The Capital Asset Pricing Model (CAPM) is a very useful model and it is used widely in the industry even though it is based on very strong assumptions. Discuss in the light of recent developments in the area.

## Introduction

In finance, “a fundamental question asked, is how the risk of investment is going to impact its expected return” **(Perold, 2004).** Introduced and developed in the early 1960’s **(Fama and French, 2004)**, the Capital Asset Pricing Model (CAPM) demonstrates the link between the risk and return of an asset, in a reasonable equilibrium market. The aim of the CAPM formula is to assess whether a stock is valued fairly when considering risk and time value of money, compared to its expected return. In order to calculate the expected return of investment for an asset, given its risk, is illustrated through Image 1. Put simply:

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## Return = Risk free rate + Beta (Market Return – Risk free rate).

This essay plans to evaluate assumptions based on the CAPM, whilst discussing limitations faced by the model. It will consider how useful CAPM is, when the returns of an asset should earn, dependent on its risk. Whilst recognising the recent developments of this model, the essay will critically compare and discuss the models’ usefulness.

## History of CAPM

There was very little understanding of risk until as late as the 1960’s – whether in terms of theory or empirical evidence **(Perold, 2004**). Theories regarding investor’s risk preferences and decision-making under uncertainty only emerged in the 1940s/1950s, particularly through the work of von Neumann and Morgenstern.

In the 1950s, Harry Markowitz introduced the Modern Portfolio Theory (MPT), being among one of the first to discuss the relationship between risk and the rate of return **(Raei, 2011)**. “Harry Markowitz provided the first truly rigorous justification for selecting and diversifying a portfolio with the publication of his paper “Portfolio Selection”” **(Sullivan, 2006**). This theory argues that the characteristics of an investment’s risk and return shouldn’t be considered solely but should recognise the broad impact the investment has on the portfolio’s risk and return. The MPT assumes that investors are all risk averse, which means they will opt for the least risky asset when investing, given its level of return. This suggests that an investor will engage in more risky investments, with the expectation of a higher return.

## What is the Capital Asset Pricing Model?

Originally introduced by William Sharpe (1964), Jack Treynor (1962), John Lintner (1965) and Jan Mossin (1966), the Capital Asset Pricing Model builds upon concepts from the Modern Portfolio Theory, yet based on the concept that the price of an asset should not always be dependent on its risk. CAPM is a theoretical representation of the behaviour of financial markets, can be employed in estimating a company’s cost of equity capital **(Mullins, 1982). **The MPT demonstrates how rational investors should build a profitable portfolio regarding their risk-return preferences. Whereas, the CAPM includes a relationship, expanding on how assets should be priced in the capital market **(Diksha, n.d.)**. “CAPM holds that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat a theoretical required return, the investment should not be undertaken” **(Capital Asset pricing model, 2014). **

The graph below illustrates portfolio opportunities and explains the story of CAPM. The axis which runs horizontally across indicates portfolio risk which is measured by the standard deviation of portfolio return. The axis that’s vertical, illustrates the expected return. The *abc *curve (known as the minimum variance frontier) demonstrates the combination of expected return and the risk of assets which minimize return.

Source: (Fama & French, 2004)

## Assumptions of the Capital Asset Pricing Model

The CAPM is the basis for most of the recent works in capital market theory, asset pricing and finance. This model “postulates that under certain assumptions, there is a linear relationship between the return of an asset and its non-diversifiable risk” **(Francisco, 1987)****.**There are 4 main assumptions on which this model is based. The first being that investors are all risk averse, basing their investment portfolios entirely through expected returns and standard deviation of return, both measured during the same holding period. Another being the assumption of the “Perfect Capital Market”, where “all assets are infinitely divisible; there are no transactions costs, short selling restrictions or taxes; information is costless and available to everyone; and all investors can borrow and lend at the risk-free rate” **(Perold, 2004).** A further assumption on which the model is based, is that all investors have equal access to the same investment opportunities. And the final assumption is that investors make the same estimates of individual asset expected returns, standard deviations of return as well as the correlations among asset returns.

## Limitations/Flaws of the Capital Asset Pricing Model

The capital asset pricing model is often faulted as a result of the basis of its assumptions. Although the CAPM is widely used as it measures the expected rate of return of a security and relates it to expected risk, however, the empirical evidence shows that it is “poor enough to invalidate the way it is used in applications” **(Fama & French, 2004)**. It can be said, the reason for this, is that the Capital Asset Pricing Model was developed at a time when “the theoretical foundations of decision making under uncertainty were relatively new and when basic empirical facts about risk and return in the capital markets were not yet known” **(Perold, 2004). **The fact that the model assumes the capital market is going to be perfect is unreasonable and is evident the capital markets aren’t perfect.

## Recent Developments of the Capital Asset Pricing Model

Since being introduced, many researchers have decided to extend and develop the standard Capital Asset Pricing Model since the 1960s. Asset pricing models have evolved considerably with the aim of improving its realism.

## Three Factor Model

“One critical assumption in CAPM is the risk premium estimation, the residual between the market return and the risk-free interest rate” (Gustafsson and Gustavsson, 2019). The Three-Factor Model was developed and proposed by Fama and French in response to accumulating empirical evidence that the CAPM performed poorly in explaining realised returns **(Gaunt, 2004)**. When developing the standard CAPM, Fama and French added two factors in the aim of better explaining the returns of the portfolio, including market capitalisation and book-to-market value. In 1995, they identified a covariance between the company’s book-to-market ratio and size, in the aim of measuring the return of the stock. After testing the Three Factor Model empirically, it was confirmed that this model had higher explanatory power than the one factor CAPM **(Gaunt, 2004).** This means that the main advantage of this model is that it includes the size and value of the firm, and the market risk factor used in the CAPM.

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## Five Factor Model

After developing the three-factor model, Fama and French went on to further expand on this theory, introducing the Five-Factor model. This model was directed at not only taking into consideration the size and value of the firm, and the market risk factor – but it also considers the profitability of the stocks, and the investment patterns in average stock returns **(Fama and French, 2014). **The empirical tests of the five-factor model aim to explain average returns on portfolios formed to produce large spreads in size, profitability and investment **(Musarurwa, 2019)**. “With the addition of profitability and investment factors, the value of the previous three-factor model becomes redundant” **(Fama and French, 2015)**.

## Arbitrage Pricing Theory (APT)

Like CAPM, this theory gives investors an estimated required rate of return on portfolios which are of risk. The Arbitrage Pricing Theory aims to reduce the limitations of the one-factor CAPM, with the understanding that different stocks will have alternative sensitivities to different market factors. The APT bases its assumption on the fact that an asset is dependent on numerous macroeconomic factors, i.e. inflation, exchange rates, market indices, changes in interest rates and market sentiments (Bulaki, **2019**), to name a few. Simply, not all assets or stocks can be expected to react to a specific and same parameter all the time, thus the requirement to consider the multifactor and sensitivities.

## Zero-Beta CAPM

Developed by Black in 1972, the Zero-Beta CAPM showed that the results from CAPM do not require a risk-free asset which has returns constantly in every state of nature. A zero-beta portfolio is one which is built without systematic risk. The zero-beta CAPM implies that beta is still the correct measure of systematic risk, and that the model still has a linear specification. This means that the value of the portfolio doesn’t fluctuate with market movements. Without systematic risk in a zero-beta portfolio, the return is the same as the risk-free rate. Thus, the return on a portfolio with zero-beta is going to be low, and without the volatility of the market exposed, it does not allow the portfolio to benefit from potential upswings in value of the overall market **(InvestingAnswers, 2009)****.**

## Inter-Temporal CAPM

Derived from Merton (1973), ICAPM focuses on relaxing the single time period assumption from the standard CAPM. It is said that investors who use ICAPM are only concerned with the end-of-period payoff, as well as the chance to consume or invest this payoff., whereas investors of the standard CAPM would be interested about the wealth of their assets at the end of the current period (Elbannan, 2015). With the Inter-temporal CAPM, there is the assumption of a perfect market; no costs or taxes, all assets have limited liability, investors believe their decision has no impact on the market price and the market is always in an equilibrium etc. It’s evident that the ICAPM extends the CAPM to a more dynamic environment, where the results almost mirror that of the APT. The difference between ICAPM and APT, however, is that the ICAPM has the ability to determine risks from characteristics of the assets **(Krause, 2001).**

## Downside CAPM (Downside BETA)

Downside BETA, or Downside-CAPM is another extension from the CAPM. This concept dates back to as Beta is used within the standard CAPM as a way of calculating the expected return of an asset. Downside beta is a way to measure the downside risk of an asset, the risk associated with loss **(Pedersen & Hwang, 2007).** Investors may try and consider constructing their portfolios by minimising the downside beta. The reason for this is to ensure they can maintain the value in times of market decline.

## Revised CAPM

This model is a further development of the standard Capital Asset Pricing Model, which includes financial, operational and economic leverages. In order to achieve a more accurate prediction of return, it focuses on systematic and unsystematic risk, including historical and estimating data completely** (Roodposhti & Amirhosseini, 2009**). When testing this model, they compared R-CAPM with the traditional CAPM, Downside CAPM and the Adjusted-CAPM, and found that there was a meaningful difference between the measures of expected return for R-CAPM and the alternative CAPMs.

## Consumption CAPM (Co-CAPM)

Founded by Robert Lucas (1978) and Douglas Breeden (1979), the Consumption CAPM is an additional extension of the standard CAPM. “Co-CAPM quantity market risk is measured by movement of the premium with consumption growth. Thus, the Co-CAPM explains how much the entire stock market changes related to the consumption growth” **(Raei, 2011). **This model is argued to be the best theoretical model, however the basic link between consumption and stock returns assumed by the Co-CAPM cannot hold. The Co-CAPM is used more from an academic perspective as it covers many forms of wealth, beyond stock market wealth, providing an understanding of variation in returns over a number of periods.

## Reward CAPM (Reward-BETA)

It was stated by Graham Bornholt in 2006, that investors require a better methodology in order to estimate the expected returns within the stock market. With this in mind, he developed the Reward-BETA CAPM. This model is based on assumptions which are consistent with the Arbitrage Theory; dividing returns of stocks into two parts: expected and unexpected stock returns.

## Conclusion

The purpose of this essay was to discuss the extent to which the Capital Asset Pricing Model is useful in light of recent developments in the area. The CAPM is the basis of all recent developments, and although very simple, is a fundamental contribution to the understanding of the determinants of asset prices **(Perold, 2004). **Recent developments from this model have proved to be more intricate and complex, solving issues which were raised regarding the simplicity of the CAPM, allowing ease when comparing investment alternatives. Although there have been various criticisms of the standard CAPM, without it, the other extensions from it would not exist.

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