Security Analysis and Portfolio Management - Report Example

Security analysis and portfolio management Part A Introduction Every stock buyer in the market would need to find a better way of managing his portfolio, through efficient diversification on the stocks he or she buys in the market. This happens because the source of risks in the market is usually varied hence calling for diversification for efficiency. Intuitively, management through portfolio diversification exposes an individual to higher returns, with reduction in the number or risks associated. This brings the need for building an efficient frontier, which provides useful information on how to reduce risks while still maintaining reasonable returns for the investors (Geltner et al, 2014, 90). Building an efficient frontier requires the investor to acknowledge minimum variance portfolio which necessarily boosts the benefits. The three inputs required for appraising the minimum variance portfolio include standard deviation, annualized expected return and correlations. Before accessing the minimum variance portfolio, it is important to consider knowing how much is invested in each of the assets contained in the portfolio. This refers to the expected return on a portfolio which is amount invested in each asset as a percentage of the total funds associated with the portfolio. Calculating for expected return on a portfolio aids in determining the weighted average for the expected returns of the stocks found in the portfolio. The formula for expected return on a portfolio to be used in achieving the objective of this report is as follows: Further, this report also compiles the determination of standard deviation portfolio which also proves significant in efficient diversification. It gives information on the extent to which movements between the pair of assets influence each other in the market. This implicates the usefulness of determining the correlation between any two assets which is calculated with the following formula: = = -.995 After finding correlation, it makes it easy to determine the standard deviation of the portfolio through the following If N=2, The standard deviation portfolio and expected return of portfolio (%) guides an individual in designing the efficient frontier curve usually used for diversification. The efficient frontier curve is a graph for return (expected return of portfolio (%) vs risk (standard deviation portfolio). This report presents a suitable model that can be helpful to an investor who would like to ensure efficient diversification. It presents a study of portfolio comprising of stock from Google Inc and Amazon Inc, whereby 10-years of monthly stock price history market capitalization stocks were obtained from Yahoo Finance. These companies prove as significant prototypical for the study because they are two of the major popular market capitalization stocks, which most of the investors identify with. Method 10 years monthly historical stock prices from two US large market capitalization stock prices were downloaded from Yahoo finance. The dates of the two stocks were aligned to ensure that the returns of the two stocks obtained were from the same month. The historical monthly returns of these stocks were calculated using the adjusted closing prices. Further, the standard deviation was also calculated (Evensky et al, 2011, 76). Another important subsequent step was the calculation of the annualized expected returns and the correlation of the returns. The changing weights of both Microsoft Inc and Amazon Inc were also determined. The three inputs obtained, annualized expected returns, standard deviation and correlation, besides the changing weight of the two stocks, were manipulated to help in building an efficient frontier for the portfolio. Results The following is the table showing the calculated inputs from the data downloaded:   microsoft inc amazon in Monthly Return (%) 0.75 2.45 Standard Deviation 6.7655556 12.10623       Annualized Exp Return (%) 9.05 29.37       Correlation 0.3455236         Wx 87.13% Wy 12.87%       Expected Return of Portfolio (%) 11.67 Standard Dev of Portfolio 6.59724 The table shows that the extent of correlation between Microsoft Inc stock and Amazon inc stocks, both making up the portfolio, was 0.345 while the expected return of portfolio was 11.67 and the standard deviation 6.59724. The 0.345 calculated for correlation shows the type of correlation between the was positive but not perfectly correlated. Wx and Wy represent weight in the stocks. Microsoft INC had a larger weight of 87.13% as compared to that of Amazon, 12.87%. The figures obtained above helped in building the efficient frontier curve, after finding the SD portfolio and Expected Return of Portfolio (%) as shown in the excel spreadsheet attached. The following is the efficient frontier curve: Observations made from the curve are as follows: The frontier shows that portfolio marked with a black star (risk of 7 and return of 15) dominates all the other efficient portfolio depicted in the efficient set with optimal risks and optimal returns The rest of the points along the curve (representing other efficient portfolio) indicate some other risky assets. Lower than the black starred point the investor experiences low returns with low risk and on the upper side, the investor experiences high risk with high returns. Discussion The result depict a better way of efficiently diversifying the two stocks, Microsoft Inc and Amazon Inc. Of all the two stocks, Amazons Inc. has the highest monthly return percentage of 2.45% against that registered by Microsoft Inc, 0.785%. This called for the need of building efficient frontier curve, which helped in determining a better combination of the two stocks that would help in optimizing the returns while maintaining lower risks. Intuitively, this helped in efficient diversification of the stock through plotting the efficient frontier, for expected return against standard deviation of the minimum-variance portfolio. Even though the correlation is positive, the results shows that the two are not perfectly correlated thereby resulting to the efficient frontier curve that curves to the left. The line shown on the graph shows the tangent line representing the optimal risky portfolio. The black starred point on the graph assures the investor of better risk premium for given lower risk amount as compared to any other point on the graph (Bacon,2013, 57). . The result shows that at a lower risk of 7, the investor is assured of an optimal return of 15. Further, the efficient frontier curve also proves useful by showing the investor the risks and corresponding return associated with other points, above and below the optima risky portfolio. Part b In this part of the report, the main objective was to investigate how treynor ratio, appraisal ratio and sharpe ratio contributes to security analysis of mutual funds. Investing in mutual funds in the market normally requires the investor to evaluate the risks associated with the investment. This occurs because the returns from the mutual funds rely on the quality and quantity of the associated risks. In order to evaluate the risks effectively, an investor requires to keep in track of the three ratios associated. These ratios include appraisal ratio, treynor ratio and sharpe ratio. Determining the appraisal ratio help the investor in accessing the picking ability of the investment done on the mutual fund. The ratio gives an investor clue on the performance of the mutual fund on the basis of picking ability of the fund and the associated risks. The process of calculating appraisal ratio involves comparing the mutual fund’s alpha to the residual standard deviation. Further, Treynor ratio helps in measuring the excess earned on the return on a riskless investment per each unit of market risk (McMillan, 2011, 68). The investor can use this ratio as a measure of the adjusted risk on the return, with reference to the systematic risks. The following is the formula for calculating Treynor ratio: (Average Return of the Portfolio - Average Return of the Risk-Free Rate) / Beta of the Portfolio In this ratio, beta of the portfolio is used to represent the unit of market risks. Sharpe ratios represents another risk –adjusted measure for the excess return received as a result of experiencing an extra volatility in a riskier market. This is the most critical ratio, among the other three, since it controls the compensation for any additional risks experienced with a risk free-asset. The following is the formula for calculating sharpe ratio: S(x)= rx – Rf)/StdDev(x) (whereby x is the investment, rx is the average rate of return of the investment, Rf is the best available rate of return of the risk-free security, stdDev(x) is the standard deviation of rx. The report uses the ratio to analyse the security associated with investing on Vanguard High-Yield Corporate Inv (VWEHX), a US-based mutual fund, for a period of 10 years. The corresponding fama-French (FF) factors are also used to help in calculating the ratios. Method Monthly historical stock prices, for a period of 10 years was downloaded for Vanguard High-Yield Corporate Inv (VWEHX), which represents a US mutual fund. The historical monthly returns of these stocks were calculated using the adjusted closing prices. The fama-French (FF) factors were then downloaded. The dates of the two (Monthly historical stock prices) and fama-French were aligned to ensure that the returns of the two stocks obtained were from the same month. The LINEST function was then run to aid in estimating the factor sensitivities for the CAPM model and the FF mode (Fabozzi, 2011, 59). Further, the performance measurement for the fund was calculated from the estimates of the factor sensitivities. The annualized alpha when the CAPM is used as the benchmark model was also evaluated. The same was done on the beta when FF model was used as the benchmark model. The sharpe ratio, treynor ratio and appraisal ratio were then calculated from the above results. Results CAPM The following is a table showing calculation of the CAPM, Beta and alfa   CAPM           Beta Alfa Coefficient 0.43 0.20 Standard Error 0.04 0.18 R2/SE(y) 0.49 1.91 F/n 112.17 117.00   408.58 426.16 Appraisal ratio = alpha/standard error = 0.20/0.18 = 1.11 Fama French The following is a table showing calculation when the Fama French was used as the benchmark model   Fama French         beta_hml beta_smb beta_mkt alpha Coefficient -0.13 -0.03 0.46 0.20 Standard Error 0.08 0.09 0.05 0.18 R2/SE(y) 0.50 1.90 #N/A #N/A F/n 38.48 115.00 #N/A #N/A   418.18 416.56 #N/A #N/A Sharpe ratio The following is a Sharpe ratio table showing the results obtained for the sharpe ratio Sharpe Ratio     Average Excess Return   0.457 Standard Deviation   2.660 Sharpe Ratio   0.172 The mutual fund witnessed a sharpe ratio of 0.172 after resulting to an average excess return of 0.457 and standard deviation of 2.660. Treynor ratio The treynor ratio = Average Return of the Portfolio - Average Return of the Risk-Free Rate) / Beta of the Portfolio (0.585 – 0.128)/0.455 = 1.005 Consequently, the mutual fund experienced a ratio of 1.005 over the period of 10 years. The following is a table showing the calculation of Treynor ratio as obtained from excel: Treynor Ratio     Average Return   0.585 Risk Free Rate   0.128 Beta   0.455 Treynor Ratio   1.005 Discussion Using the three rations, treynor ratio, sharpe ratio and appraisal ratio led to the achievement of the objectives , which was to analyze the security associated with investment in Vanguard High-Yield Corporate Inv (VWEHX). The results show that the mutual fund guarantees its investors of enough security even in the midst of risks. The calculation of the sharpe ratio, resulting to 0.172 shows that the mutual fund not good when it comes to generating returns on the basis of risk adjusted (Smith & Shawky, 2012, 96). The ratio shows that the mutual fund generated returns with reference to risk-adjusted. However, the use of Treynor ratio upholds good image of the mutual fund based on the generated returns. The mutual fund experienced a treynor ratio of 1.005 shows that it was able to generate higher return on the risk-adjusted basis. Determining the ability of the investment on the funds to pick involved the use of the appraisal ratio. The ratios show that the mutual fund assures the investor of security of their funds as shown in the resulting value of 1.11. 1.11 indicates a better performance from the manager as it shows that the mutual fund had higher chances for picking even in the presence of the unsystematic risks (Cernauskas & Tarantino, 2011, 145). Consequently, considering the ratios for the 10-year period, an investor should consider choosing this mutual fund because the security analysis favors its operations. Bibliography McMillan, M. G. (2011). Investments: Principles of portfolio and equity analysis. Hoboken, N.J: Wiley. Bacon, C. R. (2013). Practical portfolio performance measurement and attribution. Hoboken, N.J: Wiley. Evensky, H., Horan, S. M., & Robinson, T. R. (2011). The new wealth management: The financial advisors guide to managing and investing client assets. Hoboken: John Wiley & Sons. Tarantino, A., & Cernauskas, D. (2011). Essentials of risk management in finance. Hoboken, N.J: John Wiley & Sons. Smith, D. M., & Shawky, H. A. (2012). Institutional money management: An inside look at strategies, players, and practices. Hoboken, NJ: Wiley. Essvale Corporation. (2009). Business knowledge for IT in hedge funds: A complete handbook for IT professionals. London: Essvale Corp. Fabozzi, F. J. (2001). Bond portfolio management. New Hope, Pa: Frank J. Fabozzi Assoc. Danthine, J.-P., & Donaldson, J. B. (2006). Intermediate financial theory. Amsterdam: Elsevier. Geltner, D., Miller, N. G., Clayton, J., & Eichholtz, P. (2014). Commercial real estate: Analysis and investments. Read More