Modern Portfolio Theory - Assignment Example

Name : xxxxxxxxxxx Institution : xxxxxxxxxxx Title : Tutor : xxxxxxxxxxx Course : xxxxxxxxxxx @2010 Modern portfolio theory Introduction Modern portfolio theory is an investment theory which maximizes expected portfolio return relation to a specified amount of portfolio risk, or in equal manner reduces risk for a specified level of return through diligently selecting the proportions of the various range of assets. Modern portfolio theory corresponds to a formulation of the concept of diversification during investing, having the target of picking on a selection of investment assets that possess generally lower risk as compared to an individual asset. In modern portfolio theory models, the return of an asset as normally distributed function (or greatly general as an random variable that is elliptically distributed), explains a risk as return’s standard deviation, and models a portfolio as a weighted combination of assets in order that a portfolio return is the weighted combination of the returns of assets. By putting together different types of assets whose returns may not be positively related or correlated, modern portfolio theory seeks fundamentally to decrease the total variance of the return of the portfolio. Modern portfolio theory is applied under the assumption that markets are efficient and investors are rational. Assumptions The modern portfolio theory framework has many assumptions concerning markets and investors. Others are very explicit in the equations, for example the utilization of the model returns of normal distributions, whereas others are implicit which includes the neglect of transaction fee and taxes. None of the assumptions are true entirely and every one of them has some degree of modern portfolio theory (Swedroe, 2007). According to Elton and Gruber (1997), the first assumption is that returns on assets are normally jointly distributed random variables. It is widely noticed that returns in other markets and equity are not usually normally distributed. Large variations of about three to six standard deviation from the mean occur in the market far more often than the usual distribution assumption would predict. While the model can be supported by the assumption that any return distribution that is jointly elliptical, distributions that are joint elliptical are symmetrical on the other hand return on asset empirically are not. Correlations between assets are constant and fixed forever. Correlations largely are determined by systematic relationships between the asset underlying and the subsequent change when the relationships are altered for example when an overall market crash or a country declares war on another. In times of crisis that are financially oriented all assets tend towards becoming positively correlated since they all move down together, that is modern portfolio theory breaks down precisely during a time when investors most need protection from the risk. It is also assumed that all investors have the target to maximize economic utility that is, making much money as possible despite of any other prevailing considerations. It is a major assumption made in the efficient market hypothesis on which modern portfolio theory depends on. All the investors are risk averse and rational. This is another assumption found in the efficient market hypothesis; on the other hand it is known economic behavior that market participants are normally not rational. It does not apply for group behavior or to those investors who accept low returns for higher risk. Some stock traders will pay for risk the same way casino gamblers pay for risk. It is also worth noting that all the investors in a particular market have access to the same information virtually at the same time. This is also found in the efficient market hypothesis. Often real markets have information asymmetry, those who are better informed and insider trading. It is assumed that the investors possess an accurate conception of return s which are possible, in other words the investors’ probability beliefs fit in the true distribution of returns. Differently it is possible that expectations of investors are biased resulting in market prices being informally inefficient. This is found in the behavioral finance field which makes use psychological assumptions. There are no transaction costs or taxes. Real financially products are subjected to both transaction costs like broker fee and taxes, and considering this will change what the optimum portfolio is made up of. The other assumptions states that investors price takers and that is; the prices are not influenced by their actions. In practice substantially large purchases or sales of individual assets may shift the asset’s market prices and others through cross-elasticity of demand. An investor can not even be in a position to assemble to put together optimal portfolio theoretically in case the market moves greatly during the buying of the required securities. It is also a supposition that any investor can borrow and lend an unlimited amount at the risk free rate of interest. Practically all investors have a credit limit. The final assumptions states that all the securities can be divided into parcel of any size. In practice shares cannot be sold or bought in fraction and some possess minimum order sizes. Identification of the optimal The risk in a portfolio of individual stock that are diverse will be lower than the inherent risk in the holding any one of the individual stocks so long as the risks that come along with various stocks are not directly related. If a portfolio that contains two risky stocks: one that pays off when it does not rain and another that pays off when it rains. A portfolio that possess both assets will constantly pay off despite of whether it rains or it does not rain. Markowitz demonstrated that investment was not merely picking stocks but on the other hand choosing the optimal combination of stocks. Modern portfolio theory stipulates that the risk for individual stock returns possess two components which are: unsystematic and systematic risk. Systematic risks are market risks that are impossible to diversify away which may include wars, recessions and interest rates (Schwartz & Francioni, 2004). According to Swedroe, L. (2007), unsystematic risk is specific to each individual stocks and it is possible to diversify them away when the number stocks in your portfolio is substantially increased. For a portfolio that is well diversified the average deviation from the mean that is the risk, of each stock has little contribution to portfolio risk. Overall portfolio risk is determined by the difference of the covariance between levels of individual stocks. As a result of this, investors benefit from holding diversified portfolio as compared to individual stocks. The task that remains is how to identify the best level of diversification after understanding the benefit diversification. In every level of return, there exist one portfolio that provides the lowest risk possible, and for each risk, there is a portfolio that offers the highest return. The combinations can be plotted on a graph and the curve that result is the efficient frontier. The graph below demonstrates the substantial frontier for two stocks-a low return/low risk consumer product stock (Coca cola) and a high return/high risk technology stock (Satchwel, 2002). Any portfolio that is found on the upper part of the curve is efficient; meaning that it gives maximum return expected for a particular level of stock. An investor who is rational will only hold a portfolio that is found somewhere on the efficient frontier. The maximum amount of risk that the investor will take on will determine the position of the portfolio on the line. Modern portfolio theory suggests that combining a stock portfolio with a risk-free asset that is found on the efficient frontier, the purchase of which is funded by borrowing, will actually increase returns over the efficient frontier (Goetzmann, 2009). Mathematical approach: Suppose an investor is putting together a portfolio that has that possess both types of assets: w potion of the portfolio comprises of risky asset and (1-w) composes of risk-free asset. As a result, the return of the portfolio ( p R ) is defined as below: p r rf R wR (1w) R Where r R return of the risky asset rf R return of the risk-free asset, i.e. the risk-free rate Limitation of the modern portfolio theory Modern portfolio theory has had a remarkable impact on how managers perceive risk, portfolio management and return; despite of this the portfolio has its own shortcoming in the real world. It usually needs investors to rethink the notion of risk. At times it requires that the investor to take on a perceived investor that it is risky for reducing overall risk. That can be very difficult investors who are not familiar with the advantage of sophisticated techniques of portfolio management (Sumnicht, 2009). Modern portfolio has the assumption that it is possible to pick stocks whose individual performance is independent of other investments in the portfolio. On the other hand historians have demonstrated there is no existence of such instruments; during times of stress in the market, apparently independent investment act as though they are related. In the same way it is logical to borrow and hold an asset that is risk free increasing your returns but finding the asset is another task. Most assets that are considered to be risk free in real sense they are not including government bonds. There is also the matter concerning how many number of stocks required for diversification. It is hard to determine how many stocks are enough to diversify away unsystematic risk. Mutual funds will possess dozens and dozens of stocks. Conclusion In this perspective we can conclude that losses in 2008 and 2009 during the recession period cannot be attributed to lack of diversification or failure to diversify because as it has been seen the market it is hard to beat and people who beat it are people involved in risk that is above average, but despite of this, they can be affected when the market turn down. Bibliography Swedroe, L. (2007). The wrong kind of diversification’, Accounting Today, Vol.21, No.7, pp. 14-17. Sumnicht, V. (2009). MPT principles valid after 5 decades’, Journal of Financial Planning, Jun2009 Trends in Investing, pp.16-18. Elton, E.J., Gruber, M.J. (1997). Modern portfolio theory, 1950 to date’, Journal of Banking and Finance, Vol. 21, No.11/12, pp.1743-1759 Goetzmann, W. N., 2009, Modern Portfolio Theory and Investment Analysis, 7Th Ed. Wiley India Pvt. Ltd. Satchwel, C., 2002, Pattern recognition and trading decisions. McGraw-Hill Professional, Melbourne. Lossen U., 2007, Portfolio Strategies of Private Equity Firms: Theory and Evidence. DUV, Sheffield. Schwartz, R A. & Francioni, R., 2004, Equity markets in action: the fundamentals of liquidity, market structure & trading, Volume 1. John Wiley and Sons, London. Read More