Estimating Financial Risks Through the Capital Asset Pricing Model

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Table of Contents

Framework
Assumptions
Criticisms
CAPM In Comparison With Alternative Models
Conclusion
References

The capital asset pricing model (CAPM) is normally used to determine the rate of asset return if securities are invested in a group of already determined market portfolios (OECD – Organisation for Economic Co-operation and Development 2004, p. 189).

This model often considers the fact that there is always the occurrence of a non-divestible risk and a theoretical risk-free asset which has different implications when its return is to be comprehensively estimated (Contingency Analysis 1996).

Generally, the capital asset pricing model is widely used to describe the relationship between risks and their expected levels of return, considering the fact that the investments to be made have a financial risk attributed to them (Mergner 2010, p. 124).

However, the main idea behind the capital asset pricing model is that investors need to obtain returns based on two investment criteria: money and risk. Contingency Analysis (1996) explains this idea by stating that:

“The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk” (p. 3).

Normally, to get the best outcome from the model (factoring in the above argument), we calculate a risk measure (beta), which will factor in the estimated returns that the market will offer for the investment, viz a viz the market premium (Frangos 2010, p. 488). Investopedia ULC (2011) explains that:

“The CAPM says 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 the required return, then the investment should not be undertaken” (p. 3).

The CAPM model traces its roots to the sixties when it was introduced by William Sharpe and his colleagues (French 2003). The concept was developed from previous works done on Harry Markowitz’s study concerning diversification and modern portfolio theory, which ultimately won a Nobel memorial prize in economics for its contribution to the noble field of financial economics (Banerjee 1990).

The main motivation for the pioneers of the model was to develop a formula which could predict the reward-to-risk-ratio based on the market potential of where a risk is to be invested. This means that if the rate of return for a particular asset is reduced because of one or more coefficients attributed to an asset, the reward-to-risk ratio potential existing in the market can be equated to the return that the market poses as a result.

Consequently, this means that the market reward-to-risk ratio can be equated to the market risk premium and if the above analysis is rearranged to develop an appropriate relationship between market risk and returns of a particular investment, we ultimately come up with the capital asset pricing model (French 2003, p.1).

This study will further explore the intrigues of the CAPM model with a special emphasis on its assumptions, criticism and comparative models that explain the same content. Comprehensively, we will then be able to establish if the concept of the model that encourages investors to borrow money from a risk-free investment and invest it in various market portfolios, is correct or not.

To achieve this goal, the first part of this study provides a thorough analysis into CAPM model to gain a better conceptual understanding of how the model works. In the second part of the literature, this study encompasses the assumptions behind the model.

The third section of the study analyzes the criticisms behind the model and the final part of the study analyzes the alternative asset pricing models (including any areas of conflict or difference with the CAPM model).

Framework

The basic motivation for investors, as proposed by the CAPM model is to borrow money from risk-free assets and invest in the relevant market portfolio. To make this concept a reality, CAPM decomposes portfolio risk into two types of risk: systematic and specific risk, but as the market moves, each asset criterion becomes immune to the effects of the market (Blyth 2007, p. 29).

Considering, various assets are invested in markets where such movements are evident; the occurrence of systematic risk is inevitable. Nonetheless, when referring to specific risk, the unique risk attributed to a given security is often in consideration (Lhabitant 2004, p. 70).

This means that specific risks do not affect any assets, except a few. In other words, this fact simply refers to the component of asset risk that is independent from the movement of the market (Ogilvie 2007).

These definitions abound, the CAPM model establishes the fact that, investors will be compensated for taking risks which are not specific to the asset, but rather, for market risks, which are applicable to a variety of assets (Claessens 1993, p. 11). In other words, investors are rewarded for taking specific risks and not systematic risks (Das 1993, 295).

The reasoning behind this concept is attributed to the fact that specific risks are subject to diversification as is explained by Contingency Analysis (1996) which states that:

“When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor’s net exposure is just the systematic risk of the market portfolio” (p. 7). Examples of systematic risks that cannot be diversified include interest rates, wars and such like risks (Hebner 2006, p. 142).

The fact that specific risks can be diversified away is supported by the modern portfolio category (Vault 2004, p. 174). However, the major shortcoming associated with diversification is that the problem of systematic risk cannot be eliminated forever (Pahl 2009, p. 18).

From this point of view, it is also important to establish that most investors are usually disturbed by the potential systematic risk can have on their investments (Contingency Analysis 1996). Certainly, this is the framework which the CAPM model was developed from (to quantify systematic risks).

According to the CAPM model, systematic risks can easily be quantified using beta, and still, according to the model, stock is the same as the risk free rate and the market portfolio’s potential summed together (Hebner 2006, p. 28). In other words, Sharpe decided to focus on the shift in stock prices (stock volatility) as opposed to the movement of stock, per se. McClure (2011) explain that:

“If a share price moves exactly in line with the market, then the stock’s beta is 1. A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15% if the market fell by 10%” (p. 4).

Beta simply refers to the movement in share price returns when compared to the potential that the market poses, with regards to the same price returns, within the same time-frame of analysis. Based on empirical studies done by several financial consultants in the 70s, it was established that there exists a linear relationship between the financial returns of stock portfolios and their beta. McClure (2011) further explains that:

“What this shows, is that a riskier investment should earn a premium over the risk-free rate – the amount over the risk-free rate is calculated by the equity market premium multiplied by its beta. In other words, it’s possible, by knowing the individual parts of the CAPM, to gauge if or not the current price of a stock is consistent with its likely return – that is, if or not the investment is a bargain or too expensive”(p. 8).

The product of this relationship is therefore to be multiplied by the expected excess return of the market to give a resultant product which is the expectation of investing in the market portfolio.

In different way, McClure (2011) explains that “Stated another way, the stock’s excess expected return over the risk-free rate equals its beta times the market’s expected excess return over the risk free rate” (p. 9).

For instance, if a given asset has a systematic risk of 0.8; the market has the potential of giving an expected return of 12%; and the risk free rate is estimated at 2%, the asset will be expected to have an annual expected return of 10%.

This conclusion is obtained considering the fact that a market portfolio’s expected return is ultimately determined by systematic risk as opposed to the volatility of the market portfolio (Strong 2008). In other words, it can be said that, the expected returns of an investment in a given market portfolio will ultimately be determined by systematic risk as opposed to the total risk in the market portfolio (Ogilvie 2006, p. 176).

The CAPM model relies on this concept because the model was developed under the impression that all investors will agree on systematic risks, as well as the returns expected on the asset (Kapil 2010). However, it is often mentioned that such an assumption is largely unrealistic and therefore, this model is nothing more than a theoretical concept of asset return estimation.

Assumptions

Considering CAPM was developed from Markowitz’s mean-variance model, it is difficult to separate the shortcomings of the Markowitz model from the CAPM. Some of the shortcomings of the CAPM can therefore be largely assumed to lay the groundwork for the criticism of the CAPM model (Elton 2009, p. 282).

One well-known assumption of the CAPM is the fact that it assumes that all investors are risk averse and that they only pursue their investments with the sole aim of accumulating wealth (Brigham 2010, 939). This assumption is the reason why the CAPM model includes the single-time horizon for all its investors, even though this case may not necessarily be true.

The CAPM model also assumes that the market is perfect – an attribute which is impractical in the real business environment (Kürschner 2008, p. 6). With such an assumption in effect, the CAPM model assumes that certain independent variables in the real market environment, such as taxes, inflation and certain transaction costs are invisible.

The CAPM also assumes that, investors and lenders operate in a market characterised by infinity, based on the concept that at a market-free rate, investors can borrow limitlessly and lenders can lend in the same manner. This is obviously not possible because the framework which the CAPM operates does not support abundance.

In other words, the principle of economics and finances exists in a framework of limited resources and therefore, players work towards maximizing their values, viz-a-viz limited resources. Money is one such resource and therefore in the real world, money is not in unlimited abundance.

The CAPM also assumes that all assets can be easily liquidated and divided into various market portfolios (Quant Risk Group 2008). This assumption is misguided because certain assets are not easily divisible, assuming demand and supply forces are still in play in the real market environment. For instance, it is difficult to liquidate certain stocks when there are no willing sellers.

In such a situation, such stocks would be highly costly, thereby posing a challenge to their liquidation. The same scenario is also evidenced in the divisibility of assets because so long as it is difficult to liquidate an asset, it is also increasingly difficult to divide the same. In certain situations, certain assets are almost impossible to divide or liquidate because of artificial financial obstacles such as trade restrictions of prohibitive taxes.

The CAPM also assumes that the expectation of investors is the same, and that is to maximize their returns, simply by overcoming market risks (Dreman 1998). Quant Risk Group (2008) explains this assumption by stating that: “CAPM assumes that all investors agree about mean and variance as the only system of market assessment, thus everyone perceives identical opportunity.

The information is costless, and all investors receive the same information simultaneously” (p. 9). In the real world, this assumption is misguided because not all investors have the same expectations on their returns. For instance, charitable organizations, religious organizations, governments and certain non-governmental organizations do not bear the same objective of maximizing profits.

Such organizations may on the contrary be motivated by the goal of maximizing the social welfare of the people and therefore CAPM would not apply to them (Focardi 2004, p. 512).

In the same manner, information that reaches investors is not usually available to everyone at the same time (because of certain communication barriers like access to information or geographical barriers) and therefore chances of bearing the same opportunity for all investors are very minimal.

CAPM also assumes that asset returns follow a normal distribution and markets are usually in equilibrium; meaning that very few people can affect the prices of security (Sharifzadeh 2010, p. 44). This assumption is obviously false because there are unforeseen hands that may easily affect the prices of securities, such as governments (Chaudhry 1994, p. 175).

Also, it is almost impossible to achieve a completely equilibrium market. During the time of analysis, the CAPM model also assumes that the value of assets and their quantities are the same throughout the period of analysis. This is obviously not the case because the values of securities normally shift very rapidly, even in a matter of minutes (such as the case in the stock market).

Considering the CAPM model relies on a lot of untrue assumptions, it remains a controversial issue to establish if the CAPM model is true or not. The same sentiments are harboured by Mandelbrot (2004) who notes that: “While the CAPM emerges as the most commonly used approach for both institutional and private investors, somebody has to prove that this simple model really holds true in the market” (p. 5).

Criticisms

Though CAPM has been widely acclaimed to be an easy to understand model that explains financial risk and asset returns, there have been existing concerns which question if the concept actually works (Mandelbrot 2004). The answer is not clear because the model relies a lot on the concept of beta which if analyzed over long period of time, does not show the real movements of various stocks.

For instance, if analyzed in the short-term the linear relationship observed between beta and stock return is very shaky and can therefore not be conclusively assumed that the model shows the correct results (Chapman 2006).

The fact that the CAPM assumes that asset returns are distributed normally has been a ground for launching more criticism on the CAPM because returns on equity and other markets are not distributed normally and variations of between three to six normally occur as standard deviations from the mean (contrary to what the normal distribution assumption would propose) (The Hindu Business Line 2001).

More criticism has been leveled against the CAPM approach, because of the fact that the model assumes that the variance of returns can be appropriately used to measure risk. Mandelbrot (2004) explains that “This might be justified under the assumption of normally distributed returns, but for general return distributions, other risk measures (like coherent risk measures) will likely reflect the investors’ preferences more adequately” (p. 9).

Indeed, when comprehensively analyzed, the risks noted in financial investments cannot be openly assumed to be just a variance, but rather, a variance which is normally not symmetrical. In relation to this concern The Hindu Business Line (2001) notes that:

“The assumption that well-diversified portfolios are subject only to systematic risk can also be questioned. Most portfolios will contain volatile stocks and, what is more difficult, several apparently sound stocks which may suddenly turn volatile.

Wise investors, if well-diversified or not, will be concerned with the total risk of such investments, bearing in mind that if these investments include a significant holding in a company facing corporate collapse, a reconstruction, or even a serious setback in a core market, any of this could make a sizeable dent in a portfolio, even if it is well-diversified” (p. 7).

CAPM has also been criticized because it assumes that the probability beliefs of investors regarding their asset investment is equal to the true distribution of returns, because in the real sense, the expectations of investors are often biased and therefore market prices as predicted by CAPM may not reflect the expected figures (Kent 2001, p. 921).

This scenario has even led to the development of the field of behavioral finance which manages investor expectations with regards to the psychological expectations of investors regarding their returns on investments (Shefrin 2000, p. 127).

It is also interesting to note that CAPM talks little of the variation in the returns of stock as a significant element in the determination of returns-on-assets.

One ground which CAPM has been criticized in this regard is that if low beta stocks are invested, the level of returns estimated by the model may be lower than the predicted levels. In other words, it has been evidenced that the level of returns recorded of lower beta stocks are usually very high. The Hindu Business Line (2001) explains that:

“Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient-market hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes the EMH wrong – indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market)” (p. 12).

The CAPM model has also been criticized for its advancement of the concept that given specific level of returns on investment, investors would almost by default choose lower risk as opposed to higher risk and in the same manner, if investors were given another specific level of returns on assets, they would prefer a higher risk market portfolio as opposed to a lower risk (The Hindu Business Line 2001).

This criticism is based on the example that since gamblers easily pays for higher risk; certain investors would pay for higher risks as well.

CAPM has also received criticism over the fact that it proposes the view that a given market portfolio encompasses entire assets in the market and through asset capitalization; it would be easy to quantify the entire assets in the market (Roll 1977).

This criticism is based on the fact that, there are preferences in certain markets and in the same manner, there are significant preferences in various assets present in different market portfolios; therefore, investors normally perceive their asset as a function of their profile concerning the returns they are likely to get from their assets.

In theory, it is also established that in quantifying the value of all assets in the market, all assets should be included in the analysis.However, the CAPM model does not factor this concept because it excludes certain assets such as art and real estate. Roll (1977) explains that:

“In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio.

Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by Richard Roll in 1977, and is generally referred to as Roll’s critique” (p. 129).

The CAPM also has a major weakness of assuming that all investors easily invest their assets into one market portfolio because in reality, individuals normally have their investments in various market portfolios (Alexander 2008, p. 252).

In certain instances, there is the possibility of fragmented market portfolios occurring and from a behavioral point of view, it is affirmed by the behavioral portfolio theory and the Maslowian portfolio theory that human beings normally take various channels (market portfolios to achieve one goal) (Brouwer 2009, p. 359).

The great reliance on beta, by the CAPM, is also a major point of concern for users of the CAPM because beta primarily entails a lot of past information which is not beneficial in estimating future values. Moreover, the concept of the CAPM model is to predict future values and it is therefore quite difficult to achieve this goal if past values are relied on.

Though the CAPM is a single-period model, it can be adapted to be multi-period, but its assumptions, just like other financial models, greatly limit its validity (United States. Congress. Office of Technology Assessment 1993, p. 276). To a large extent, these insights assume that the CAPM model is incorrect.

CAPM In Comparison With Alternative Models

The arbitrage pricing theory shares some similarities with the CAPM model in the sense that they both try to predict the returns on assets, given several uncertain market factors (Donovan 2007). However, the latter differs with CAPM on the basis that it is more articulate on the market risks (Levine 1995, p. 9).

This means that the ATP model breaks down market risks into very small components that would generally make it a better and reliable model as compared to the CAPM (Donovan 2007, p. 5). When compared to the dividend growth model, CAPM shares some similarity with the latter, based on the fact that they both fail to deal with risk directly (Ezine Articles 2010).

However, the dividend growth model cannot be applied to organizations which lack a dividend policy or those which do not pay dividends altogether (but the CAPM has a wider application in the sense that, it can be applied to several companies) (Glen 1994, p. 9). Nonetheless, the CPM is limited in the sense that, the companies to be analyzed need to have their shares listed in the stock exchange.

Conclusion

Though the CAPM is not a perfect model of estimating financial risk, it should be acknowledged that the spirit of the model is correct. In an abstract manner, the model ensures that investors can be able to estimate the risk attributed to their investments and the expected returns they should receive.

This is the reason why though the model has been known to have various flows; it is still widely used in the financial investment community. McClure (2011) affirms that:

“Although it is difficult to predict from beta how individual stocks might react to particular movements, investors can probably safely deduce that a portfolio of high-beta stocks will move more than the market in either direction, or a portfolio of low-beta stocks will move less than the market” (p. 4).

CAPM is therefore important for fund managers because they may be prevented from holding cash if they believe the market will collapse and in such a scenario, decide to hold stocks that have a low systematic risk.

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