Portfolio Mangaemnet Skills

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Introduction

This assignment will contain full analysis of the nine underlying security assets as forming a portfolio with FTSE 100 Index. Securities are analyzed and compared of the historical data from 2006 to 2012 by descriptive statistic tools. The second and third part use Markowitz procedure and Single index model to simulate portfolio in order to achieve the optimal risky portfolio. In addition, the final part summarizes the major findings through the two methods to simulate the portfolio and illustrate their implications for investors.

Normal Distribution Analysis

The descriptive statistics include mean, standard deviation, minimum and maximum return, skewness and kurtosis, which are derived by using Eviews. The variety statistics analysis tools can have corresponding meanings on investment. In portfolio analysis, mean is used to measure the expected return of individual assets or portfolio. The average return of FTSE100 is 0.0655% during the 6 years since 2006. Finance sector and tobacco had the lowest and highest figure that were -1.3932% and 1.1781% respectively.

Standard deviation (SD) is another basic mathematics measurement to quantify the risk of assets. The finance company possesses the highest SD that is 9.30 and the largest difference between the maximum and minimum returns. On the contrary, the SD of Utilities reaches 3.36, which indicates that the return of finance has the largest fluctuation among the nine securities. Utilities security has the lowest volatility during those years. According to Table 1, most of the securities have lower expected return and higher volatility than that of FTSE100.

Table 1. Descriptive Analysis

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From investment perspective, it is difficult to find a company whose return is perfectly consistent to normally distribution. Skewness and Kurtosis are common indicators to describe the normality of distribution. Skewness estimates the asymmetry of the probability distribution (Abramowitz, 1972). All the securities have the negative skewness, which indicates that they are asymmetry distribute. As for Kurtosis, it measures the "tailed-ness" of the probability distribution of a real-valued random variable, the test results also need to be compared with normal distribution. Besides, outliers can also be seen from the kurtosis figure. Except tobacco security, the rest have extreme outliers returns (kurtosis > 3.0). The abnormal fluctuation of securities and time-series of data sets could be the reason to drive the abnormal kurtosis.

Time-series of security returns often demonstrate volatility clustering. As noted by Mandelbrot (1963), "large changes tend to be followed by large changes”. In terms of the nine securities, there has a very high changing of volatility period around 2008, because the financial crisis around this period (Appendix 1). Through observation of the plot, the high volatility fluctuation of the return seems to start from a declining. The finance security shows a very high changing of volatilities. It means that the huge fluctuation of the security price lead to big uncertainty for investors.

As mentioned before, most of the securities are showing fat tail distribution in varies degrees. Normally, the ‘fatter’ the tail, the higher probability to receive extreme values, such as, the media and retailer security. And the utilities and tobacco security has a high level of fitness to normal distribution (Appendix 2). Through observations, the nine securities have various levels of return and SD. Hence, they could be used to form a portfolio by adjusting weight.

Mean Variance Optimization Model

In this case, the portfolio formed by 10 risky assets in different sectors. Portfolio manager uses the diversification strategies to diversify the systematic risk into a basket of securities. The long-constraint and long-short efficient frontier diagram can plot by Markowitz procedure. Furthermore, the optimal portfolio determines by excel solver to maximize the Sharp ratio.

In order to complete the preparatory work, using excel data analysis receiving the covariance matrix by monthly data excessed return sets of the 9 securities and FTSE 100 market index. Fill the covariance matrix with the symmetry, the result of covariance matrix is shown in Table 2. Noted that the monthly risk-free rate applies for 0.0067%^[1], that is according to the 5 years UK Gilts yield.

Table 2. Covariance-Variance Matrix

For plotting portfolio’s efficient frontier, excel solver uses as the tool estimating the standard deviation. Sharpe ratio and weight of each security within the portfolio estimated by designed excessed returns (Table 3 and Table 4). The exact minimum variance point cannot be direct acquired by excel solver. The real MVP point can be estimated around someone numbers.