible investors will take advantage of the likelihood of investing as much as possible in this strategy since it's similar to obtaining something from nothing ("Chapter 3 -- The Arbitrage Pricing Theory," n.d.).

Therefore, the underlying principle behind the Arbitrage Pricing Theory is that investment situations like those described above shouldn't be allowed in financial markets that are functioning well. As a result, if the…

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