Portfolio Theory and the Capital Asset Pricing Model - Coursework Example

Portfolio Theory and the Capital Asset Pricing Model Introduction Humans are economic beings – that is, we all tend to make choices of which among aset of many possible alternatives should we devote a limited amount of resources to. The aim is to get the highest level of benefit, with the lowest possible use of resources, among the various alternative choices. A consumer with a certain amount of income is normally confronted with two types of decisions that are of an economic nature. The first is how to allocate his current consumption among a number of goods and services. A study of how to do this has been the subject of study of many researchers who have developed theories relating costs and utility. The second type of decision concerns how a person with funds not used for consumption could effectively invest these funds among a number of different assets. This second type of decision has not been investigated as thoroughly as the first and continues to be the subject of academic research today. Together, the two types of decisions are known as the consumption-saving decision and the portfolio selection decision. Of the portfolio selection process, two of the most fundamental and often-used theories that have been developed are the portfolio theory and the capital asset pricing model (CAPM). Both the portfolio theory and the CAPM contain principles that would prove useful to ordinary investors as guidelines in arriving at their own investment decisions (Block & Hirt, 2006). However, much of the theory and its several variations are highly complex and mathematical that they are applied mostly by market professionals rather individual investors, because the incremental benefit will only be significant for sizeable portfolio values, sufficient to the effort of undertaking the calculations. Inasmuch as this paper examines application of these theories for the individual investor, it shall treat on the practical application of the theories’ principles rather than the mathematical derivations thereof, although the basic equations shall be introduced. Portfolio theory According to Scott (2003), the portfolio theory holds that the basis for choosing assets for investment is the manner in which they interact with one another instead of how they perform individually or in isolation. The combination of assets is termed the portfolio. The theory states that an optimal portfolio is one that secures for the investor the least possible level of risk for a given return, or conversely, the highest possible return for a certain given amount of risk. The figure that follows is a graphical depiction of the most important features of the portfolio theory. Foremost among the concepts of this theory are those of risk and return and their significance to the investor. Risk in investment is the measurable possibility that an investment may lose, or not gain, in value. It is different from uncertainty, which is not measurable. On the other hand, return is the profit on a securities or capital investment, expressed in terms of an annual percentage rate (Downes & Goodman, 1995). In the diagram above, there is a line that describes the risk-free asset. The orientation and slope of the line shows that as risk increases, return also increases. This is the most fundamental principle behind the portfolio theory, which all investors must be aware of to make educated, informed decisions. Normally, when a portfolio aims for higher returns, it necessarily has to assume higher risk. On the other hand, a risk-averse person will usually be satisfied with lower returns, in exchange for the greater certainty associated with less risky investments. (Litterman et al., 2003) The risk-free asset is the hypothetical asset that yields a risk-free return. The benchmark for the risk-free instrument is the short-term government security; it is considered close to risk-free because it is an unconditional, direct obligation of the government, and its terms is short enough to be impervious to risks of inflation and market interest rate changes (Downes & Goodman, 1995). Finally, the efficient frontier is that locus of curves that describe risk-return tradeoff for various portfolio combinations, at the point when the portfolio is optimized. The point where the efficient frontier intersects the risk-free asset is known as the market portfolio – that combination of assets that assumes no more risk nor performs no less profitably than the market. Mathematically, the return for a portfolio is computed as the weighted average of the risk free asset, f, and the risky portfolio, p, and is therefore linear: On the other hand, the generally accepted measure of risk is the standard deviation, which is the statistical measure of variability of a sample distribution about its mean. In our example, the portfolio standard deviation is simply a function of the weight of the risky portfolio in the position (since the accompanying asset is risk-free and thus exhibits zero standard deviaiton). This relationship is thus linear. Capital asset pricing model (CAPM) The capital asset pricing model is a model that indicates what should be the expected or required rates of return on risky assets. (Reilly & Brown, 2006) This theory also provides the function of linking together the risk and return for all assets. Because of its simplicity in use, it is an ideal model by which a new investor may understand the trade-off between risk and return. Mathematically, the model is expressed in the following equation: In the equation above, β, Beta, is the measure of asset sensitivity to a movement in the overall market; Beta is usually found through a regression of historical data linking the market return Rm, risk-free rate Rf, and the return on the asset Ri. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. The concept of the beta is of such importance in investing that many investors use an asset’s beta as the indicator of the asset’s risk. The equation shows that the beta is a factor applied to the expression: which is the market premium, the historically observed excess return of the market over the risk-free rate. It is thus evident that the higher the beta of an asset, the higher the expected return of the asset compared to the general market – and the higher the return, the higher the risk. The beta being a measure of variability, it is, like the standard deviation, a measure of risk. The beta of an asset may have a positive value, a negative value, or a value of 0. Its absolute value may be greater or less than one. An asset with a beta of 1 means that the asset has exactly the same risk-return profile as the general market. If the asset beta is 0, this means that the asset does not vary with respect to the market – thus the asset risk is zero, indicating that it is a risk-free asset. Assets with beta values that are positive vary in tandem with the market – when market returns go up, the return on the asset goes up also, and vice-versa. Assets with beta values that are negative move counter to the market. Thus, when the market returns go down, the asset return goes up, and vice-versa. Finally, if the beta’s absolute value is greater than 1, the asset is riskier than the market because it tends to have higher volatility (movement) than the market; and if the beta’s absolute value is a fraction of 1, then the asset is less risky than the general market, exhibiting less volatility than the market. (Fabozzi & Markowitz, 2002) In creating a portfolio, the beta is a most helpful tool. A porftolio must be sufficiently diversified so that it does not assume an inordinate amount of risk. For instance, in a sotck portfolio, some stocks would be risky: these would include the oil and mining stocks, the new and untested business ventures, and stocks of companies that are situated overseas. By the nature of their business and the circumstances of the companies underlying them, the return expectations associated with them would be relatively uncertain and unpredictable. However, their greater volatility tends to make them good speculative short term plays, and they tend to outperform the market on good runs. These stocks would have betas whose absolute values exceed 1. On the other hand, there are the blue-chip and defensive stocks, those whose underlying companies are solid and mature businesses with a reliable dividend history and proven earnings track record – these are usually the food and beverage companies, pharmaceuticals, retail merchandising, utilities, and other business that thrive even during crises. Normally, even when the general market becomes volatile, the prices on these stocks will vary to a lesser degree because they are considered good long-term investments and would be less prone to sudden buy-ups and sell-downs. The betas of these less-volatile stocks would have an absolute value somewhere between 0 and 1. In creating a stock portfolio, it is usually a good idea to combine some stocks with high betas (speculatives) with stocks with low betas (defensives), so that risk is balanced with higher returns. It is also a good idea to combine contrarian stocks – those with positive and negative betas. This is a technique by which an investor may hedge against sudden changes in the market. If the general market goes down, the stocks with positive betas will go down with it, but those with negative betas will tend to go up, thereby lessening the blow for the investor and reducing his losses (Bernstein & Damodaran, 1998). With all the studies about the CAPM, however, there are those who have concluded that CAPM is not a good model for expected return for risk-aggressive portfolios (Koo & Olson, 2004; National Bureau of Economic Research, 2003), or at best continues to be at the crux of controversy (Jagannathan & McGrattan, 1995). Other principles relevant to the investor Armstrong and Brodie (1994) conducted a survey among investors who were familiar with the use of portfolio theory and various asset pricing techniques in analysing their investment alternatives. Of those 198 respondents surveyed, at least two-thirds believed that the technique they are using are effective and instrumental in making correct investment decisions. However, when the researchers tested the theory with empirical data, the result was far from corroborating of the majority opinion. Until the time of the study, theirs included, could conclusively demonstrate that the use of any of the asset pricing models or theories was a significantly useful decision aid. This study suggested that the asset pricing models and theories may even interfere with the profit-maximizing prospects of the investor. Out of all the investors who participated in the study, only the portfolios of about 13 percent of the investors who used one or another form of the models had successfully invested in the more profitable project. This study was replicated in 27 succeeding experiments, and its coverage extended to more than 1,000 subjects in six countries over a five year period, with similar results. More recent studies, however, tend to point to the relevance of the CAPM on investor decisions in the market. For instance, Omran (2007) found evidence that modern portfolio theory and capital asset pricing models are valid and applicable to the Egyptian emerging stock market. The results of the study show that market risk, measured by beta and preference for skewness, plays a significant role in the returns dynamics of this country’s stock market. A test portfolio based on consumer staples and financial companies with low betas outperformed a second test portfolio that contained construction materials, hotels, and weaving companies with large betas. According to Constantinides and Malliaris (1995), in the conceptual development of portfolio theory, an essential assumption is that market imperfections are inexistent. This was done implicitly by assuming: (a) that transaction costs are equal to zero; (b) that the capital gains tax was equal to zero; and (c) that the assets may be sold short and the investor may fully use the proceeds. In a riskless market, this condition implies that the borrowing rate and the lending rate are equal to each other. There are some other conditions which the portfolio theory and the CAPM. One of this is that the market for securities has perfect liquidity – that is, there is sufficient demand and supply of the security at any one time at the price the investor wishes to transact, so that the investor could sell or buy any number of shares of the security at all times. In truth, this is not the case. There are assets that are not liquid, or times when a normally liquid asset does not have sufficient buyers or sellers at a certain price. Garleanu (2009) had occasion to conduct a study on the effect of market illiquidity on portfolio choice and pricing. The effect on trading in an illiquid market is that the transactions are not executed at the time the order to buy or sell is made, and when execution is finally achieved a considerable delay has elapsed. Findings show that liquidity levels have a strong impact on the choice of portfolio. Empirical evidence points to the tendency for smaller blocks to be traded in illiquid markets. Also found by this study is the tendency for agents with relatively high asset valuation to diminish their demands, while those with relatively low asset valuation tend to increase their demands, as market liquidity becomes worse. Finally, transaction costs do not appear to be affected by market illiquidity, because frequency of trade does not determine the price discount. The trading frequency which is relevant is that at which the trader is compelled to liquidate in order to avoid going on the margin. In future studies on liquidity, frequency of trading may understandably be ignored as a determinant of transaction costs. Other findings of relatively recent researchers are briefly described here as follows: 1. Daly, Crane & Ruskin (2008) showed that portfolio optimization can be achieved by a process called random matrix theory filtering to reduce average realised risk over time. 2. Mo & Wu (2007) found that global return movements possess a larger discontinuous component, and global return volatility more deviations, than country-specific returns. Furthermore, investors tend to charge positive prices for global return risk and negative prices for volatility risk, indicating that investors are willing to pay positive premiums to head against downside global returns and upside volatility movements. 3. Pastor & Stambaugh (2000) compared among different portfolio pricing models, and found that there is little or no difference among the returns realized by the models when the portfolio’s ratio of position size to capital is subjected to reasonable constraints. 4. Sendi, Al, Gafni & Birch (2004) demonstrated that the failure to adopt a formal portfolio theory approach does not necessarily identify the portfolio that optimizes results for the allocated resource. 5. Van Wyk (2009) reported that the CFA Institute developed a method to judge the technological strength and potential of companies that involved a comprehensive technology due diligence exercise based on the management of technology functionality grid. And finally, 6. Xu & Hou (2008) showed in their study that CAPM with generalized elliptical distribution can better predict the behaviours of risky asset prices rather than CAPM with normal distribution. Conclusion The portfolio theory and the capital asset pricing model have proven to be useful concepts by which investors and fund managers may be guided in their choice of assets to invest in. The financial markets have developed to such a degree and complexity, linking with markets across the globe, that the risks of investing one’s hard-earned money requires a reliable method by which one may assess his chances of earning his required returns. This study provides a brief introduction into the possible practical application of these theories in investment decision-making. There are limitations to the study, however. Firstly, the treatment was rather exploratory, therefore a deeper examination of these theories and their theoretical use is in order. Furthermore, different investment instruments require more finely-tuned theories in order to determine such particulars as target prices, time horizons, and cut-loss provision. Finally, these investment theories and models are never perfect; they are built on assumptions that are seldom, if ever, truly present in the real market. There will be times that even with the most detailed calculations and well-thought out plans, success rates of slightly better than half of all trades made will already be an outstanding accomplishment for the astute investor. In light of these findings, the study makes the following recommendations: 1. The investor should devote much time in the fundamental analysis of his prospective investment choices, so that he may qualify the various quantitative indicators used, such as the beta. He must keep in mind that at best, any supposedly constant indicator is a guess. 2. The results of the application of these theories are a numerical number, the importance of which must be interpreted with much sensitivity to the prospects in the general market. These theories are grounded on the conditions prevalent in an efficient market. Particularly in the context of the present crisis, markets now are far from efficient. 3. In creating an optimal portfolio, a proper balance should be designed among the different investment alternatives, with attention given to the investor’s tolerable level of risk and required level of liquidity, as these vary for each individual investor. REFERENCES Armstong, J. Scott & Brodie, Roderick J. 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