Evaluation and Comparison between Mean-Variance Optimization Model and Capital Asset Pricing Model - Essay Example

EVALUATION AND COMPARISON BETWEEN MEAN VARIANCE OPTIMIZATION MODEL (ONE PERIOD) AND CAPITAL ASSET PRICING MODEL (CAPM) by Student’s Name Code + Course Name Professor University City/State Date Introduction Studying, practicing, and understanding finance cannot be complete without an understanding of various models that are useful in giving a comprehensive knowledge and applicability of facts and figures applied as a basic in the study of finance as a course. This discussion focuses evaluating and comparing the mean Variance optimization model and the capital asset pricing model in a whole market. A complete market A complete market can be defined as that which has enough security and stock to ensure that there is no restriction on the outputs and on the profits, and where the market worth is highly dependent and determined by investment decisions. Wrong investment choices and decisions mean less market value. Sharpe (2010, p.63) looks at it as taking a sequential approach whereby investors first weigh the market worth before venturing into trading in such a venture. A complete market entails orientation into the market and understanding paradigm shifts before deciding to risk and invest many funds in market. Knowledge of a complete market helps in making an informed decision, which can in turn result in lump sum returns. A complete market also gives provision and considerations to emerging markets and trends whose characteristics may differ from the existing markets. As Kvint (2009, p.82) explains, with new emerging markets raises the expectation of growth in a number of projects with increase in financiers while at the same time leads to losses in those that do not rise to the standards in order to compete effectively in the market. A complete market involves competition, which releases pressure in the market and in return. It leads to the revisiting of prices and production of relevant products and services in order to remain significant amidst competition (Koenig 2009, p. 239). Mean Variance Optimization Model (One period) The mean variance optimization model can be defined as the model that quantitatively establishes the mean between the risks and returns in a portfolio by increasing the profits and reducing the possible risks. In this model, it is clear that investors or other people with an interest in the market will weigh between risks and profits, and will prefer to cast the net wide by spreading apart their investments in the risks and returns portfolios. It is based on Harry M. Markowitz algorithmic calculations that weigh the returns over a definite duration. The number of risks involved affects the amount of capital investment in a certain market. The higher the risks involved, the lower the investment on the market. An investor will prefer a less risky plan to avoid massive losses that might happen, especially in an environment where market trends have not yet fully been established and made predictable. Under the mean variance optimization model, investors record and calculate their expected incomes within a particular period depending on the risk involved. The relationship between the expected returns and the variation or difference in returns can be determined by the use of standard statistical formulae. In this case, the choices that are made by the investor determine the profits. It involves relying on current actual position rather than relying on misleading past records. This model helps in devising plans in security markets and can be referred to as one term or period because decisions are made in the beginning, and its results come at the end, meaning that no action is taken in the course of the term (Korn & Korn 2000, p.1). It is a static model because decisions are made only in the beginning, and the returns are seen at the end of the set timing and no adjustments can be made until the duration is over. The static nature could mean that if the decision made from the start were wrong, then, the result would be a loss and negative effects, with nothing to be done to alter this until the duration is over. Capital Asset Pricing Model Capital asset pricing model is a theory that determines asset prices by concentrating on co- movements within the market (the beta). It is based on the argument that not all risks are in a position to influence asset worth (Perold 2004, p.3). It is one of the asset pricing models since it explains how asset pricing is done. This model looks at the market as highly competitive and that the returns from such an environment reflect the chances of more ventures in the market. This theory looks at all financiers as investing on the same timing or equal time frame. It also based on the hypothesis that all investors can borrow and give loans at a similar rate exclusive of a risk. Investors have to be knowledgeable on the process of allocation and proceeds of the publicly traded property. This theory looks at portfolio as the efficient of the mean- variation. Here, returns are dependent upon the risk free charge, market risks quality rate and the beta asset. Under this model, the expected returns are what are seen as rewards whereas the portfolio risk becomes the market beta for the venture. In an ideal whole market, competition will be required on those investments that involve low risks and high returns. This model will work under complete market where if the risks involved in the project will be high, then the expected returns should be high in order to convince investors to buy the project, meaning that the higher the risk, the higher the expected return rate. Inputs and Outputs in the Models The input in used this model is the funding and stock allocated and the amount of risk taken by an investor while the outputs are the actual and the expected returns, which may be variant. The inputs are seen in terms of investments made on a project that is deemed useful. The expected return is used as a benchmark to measure the actual returns and the variance between the portfolio and the real returns. If the variance is found to be low, it means that the portfolio has been highly diversified to minimize risks (Rachev, Stoyanov, & Fabozzi 2008, p. 247). The efforts and inputs under the mean variance optimization Model are aimed at reducing total costs culminating from price changes. It seeks to optimize returns by striking a balance between price and risk, and exploring means in which a specified cost can be maximized to yield higher returns. It is useful tool that managers can use understand how they can be able to manage market risks and increase returns at the same time. Investment decisions are made once the measurements have been made on a continuous basis, whereby the reviews determine investments decisions, depending on how useful the returns are. The decision as to whether to allocate more funds or not to the market is made after reviewing certain duration’s results (Kissel 2014, p. 298). The input on the capital asset pricing model is the market beta, which is also the amount of risk an investor decides to take. The output will return rates, which will be used to judge whether or not to engage in new investment schemes. The market beta is seen as the measure of the market contamination. Under the capital asset pricing, all investors will choose a market portfolio that will be in equilibrium with the capital market location. For the two models to be successful as Kyriakopoulos puts it (2000, p.68), it requires investors in both models to have market knowledge. This information involves the ability to interpret market complexities in cause and effects, and giving meaning to the available market data to avoid ambiguity and uncertainty. For both, therefore, knowledge of a complete market is a necessary input that gives an understanding of the market itself. Methodology and variables on Inputs Data The methodology used on variables varies depending on assumptions and the basis in which the models are formed. The mean variance optimization theory is based on a single time whereby a portfolio’s mean and its variance is used to predict the future and is reused in the future of the next market period. Methodology involves replacing the mean with sample approximations. Under capital asset pricing model, the anticipated returns are used as capital to budget and monitor the process, and helps assess estimates of returns and risks. When evaluating variables in capital asset pricing models, it is evident that the beta has different effects on stock and returns, which directly influences input data. The evaluation on high positive beta will show huge cost variation, increment in market risks that will result in the investors claiming for higher compensation. On the other hand, negative beta will tend to shift variables against the market that will in turn reduce risks and work to the benefit of the investor. Under capital asset pricing model, investors will not need compensation for risks (Shapiro, n.d, 11). In this case therefore, price= P = E[CF]/(1+E[r]). For both models, evaluation of variables help in measuring market performance measured through effectiveness and completeness of a given market (Ho & LEE 2004, p. 24). Effectiveness majors on the amount of emphasis placed into the pricing of products. On the other hand, completeness centers on the availability of security in order for the investors to indicate their marketplace inclinations or preferences. Model Assumptions The assumptions made in the Mean Variance Optimization model are that the security or investments can be flawlessly divided to avoid a negative final return; that the investor can buy as much as he wants and this will not affect the product’s overall price. The model assumes that there is no transaction cost in the purchase of an asset. The start will not work with a negative position from the onset. Another assumption made is the information of estimations variances of the returns. Before returns are defined, assumptions of possible security profits are made which act as the guide. The other assumption made under this theory is that the factors will be constant in the set duration of the investment and that prices be the same in the long or short durations, meaning that all factors will remain constant and under minimal set risks. This model assumes that all investors are initially aware of the risks involved in any market they set to enter and that the decision they make wise judgments that will help them reduce more risks. The investors will be prompted to choose the one with fewer risks and higher returns. In the capital asset pricing model, investors are assumed knowledgeable and wise enough to diversify and have many assets in order to continue in tandem contact with the market portfolio. This theory also works on the assumptions that all investors are able to access similar assets in the market. There is also the assumption that investors are interested in reaping maximum returns in one period. This model assumes that there are neither taxes nor commission are involved and that investors are able to borrow and give out minus risk. This theory implies that investors vary whereby those that are risk hesitant will invest in more risk free assets, and those that are tolerant will tend to invest heavily in risky assets. The capital asset model is based on an assumption of the economic behavior of investors as being under equilibrium. This performance is the benchmark in which prices and profits are determined. It assumes that there is stiff competition between investors who have a fixed and related period of strategizing. The complete market plays a major role here whereby it simplifies the investment project selection and provides validation for a given investment strategy. Effects of Availability of Market Constraints If a market imposes constraints like borrowing and lending constraints within the mean variance optimization model, then the mean variance optimization model will not be able to make clear predictions of its future profits, therefore risks will go higher than the initially expected. This will mean fewer profits or investor returns. A complete real market incorporates rates and charges in borrowing despite having paid the initial amount as risk. Constraints affect the investor’s ability to borrow funds. The investor will not have capacity to be a price taker when borrowing constraints are imposed on the market since the price per share will no longer be autonomous of the number of units or shares bought. With the introduction of short- sale constraints, increasing the required results without tampering with the risks is difficult. Variance will not decrease without affecting causing the decrease in returns when constraints are at play. A large variance will in exchange pull down the returns. With short sale constraints comes the probability of the portfolio required being much varied from outcome because no shortcuts can be taken once kick off begins. In the capital asset pricing model, introduction of constraints in terms of declines in the assets’ market value leads to the recording of a negative market beta, which is preferred more by investors because they see the situation as less contaminated. Negative market beta works to the benefit of investors with portfolios that are similar to that of the market, which in returns culminates to reduction of asset risks. Under this model, short sale constraints will not affect the model when no financier shorts the market range, especially when the investor lends small amounts into some investments, which will mean fewer risks (Rubinstein 2013). The Limitations of the Mean-Variance Optimization Model Although it gives a great outline for asset placement, the mean-variance optimization model is not without limitations. It looks at returns as the anticipated future outcomes and at the same time looks at unpredictability as a risk substitute. Current pricing cannot be used clearly to predict the future clearly, since changes are bound to happen, which means that the profits predictions will be faulty, leading to a large variance. Using historical data to predict future investment returns is misleading. In this model, the investment inputs are usually past record estimates records (Floudas & Pardalos 2008, p.1041). These estimates cannot be free of errors, which means that classification and division will not be correctly statistically captured which will result in investing very minimally in some projects or highly on others, whose returns may not be congruent to the input. This results in erroneous portfolio. Another limitation associated with this model is that it can result in unsteady final results of an investment which means that minor changes have to be done, and at the end of the duration these small changes causes a significant change in variance. Instability in results leads to allocation of a different amount of money to a certain portfolio. Small changes will lead to changes and imbalances in the entire portfolio, which also affects the allocation in all assets. REFERENCES FLOUDAS, C. A., & PARDALOS, P. M. (2008). Encyclopedia of optimization. New York, Springer. HO, T. S. Y., & LEE, S. B. (2004). The Oxford Guide to Financial Modeling Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions. Oxford, Oxford University Press, USA. PEROLD, F A., (2004). The Capital Asset Pricing Model: Journal of Economic Perspective. Vol 18 (pg. 3-24). http://www1.american.edu/academic.depts/ksb/finance_realestate/mrobe/Library/capm_Perold_JEP04.pdf KYRIAKOPOULOS, K. (2000). The market orientation of cooperative organizations: learning strategies and structures for integrating cooperative firm and members. Assen, Netherlands, Van Gorcum. SHARPE, W. F. (2010). Investors and Markets Portfolio Choices, Asset Prices, and Investment Advice. Princeton, Princeton University Press. KVINT, V. (2009). The Global Emerging Market: Strategic Management and Economics. Rutledge, New York KOENIG, C. (2009). EC competition and telecommunications law. Austin, Wolters Kluwer Law & Business. RACHEV, S. T., STOYANOV, S. V., & FABOZZI, F. J. (2008). Advanced stochastic models, risk assessment, and portfolio optimization: the ideal risk, uncertainty, and performance measures. Hoboken, N.J., Wiley. KISSELL, R. (2014). The science of algorithmic trading and portfolio management. http://www.sciencedirect.com/science/book/9780124016897. KORN, R., & KORN, E. (2000). Options pricing and portfolio optimization: modern methods of financial mathematics. Providence, RI, American Mathematical Society. SHAPIRO, A., (n.d). Foundations of Finance: The Capital Asset Pricing Model (CAPM). http://people.stern.nyu.edu/ashapiro/courses/B01.231103/FFL09.pdf RUBINSTEIN, M. (2013). A history of the theory of investments my annotated bibliography. Hoboken, N.J., Wiley. Read More