Central Assumptions Made in Mean-Variance Analysis and Capital Asset Pricing Model - Essay Example

CENTRAL ASSUMPTIONS MADE IN MEAN-VARIANCE ANALYSIS AND CAPITAL ASET PRICING MODEL By Foundation Department: Central Assumptions Made in Mean-Variance Analysis and Capital Asset Pricing Model Introduction In mean variance analysis and capital asset pricing model, a central assumption is made that investors prefer to invest in the most efficient portfolios available to them at the time of investment. In the capital asset pricing model, several assumptions are made such; the existence of risk free asset, investors are rational, investors are risk averse and investors maximize the utility of the end period (Fama and French, 2004:216). Portfolio refers to a combination of assets held by investors for investment purposes. Efficient portfolio refers to a portfolio that yields the greatest expected return for a given level of risk or the portfolio that yields the lowest risk for a given expected return. The expected return also referred to as portfolio mean refers to the minimum amount of return that investors expects from a given portfolio. The portfolio risk or the variance shows the deviation of the returns from the expected. Portfolios that have a high level of return cannot be diversified further to increase the expected rate of return without increasing the level of risk. The same case applies, as one cannot reduce the level of risk without decreasing the level of the expected return. In reality, the investor wishes to maximize the expected returns from the portfolio and thus he would place all his funds in the portfolios that yield the maximum amounts of returns (Markowitz 1952:79). To achieve this, the investor should diversify his portfolios as well as maximize the expected risk. Therefore, a high risk- high return portfolio is more preferred by the investors because it yields the highest level of the returns that the investors expect. Nevertheless, this portfolio carries a higher level of risk and therefore sometimes can fail to yield any returns depending with the performance of the portfolios. The low return-low risk portfolio on the other hand gives a low expected return to the investors, which are more certain because the level of deviation (risk) is low. This explains why sometimes the low return-low risk portfolios perform better than higher return-high risk and thus high return-high risk portfolios are not necessarily better than the low return-low risk portfolios. Comparison of a diversified portfolio and individual stock The level of risk can be greatly reduced through portfolio diversification (Goetz man, 2008:433). Diversification is the combining of assets with returns that are considerably not perfectly positively correlated to bring down the aggregate risk of entire equity portfolio. Therefore, the investor tries to invest in well-diversified portfolios. The level of risk diversifiable risk reduces as the number of stock increases from one to about eight (stratman2008:354), at this point nearly all the diversifiable risks are eliminated. As such, a well-diversified stock of about eight to twelve stocks can adequately yield the highest return (Statman, 1787:354). Diversification can only be increased if the marginal costs of diversification are lower than the marginal benefits. Diversification of assets that are positively correlated does not reduce risk at all and investors shy away from increasing their investments in such type of assets because if one asset does not yield the expected return, all the other assets will not yield the expected return. A well-diversified portfolio is the one that greatly reduces the viability (risk) of the returns. If one of the assets in the portfolio does perform better the other assets will still perform better and the degree of loss to the investor is greatly reduced. Portfolios with which are positively correlated yields a higher standard deviation symbolizing of a higher rate of risk and thus they will greatly make the level of expected returns more volatile and the investor might incur a bigger financial loss if the class of the asset does not perform well. In the case of an individual stock, the level of risk depends entirely on the asset and its performance is not affected by the other assets, but a poor performance means that the investor will incur a loss with no compensation from other assets. The individual stocks are sometimes more certain than a diversified portfolio, but the fact that they can result to a bigger financial investor makes them inferior to a well-diversified portfolio. This is the reason why investors prefer a well-diversified portfolio so as to maximize the returns as well as minimize the risks associated with the assets, therefore a well-diversified portfolio is better than individual stocks. The fact that all the investors want to maximize the returns and minimize the risks does not mean that all invest will invest in the efficient portfolio. The capital asset pricing model assumes that there exist a risk-free asset and investors would want to invest in it, but the choice of investments among the investors depends on several factors apart from the returns. In the capital asset pricing model, investors are assumed to be rational and they choose among alternative portfolios depending on each portfolio expected return and standard deviation. The different factors that affect investors include the age, gender, income, wealth and education. The investment experience of different investors will also play a big role in determining the type of the asset, which an investor will invest in. This is the reason why most of the retired investors hold more asset than those who were in non-professional employment (Goetman, 2008:435). Therefore, not all the investors are likely to invest in a combination of the available risk free asset and the market portfolio. Accessed from http://www.edupristine.com/wp-content/uploads/2013/04/efficient_frontier.png The above figure shows the market efficient frontier, which shows the portfolio with the highest return on a given risk or the lowest risk at a given return. The efficient set of investments will therefore be from the point of tangency of the capital market line (best possible CAL) and the efficient frontier going upwards (financial and qualitative analysis.p354). Any point on the efficient frontier dominates all other points of the individual assets. The security market line is the line that shows the pricing of all assets if the market is assumed to be at equilibrium. It represents a measure of the required rate of return if the investor were to undertake a certain amount of risk. Accessed from http://stockshastra.moneyworks4me.com/wp-content/uploads/2010/08/Risk-Return-graph.png The risk and the return relationship in the figure above shows that higher the risk than then the higher the rate of the expected return, and the lower the rate of the expected return the lower the risk. This shows that for a given investment, the level of risk will be of consideration to the investor. The risk altitude of different investors also influences the choice they make for their investments. Depending on the risk profile, different investors will invest in different portfolios given the same risk and the returns. This is because a risk adverse investor will always prefer a less risky investment that consequently will have a low rate of return. While the risk seeker investor will invest in the project that has the highest level of risk because he expects higher returns from that investment. The rate of return from the investments does not greatly affect the risk seeker investor when making investment and efficient decision, but his main concern in the level of risk. The last class of investors’ attitude is the risk indifference investors. This type of investor does not care about the level of risk and will invest in an asset provided the expected return is acceptable. This also explains why not all of the investors will invest in the risk-free asset and the give rate market of return (Markowitz, 1959:254). In the capital asset pricing model, a general assumption is that there exists a risk free asset, but practically the risk-free asset does not exist. This is a reason why even the investor will be given to the risk-free asset; they will always ignore it and make their choices of investments based on other factors such as the interest rates and market condition like the inflation rate. This is the reason why not all the investors will invest in combination of risk free asset and the market return. The capital market is also assumed to be perfect. This is not practical since today’s markets are always inefficient and therefore the investors will always strive to invest in a portfolio with the maximum expected returns (Andrei, 2000:156). This is the reason behind the investors market segmentation theory which recognizes that invests have preferred habits dictated by saving and investments flow and thus they have a preferred investment market section and will not move away from it despite the existence of risk-free asset or not. References Andrei Shleifer, 2000. Inefficient Markets: An Introduction to Behavioral Finance. Clarendon Lectures in Economic Fama, E., French. 2004. “The Capital Asset Pricing Model: Theory and Evidence”, Journal of Economic Perspectives, Vol. 18, No. 3, pp. 25-46 Goetzmann, W., Kumar, A. 2008. “Equity Portfolio Diversification”, Review of Finance, Vol. 12, No. 3, pp. 433-463 Markowitz, H. 1952. “Portfolio Selection”, Journal of Finance, Vol. 7, No. 1, pp. 77-91 Markowitz, H.M.1959. Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley and Sons. Sharpe, W. 1964. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”, Journal of Finance, Vol. 19, No. 3, pp. 425-442 Statman, M. 1987. “How Many Stocks Make a Diversified Portfolio?”, Journal of Financial and Quantitative Analysis, Vol. 22, No. 3, pp. 353-363 Read More