# An Introduction to the concepts of CAPM AND APT

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In the past, the most investors have seen the national barriers as insuperable and hence have delimited their decision and options to only the domestic markets or the regional markets. However, disposing the restrictive barriers over time leads investors or financial institutions to open up to the world and so that, particularly investors in developed countries hold the foreign investment instruments in their portfolio. However, this situation affects the expected rate of return and to increase the risk exposure of investors. Because, with removing the investment frontier, a determination in a country's economy worsens the other countries' economy and rises the risk. All investments are future proof and the risk of market affects the return of investment. This case leads to improve the importance of portfolio and portfolio management. In brief, portfolio management tries to allocate available capital by taking account maximum return and minimum risk and has techniques and methods which includes how to allocate capital. The choice of assets and in this sense, the asset pricing are the most important stage of portfolio management. In the financial literature, there are two approaches which determines the changes in the returns of assets. To be more precise, general equilibrium models of asset pricing states to measure the risk of assets and explains the link between expected return and risk. First of these models is The Capital Asset Pricing Model (CAPM ) and Second one is The Arbitrage Pricing Model (APT).

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The Capital Asset Pricing model is based on Markowitz's portfolio theory (1954). Basically, the CAPM has been developed for asset valuation. The CAPM has been developed gradually over a period of 12 years in studies of William Sharpe ( 1964 ), John Lintner ( 1965 ) and Jan Mossin (1966). The main aim of the CAPM theoretically characterises the prices of capital assets by examining the relationship between risk and expected return. It is often widely used by academician and people. Furthermore, the most important apple of the investments courses' eye has been the CAPM as an asset pricing model. Unfortunately, the empirical results of the CAPM is poor and this case obstructs the way of its applications and the yield of tests of the model. The opinion of Fama and French (2003 , p. 1) are that "The CAPM's empirical problems may reflect theoretical failings, the result of many simplifying assumptions. But they may also be caused by difficulties in implementing valid tests of the model". Given this evidence, it can be seen that the weaknesses of the model ,which are unrealistic assumptions and the empirical results of CAPM , triggers the genesis of the new asset pricing model which is the Arbitrage Pricing Model.

The Arbitrage Pricing Model has been developed firstly by Stephen A. Ross in the 1970's and once again , in an article by Ross (1976) firstly formulated the APT. However, this model is the most discussed among alternative models. Ross' the APT formulation has less restrictive features with respect to the capital asset pricing model. Basically, it is based on the basis of economic and it is relationship with risk and return which the arbitrage pricing model uses the weighted mean of the default risk, the interest rate risk, the market risk, the purchase power risk and others risks related with asset pricing. As Francis and McGowan have indicated that the arbitrage pricing model shows how to determine the rate of return of assets by using risk factors. The basis of the APT exists important systematic factors which affect the average return of financial assets in long term. APT does not think littleof factors affecting the daily changes in the price of bonds and securities, however it is more interested in factors that affects the total return on whole portfolio. To identifying these factors let us to the intuitive evaluation on portfolio. Research by Roll and Ross ( 1984) suggest that the last purpose obtains the comprehensible level of the portfolio configuration and evaluation and so that improving the portfolio performance and concept.

In brief, the discussion of differentials and similarities between the CAPM and the APT begins with their assumptions and then their formulas. Besides, both models use the different risk factors and differently determine the rate of return. There is a large different between The CAPM and the APT in terms of the easy utilisation in the market.

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I mentioned the definitions of both models and informed the genesis of the models .The aim of this paper is to critically analyse both models in the way of their assumptions and methods in the next section. Then i will examine the differences and similarities between the CAPM and the APT. After that , I will select one of the models and will try to explain my selection in the light of the capabilities of the models. Last section will offer a summary and conclusion.

## CAPM

As every model is based on assumptions, there are assumptions behind the capital asset pricing model. Bodie , Kane and Marcus (2009) state assumptions below;

There are many investors in the market. However, Investors are price takers which means that their investments has no impact on stock prices. this is the basic assumption of microeconomics which is the usual perfect competition.

There is one identical holding period for all investors. Basically, this assumption ignores every situation which may happen after the single period. Therefore, this behaviour is completely mediocre.

Investors use the Markowitz portfolio selection model which means that all investors select mean-variance efficient portfolios. In other words, they hold diversified portfolios and need return for market risk or systematic risk because of ignoring unsystematic risk of specific risk of their portfolios.

There are no transaction costs and taxes. All investors pay no commission or charges and taxes on their returns from assets when they trade on securities. This is unrealistic assumption. In reality, there are costs on trades and the amount of costs and taxes lie on the size of trade.

All investors might borrow or lend at the risk free rate. Furthermore, investments are finite to legally trade on the universe of financial assets . This assumption omits some particular investments in not traded financial assets that are self improvement education, special enterprises and so on.

All investors act rationally and have homogenous expectations because of they derive the same input list . Moreover, all investors aspire to maximise their benefits or utility and the first priority of them is risk averse.

When examined generally, assumption 1 , 4 and 6 denotes the perfect capital market condition of macroeconomics which means that there is no arbitrage opportunity in the market. critically, the assumptions of CAPM is unrealistic, if comparing with the real world. According to assumptions, The CAPM concentrates on the link between systematic risk and return. However, the assumptions of the ideal world does not overlap to the recent real world. Thus, in real life or the real world, companies and investors made decisions in respect to investments. For instance , the recent real world does not have the perfect capital market. In contrast, the capital market of the real world is imperfect or limping. Even though it has discussed that ,in the developed market, there is a possibility for the incorrect pricing of the financial assets , although they have high level of the efficiency stock markets.

The above mentioned assumption of a single period horizon is introduced as a suboptimal behaviour by Bodie , Kane and Marcus (2009). Nevertheless , a single period horizon for investment is plausible in terms of a real world viewpoint. Since, a study by Student Accountant (2008) summarises that returns on financial assets is generally quoted annually, although the most investors hold their securities in their portfolio or as a investment instrument for longer than one year.

All investors hold a well diversified portfolio because of all investors are rational optimisers. According to the CAPM, this portfolio represents the whole stock market. Diversifying portfolio away from unsystematic risk is fairly simple and inexpensive for investors due to the CAPM is related with systematic risk or market risk instead of firm specific risk. Moreover, the constructed portfolios follow the stock market because of reflecting the stock market. Supposing that the most investors are worried only about obtaining monetary compensation for market risk, thus, this assumption seems to be judicious.

A more critical issue is that Student Accountant (2008, p.51) stated "it is not possible for investors to borrow at the risk free rate e (for which the yield on short-dated Government debt is taken as a proxy)". Because, the reason is that individual investors have much higher risk rather than the risk in relation with the Government. To be more precise, the weakness of borrowing at the risk free rate indicates that investors expect the much lower rate of return at the higher level of risk.

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Examples of our workAs a result, even though the CAPM has some of unrealistic assumptions with respect to the recent real world, there is a strong link between the expected rate of return and systematic risk.

## METHOD

The CAPM takes into account the susceptibility of asset to market risk of systematic risk (its ) with the return of risk free asset and the expected rate of return on market. the risk premium on the individual assets refer to the risk premium of the market portfolio (M), since according to the assumption 6, all investors use the same input lists in their portfolio ,which means the Market Portfolio (M). Furthermore, beta coefficient of financial shares measures the returns on stock and changes in the market at the same time. And beta coefficient formulates as follow :

Where ) denotes the covariance between the return on securities and market, is the variance of the market. in this sense, the CAPM formula illustrates as follows:

Where,

is the required return on securities

is the risk free rate, based on the rate of treasury bills

is the beta coefficient of securities. It measures the systemic risk on securities comparative to the systemic risk on the market

is the return on the market and based the return on the stock markets share index such as FTSE, DJI and so on.

is market risk premium. Lynch (2004, no page) explains it as "this is the reward that investors receive over and above the risk free rate for investing in shares that have the same level of risk as the market."

If the CAPM holds for individual shares, portfolio as the combination of shares illustrates:

There are two ways for investors to compensate. One of them comes true upon risk free assets () which is time value of money. All investors can be compensated by investing their money at frisk free rate. Second one is that the amount of compensation depends on the additional risk took by investors. This risk is measured by beta coefficient () in the formula.

Basically, beta coefficient measures the systematic risk of financial asset or the sensitivity of a shares to changes in the market. if assets have higher betas indicates more sensitivity for the market. To be more precise, higher beta generates higher returns on asset. The issues associated with measuring beta coefficient damage the ability of CAPM to explain systematic risk. First issue is that when securities have high volatility, the estimations of beta generally have high standard deviations. For this reason, in the CAPM, the market portfolio is used rather than individual assets to measure beta. Second problem is about the stability of beta. Blume (1975) tried to measures of beta coefficients of companies by using the data of two different consecutive time period and he founded that in the next time period, the beta coefficient constantly decreases to 1 with respect to the previous time period.

The security market line (SML) shows the relationship between beta coefficient and the excess expected returns. The SML illustrates asset risk premium as an indicator of asset risk. Figure 1 shows the Security market line and the slope of its equals to the excess expected return. The excess expected return equals to , while beta is at 1. Furthermore, SML asses the investment performance. In other words, it analyses fair expected return on a risky stock while assaying security probably fulfils to compute the return actually expected in the next step. The differences between the fair and actually expected rate of return is called the alpha () of security. This case of stock valuation illustrates in terms of the SML in figure 2. For instance, given the risk of an investment( measured by its beta coefficient), the expected rate of return of securities is smaller than estimated by CAPM (point B). The excess of the fair return denotes positive alpha by the SML and so that, positive alpha ( ) denotes a good buy ( underpriced ) for stock. The area of underpriced stock (N) is above the SML. Antithetically, if the expected rate of return of securities is higher than estimated by CAPM (point A), this case points out negative alpha (). Overpriced stock (N') arises below the SML as an area. This case of stock valuation illustrates in terms of the SML in figure 2.

## Figure 1. The Security Market Line

Note: the graph has collected from http://www.sy-econ.org/finance/finance-invest-CAPM.html

## Figure 2. The Stock Valuation and The SML

Note: the graph has collected from http://94.101.144.194/MagellanDemoStatic/tp/c10047/cc_0_82_0_0_14_10047_u10328_74_2.htm

## APT

The arbitrage pricing model (APT) has developed as a response to the CAPM by Ross (1976). Like the CAPM, the APT examines the relationship between expected returns and the risk. however, according to the CAPM, all investors invest in terms of the expected return and risk of the individual assets. Ross (1976) advocates that this factors as a investment decision are less significant for investors and utility is more important for this. Moreover, the APT has less assumptions behind the model with respect to the CAPM. Therefore, it is the simplified model. The assumptions of the APT explain below by Bodie , Kane and Marcus (2009):

Securities returns on financial assets are determined by a factor model.

There are adequate shares to diversify away idiosyncratic noise.

The permanence of arbitrage opportunities is not possible in the function of security market that is well.

Basically, the arbitrage opportunity is the opportunity for investors to obtain profits without any risk and making net investment. According to assumption 3, in a condition of well functioning market , the APT is based on that there is not any arbitrage opportunity. This case denotes that the APT is based on the Law of One Price. According to this theory, there is no opportunity to sell an asset from 2 different prices. this situation builds up the core of the model. Suppose separately mention that if a expected return appears on the score of out of the model equilibrium, all investors might build a zero wealth portfolio in order to following up the mispricing of the stock. this case is denominated as arbitrage in expectations.

As we examine the risk of portfolio's stocks, if investors hold a well diversified portfolio, its firm specific risk or unsystematic risk is ruled out. Therefore, in the portfolio, there is only systematic risk (non diversifiable risk factors). The reason of excluding non un systematic risk is that when the portfolio approaches a well diversification, extends the amount of stocks of portfolio, firm specific risk is excluded by the model. Mathematically, the weight of portfolio shows as wi = 1/n and in this sense n is the amount of stocks in the portfolio. If portfolio has large n , portfolio's non systematic risk ( firm specific risk , ep) approaches zero. In the context of zero ep, the return on portfolio shows as following equation :

Where

is the expected rate of return on portfolio

is the sensitivity of portfolio with respect to factors

is macroeconomic risk factors

The side of equation is related with systematic or non diversifiable risk. if the amount of assets is large in the portfolio, the relationship between risk-return is illustrated by following formula :

E(ri) = rf + (E(r1) - rf)) + (E(r2) - rf)) + ... + (E(rj) - rf))

Where

E(ri) is the expected rate of return on a security

rf is the risk free rate of return

is security's sensitivity with respect to risk factor

(E(rj) - rf) is the risk premium with respect to risk factor

According to formulas, if portfolio is a well diversified , there is no specific firm risk. The expected

rate of return lies on systematic risk, and there is the impact of non diversifiable risk factors on the rate of returns. The risk factors means unpredicted changes in inflation, interest rate , industrial production, oil prices, GDP and other macroeconomic factors. Moreover, as it is seen from its formula, there is a linear link between the return on securities and the market risk with respect to factors

## Differentials and Similarities

In overview, Huberman and Wang (2005) the CAPM is a theory as market basis , the APT is more specific basis. whilst The following stages show the differentials and similarities between both model in terms of risk elements:

The systematic risk or market risk determines the expected rate of return in both model, however in the APT, there are non diversifiable factors to affect the expected return on portfolio.

If there is a well diversified portfolio, both model rule out the firm specific risk or unsystematic risk.

To building the APT requires only 3 assumptions , while the CAPM have more assumptions. The differentials of assumptions of both model are :

Even though both theories make the realistic assumptions of " investors would rather bigger property than less and avoid risk", the quadratic utility assumption of the original CAPM is much more limiting vis-a-vis the APT.

In the APT, different than the CAPM, there is no need for the assumption of normal distribution of earnings with many variables. The APT does not make the probability distribution and does not assume that investors choose the portfolios according to expected earning and variance or standard deviation.

The CAPM requires the market portfolio whilst the APT does not need it. Because of the difficulties that combines with market portfolio, the APT does not give credit to conditions as defining market portfolio or assignee (example). However; to have a applicable assignee for systematic risk factors, expected earning of a portfolio( a market index) is chosen.

The CAPM considers the conditional of risk free asset necessary with respect to the APM.

The APT's beta coefficient fairly allows some risk factor and the APT is more realistic when we consider FVFM has only one beta coefficient.

The APT could be applied both single period and multi period while the CAPM is with one period.

In addition, both models make definite assumptions that reach to same results. These assumptions are:

The capital market is perfect without any issue.

Investors have homogeny expectations: they claim they share the same understanding of risk and earning for an asset that is given to all investors.

There is a linear relationship with the expected return and risk.

## The Model Selection

Before making decision, i would mention that the suitable of used model depends on the sort of financial investments. However, it is significant to ask two fundamental questions for my personal decision about the model selection :

How does a asset pricing model measure the risk of asset?

How does a asset pricing model calculate the required return on assets?

Conceptually and theoretically , the APT can be taken in to consideration as an advanced version of the CAPM. However, the APT does not work as required in the practice, although it has more realistic assumptions and is more flexible( less restrictive) and strong. The APT does not mention how many risk factors or what type of factors we ought to use to measure risk in the model with regard to first question. In my opinion , this case causes to obstruct the model to compute efficiently the returns on asset because of the difficulty of determining the factors. Wang (2003), Dhrymes (1984), Shanken (1982) and Lim (2009) rightly points out that the issues of factor can induce to higher prediction error and greater computation mistake. In addition, the APT is not easy to understand and apply from investment managers.

The CAPM is widely used and accepted as an asset pricing model by the financial management field. Even though It has more restrictive and limitations, it is easily applied by the financial investors and managers. The CAPM reflects the systematic risk much better and more substantial on the assets than the APT in terms of measuring risk. Furthermore, it generates a robust link between return and risk and so that this state is likely to provide lower estimation mistake. It is usually seen as a better model of calculating the required return on assets ( Taylor (2005), Donovan (2007),Lim (2009) and Student Accountant (2008)). Overall, the CAPM is simpler model and more easy to understand and employ vis-a-vis the Apt.

In my opinion, the CAPM is more suitable on account of the model selection, since its responses to above-mentioned questions is more reasonable and understandable. In addition, another criteria to select the CAPM is that it is more useful the investment and financial management field. Nevertheless, the APT is new theory, because of this , it is required to make more research and tests on the APT to prove itself.

## Conclusion

The CAPM and the APT let us to determine and measure the link between return and risk with the different and similar ways. Principally, even though both models is established as a general equilibrium models of assets pricing , in the portfolio management they are widely used for the financial assets selection.

The CAPM deduces that the only one element to determine the expected rate of return of assets lies on the relationship with each assets and their average market returns by using some assumptions and mean variance analysis. This relationship indicates the systematic risk and it measures with the beta coefficient in the model. Especially, criticisms about the CAPM committed by Roll and Ross is that