Optimal Number of Securities in a Risky Asset Portfolio - Essay Example

Finance and accounting [Insert al Affiliation] Efficient portfolio It is an optimal portfolio in the market that offers the expected rate of returns that are high with the lowest standard deviation (risk) involved. Investors prefer the lowest standard deviation because of the axiom CAPM model that states that investors fear risks most, and they are, therefore, careful when making their investment choices. Normally, they devote their due care on the average and deviation of their returns from the investment to minimize the deviation of the return on the portfolio given an anticipated return and maximize anticipated return, given a certain variance (Capital Asset pricing model 2015). To determine an efficient portfolio, an efficient frontier is drawn. The efficient frontier is a graph drawn to exhibit different portfolios with a different combination of returns and risks. To achieve such optimal portfolio, there must be a combination of the lowest risk with the highest expected return. The figure below shows the efficient frontier. The efficient frontier has a Y- axis that measures the anticipated rate of return (ER) and X- axis that measures the standard deviation (∞). The curve JKL drawn in the graph is the minimum variance frontier which combines the risk of a portfolio and anticipated return on portfolio to minimize the return deviation at distinct levels of return expected. On the efficient frontier, there are some points that are found either below or above it. Those portfolios that lie below the frontier provide an inadequate return for a given risk hence they are sub-optimal. In other words, they are attainable but insufficient. Conversely, those that lie to the right of the frontier have higher risks given a certain rate of return. Why a high risk with high return portfolio is not necessarily better than a low-risk low return portfolio. In theinvestment of securities, the main objective is to earn returns from a respective investment. High-risk with high returns is always avoided because they require high capital for investment. An investor can anticipate earning a lot from a given security but because of the fluctuations of the market prices and inflation, such investor can incur a loss simply because the future movements of the portfolio cannot be predicted (Fama 2009, p.452). Given an axiom that all investors fear risk, none of them will be willing to invest in a portfolio that has a high possibility of a loss. However, investors prefer a portfolio that has low-risk because they can be certain of the expected returns from a certain portfolio. Though they will not be getting the maximum returns they wish, they are able to get the returns for unforeseen future because the possibility of them incurring a loss is too low. This will make them become fearless when it comes to investing, unlike the high risk-return portfolio. Therefore, there is a high possibility of earning a loss in a high risk return portfolio than in low-risk return portfolio hence the opinion “high return portfolio is not necessarily better than a low-risk low return portfolio’’ Whether well-diversified portfolios are likely to be more efficient than individual stocks A diversified portfolio involves the buying of several securities that have different risks and returns. The quantity of shares in the portfolio is used to measure the extent of diversification. To precisely measure the diversification, the covariance of portfolios of investors is exploited. The risk to an investor is reduced by holding more than one stock. The other way of reducing the risk is through having diversification skill to choose correlated securities. Investments involve some maintenance funds and concentration to be able to perform healthily. Once an investor invests in a wide variety of securities, they are in a position to remain for a relatively long time without much safeguarding. This reduces fatigue and allows the investor to practice other economic activities and consequently reduce the stress in the market, unlike individual stocks that require high maintenance cost and time or their performance. An efficient, diversified portfolio gives the investor an option of spreading the securities for example to bonds, stocks and minerals. Since each of these assets displays different risks and returns, holding all these securities creates an unwavering portfolio that will consequently scale up their value in long-term. In contrary, individual stocks that do not allow the spread because of exclusive rights of the stockholders hence diversified portfolio is more efficient than the individual stocks. Preference for efficient portfolios would all investors to only invest in combination of an available risk-free asset and market portfolio Investors view the result of an investment in probability perspective; they perceive probable results in terms of some likelihood allotment. In evaluating the feasibility of a certain investment, they work basing on expected return and the standard deviation (risk). The two factors can be represented using a utility function as U= f(ER, σ²). In the function, ER represents expected return and σ² represents the risk that is a variance from the expected return (Portfolio management 2009) Risk-free assets are the assets that have a certain return in the market. Such assets give the investors certainty in their expected return given the assumption by the CAPM that almost all investors are risk averse. The market portfolio contains available security in an equal fraction of the value of it that exists in the market. Such portfolio exists where the market securities line touch the efficient frontier. Additionally, the market portfolio provides a link between the efficient combination of assets and a capital asset. The curve OPQ indicates all the expected return ER and standard deviation values which is obtained by combining with asset k and l. Such combination in terms of a proportion b of an asset l and 1-b) of combination l. The value where b is equal to 1 indicates pure investment in asset k while b is equal to zero implies investment in combination l. The curve OPQ in the graph is tangent to a capital line (GH) at point P. in an equilibrium position, and all curves should be tangent to the line of the capital market. The point P represents a point of efficient combination, and they are uninterrupted at this point. The absence of the tangency implies an intersection of line GH. In such a case, there is possibility that some securities will lie in front of the capital market line that is impossible because the capital market line GH represents the efficient boundary of the expected returns and the standard deviation. The tangency of curve OPQ to the market line leads to a formula that relates expected rate of return to several risk associated with assets in a combination P. for an economic meaning to be revealed, a relationship between asset k and the asset at combination P should be viewed in a similar way to the regression analysis is carried out (Carmichael & Alain 2008, p.148). Given a collection of data on returns of two investments and consequent points are then plotted on a graph, the result will be observed as in the figure below. The scatter of the observations S1around the average mean is a clear evidence of the risks of the asset. Some part is shown by SKP because of the underlying relationship with return combination P. The line of regression is a straight line (Brennan 2012, p.487). The response to S1 and the SP is a justification f consideration of variation in S1. This is the systematic risk. The rest of the returns that are uncorrelated with SP represent the unsystematic risk. From the above analysis, it can clearly be seen that efficient portfolios can lead to investors to invest in combination of risk-free assets and market portfolio to have high returns with associated low -risks. Works Cited "Brennan, M. J. (2012) The Optimal Number of Securities in a Risky Asset Portfolio When There are Fixed Costs of Transacting: Theory and Some Empirical Results,Journal of Financial and Quantitative Analysis10, 483–496." N.p., Web. 12 Apr. 2015. Available at:  http://journals.cambridge.org/abstract_S0022109000018421 Carmichael, Benoît, and Alain Coën. "Asset Pricing Models with Errors-in-variables."Journal of Empirical Finance 3 (2008): pp 120-164. Fama, Eugene F. 2009. "Multifactor Portfolio Efficiency and Multifactor Asset Pricing." Journal of Financial and Quantitative Analysis. 31:4, pp. 441-465 (n.d.). "Finance: Efficient Frontier and Capital Market Line (CML)." Finance. Astha, 28 Sept. 2008. Web. 12 Apr. 2015. Available at: http://riskencyclopedia.com/articles/capital_market_line/ Goetzmann, W. "MPPM540: Chapter 2." Will Goetzmanns Home Page. N.p., 9 Apr. 2015. Web. 12 Apr. 2015. Available at: http://viking.som.yale.edu/will/finman540/classnotes/class2.html Grauer, Robert R. Asset Pricing Theory and Tests. Volume 2. Cheltenham: Edward Elgar Publishing Limited, 2011. "Capital Asset Pricing Model (CAPM) Definition." Investopedia. N.p., n.d. Web. 12 Apr. 2015. [Online] Available at: http://riskencyclopedia.com/articles/capital_asset_pricing_model/ Ibbotson, Roger G., and Carol L. Fall. "The United States Market Wealth Portfolio."Journal of Portfolio Management (2009): n. pag. Print. Read More