The Concept of Diversification and Markowitz Efficient Frontier Model - Essay Example

Portfolio Analysis Outline the concept of diversification. Use a numerical example of your own design to illustrate the concept. Answer: Diversification: As we know that an asset held as part of a portfolio usually is less risky than the same asset held in isolation. Accordingly, most financial assets are held as parts of portfolios. Banks, pension funds, insurance companies, and other financial institutions are required by law to hold diversified portfolios. Even individual investors - at least those whose security holdings constitute a significant part of their total wealth - generally hold portfolios, not the stock of only firm. This is being the case from an investor's standpoint the fact that a particular stock goes up or down in not very important; what is important is the return on his or her portfolio, and the portfolio's risk. Logically, then, the risk and return of an individual security should be analysed in terms of how that security affects the risk and return of a portfolio in which it is held. As mentioned in Finance for Non-Financial Managers by Lawrence W Tuller, Diversifiable risk is also known as company-specific, or unsystematic, risk. Market risk is also known as non diversifiable, or systematic, or beta, risk; it is that risk remains after diversification. Diversifiable risk is caused by such random events as lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm. Since these events are random, their effects on portfolio can be eliminated by diversification- bad events in one firm will be offset by good events in another. The riskiness of a portfolios declines as the number of stocks in the portfolio increases. The smaller the correlation coefficient (the movements of two variables with respect to each other), the lower the risk in a large portfolio. If we could find a set of stocks whose correlation were negative or zero, all risk could be eliminated. For example: Consider Stock M with the beta coefficient of 2 i.e. it is 2 times more responsive to the change in the stock market and Stock N with beta coefficient of 1. Individually Stock M is riskier than Stock N. An investor who is risk averse will not buy such stock, but if a portfolio is concerned then the risk is reduced. This is due to the diversification of risk in a portfolio. (2) Explain carefully how diversification leads to the construction of the Markowitz efficient frontier. Answer: As explained by Eugene Brigham and Gapenski, the computational procedure for determining the efficient set of portfolios was developed by Harry Markowitz and first reported in his article "Portfolio Selection", Journal of Finance, March 1952. Markowitz developed the basic concepts of portfolio theory. With only two assets, the feasible set of portfolios is a point within the curve. However if we increase the number of assets, we would obtain an area under the curve. The points A,B,C and D represent single securities. All other points with in the curve, including its boundaries, represent attainable set. The above Curve boundary from A to D however defines the efficient set of portfolios, which is also called efficient frontier. Portfolios to the left of the efficient set are not possible because they lie outside the attainable set. Portfolios to the right of the boundary line (interior portfolios) are inefficient because some other portfolio would provide either a higher return with the same degree of risk or a lower risk for the same rate of return. Markowitz efficient frontier model. The optimal portfolio for each investor is found at the tangency point between the efficient set of portfolio and one of the investor's indifference curves. This tangency point marks the highest level of satisfaction the investor can attain. The investor's risk/return trade off function is based on the standard economic concepts of utility theory and the indifference curves. Here we have 2 Stock holders. Mr Y and Mr Z. Mr Y is more risk averse and chooses a portfolio with lower expected return (about 5.5 %) but a riskiness of only = 5%. Mr Z picks a portfolio that provides an expected return of about 7.5%, but has a risk of about = 7%. This show that Mr Z's portfolio is more risky as his indifference curve is higher than that of MR Y. Therefore his return is also more. (3) Select 5 shares from the FTSE 100 to be placed in an equally weighted mini-portfolio for the next year. Explain the rationale for choosing the shares. Answer: Chosen Stocks: Gilead Sciences (GILD) 20% beta =1.46, k=59% Merrill Lynch (MER) 20% beta=1.23 k=19% Apple Computer (AAPL) 20% beta=1.9 k=43% Caterpillar (CAT) 20% beta=1.46 k= 25% Lehman Brothers (LEH) 20% beta=1.31 k= 24% An optimal portfolio is when there is a feasible ratio between the risk and return. Optimal portfolio as discussed in the previous question is that combination of the risk and return where the risk/return ratio falls in the feasible area in the Markowitz efficient frontier model. However in real world the efficient frontier is not easy to achieve therefore while making a portfolio the main objective is to attain such a risk/return ratio which falls within the feasible area and provides the maximum return on the given risk. Therefore, while choosing these shares for the portfolio the main emphasis is on the maximum return on the given risk. Risk here is determined by the beta coefficients of the individual stocks which further carries on to calculate the portfolio's beta coefficient. Beta for a portfolio is calculated as follows: b = WiBi Where: W is the fraction of the portfolio invested in the stock. Bi is the beta coefficient of the individual stock. And comes out to be 1.472 from the formula. With the above discussion in consideration the risk 1.472 is acceptable with the return, calculated in the next question, and therefore the above coefficient is formed. (4) Assuming no transactions costs, calculate the return of the mini-portfolio return over a one-month period this term. Comment on the result. State clearly relevant dates and where your data is sourced from. Answer: Rate of Return: K (cap) = Wi Ki = .20x59+.20x19+ .20x43+.20x25+ .20x24 = 34% As from the result, the rate of return is 34%. Also note that the beta coefficient calculated in the previous question is 1.472. Therefore from the above discussion the rate of return is more than acceptable with the given risk. Source: http://www.investors.com/yahoofinance/YahooCheckup.aspt=GILD, 06/03/06. References: Brigham,Eugene, Gapenski, Financial Management, 8th Edition, Dryden Press, 1997, 150-190. http://www.investors.com/yahoofinance/YahooCheckup.aspt=GILD, 06/03/06 Lawrence W Tuller, Finance for Non-Financial Managers,1996, 200-250. Read More