Portfolio Management - Report Example

Portfolio Management al affiliation: The major objective of financial economist and market professionals is to estimate or determine the performance of hedge funds, mutual funds as well as any financial investment and quantification of risk/return investment strategies characteristics (Barras and Wermers 2007). After fund selection, there is always quantifying of the past performance over a given period of time. By definition, Return is an asset’s rate of change in a given period of time while Risk is defined as the uncertainty on how the security price as well as the return could be at a given point (Sornette et al. 2007). Return and risk describes the whole CAPM and in this case, the characterization of risk is through variance (Fabozzi 1998). Various combination of return and risk/return as well as combination of various risks with securities it leads to an investor to attain a security market. The more risk an individual takes the more he benefits or rewarded (Brentani 2003). Evaluation of portfolio performance involves applying of benchmark or index and in this case, there is comparison of the portfolios return. Thus there is a consideration of the methods applied in measuring market return in case there is use of indices as benchmarks (Levine 2005). Investors benchmark their portfolio against a stock index such as S&P 500 since they believe that index of this kind are the only which they are familiar with or used in the past by their financial advisors (Smithson 2003). Portfolio performance measure is based on the portfolio returns which are adjusted for the risk it is based on for a given period of time. The adjustment is either based on capital market line or security market line (Levine 2005). The performance that is based on security market line is Treynor Index as well as Jensen’s alpha. Portfolio measures based on capital market line are Sharpe Ratio and Risk adjusted performance. Regarding my efficient portfolio Treynor Index The risk adjusted measure was introduced by Treynor (1965) to measure the performance of mutual fund performance. In this case he used beta as the measure of risk and the beta represents the non-diversifiable security total risk portion and is calculated as below Treynor ratio = (RI-Rf)/beta Where; Rf is the risk free rate RI represents the return average rate of the investment Beta represents portfolio sensitivity to market return changes It is known that Treynor provides the security market line slope and the higher the Treynor Ratio, the better the portfolio in terms of ranking. ANNUAL RETURN AVERAGE RETURN% RISK-FREE RATE % BETA TREYNOR RATIO 18 7.8 0.6 0.61 0.085243 Basing on the above results it is clear that Treynor Ratio of my efficient portfolio (0.08) is greater than that of S& P 500 portfolio (0.019).This means that, my portfolio might outperform the S & P 500 portfolio and it’s a good indication to consider such a portfolio Jensen’s Alpha It measures the negative or positive abnormal return that is relative to predicted return It is calculated as below R ( p) -R( p) -R( f ) +R(m) -R( f )( p) Where; R (p) represents the portfolio mean return R ( f) represents the mean risk free rate R (m) represents the market mean return ( p) represents the portfolio sensitivity to market return changes Optimal completed Risky portfolio(restricted Risk-free Asset Optimal Risky portfolio Overall portfolio Jensen’s Alpha Average return 3.01 13.705 8.56 Risk-free rate 0 15.547 9.282 0.01274 market mean return 0.28 0.4973 portfolio sensitivity 0 0.457 The above ratio is greater than the benchmark, hence it can outperform it. Sharpe Ratio It basically used in measuring the average performance of the portfolio over a given risk free rate for every unit of the portfolio’s total risk (Sharpe 1992). It is calculated as below; SR (P) =(R (p) –R (f))/ (p) Where; R ( p) represents the portfolio mean return R ( f) represents the mean risk free rate  (p) represents standard deviation of the portfolio Optimal completed Risky portfolio Risk-free Asset Optimal Risky portfolio Overall portfolio Sharpe Ratio return 3.01 11.401 7.246 Risk-free rate 0 12.507 8.232 0.02164 Std Dev 6.4754 Basing on the above results, it can be concluded that the efficient portfolio performance is better when compared with the S &P 500(benchmark) which has a Sharpe Ratio of 0.019 (Sharpe et al. 1998). Concerning my Investment Fund Portfolio WEIGHT RETURN CONTRIBUTION Asset 1 0.5 4.5 1.5 Asset 2 0.10 3.8 1.6 Asset 3 0.25 1.2 0.2 TOTAL 3.3 BENCHMARK WEIGHT RETURN CONTRIBUTION OVERWEIGHT PERFORMANCE Asset 1 0.4 3.5 0.5 0.1 0.2 Asset 2 0.210 2.7 1.2 0.05 1.5 Asset 3 0.325 3.2 0.2 0.1 0.5 TOTAL 1.9 TOTAL 2.2 ATTRIBUTION -- SELECTION ALLOCATION INTERACTION Asset 1 0.02 -0.10 Asset 2 0.03 0.25 -0.02 Asset 3 0.7 0.17 0.35 Total: 0.73 0.44 -- ACTIVE MANAGEMENT EFFECT 0.680 ERROR -0.035 OVER PERFORMANCE 0.735 Treynor Index ANNUAL RETURN AVERAGE RETURN% RISK-FREE RATE % BETA TREYNOR RATIO 13 6.3 0.3 0.51 0.06243 S &P 500 Treynor index;0.012 Jensen’s Alpha Optimal completed Risky portfolio Risk-free Asset Optimal Risky portfolio Overall portfolio Jensen’s Alpha Average return 1.01 10.705 9.306 Risk-free rate 0 17.547 8.102 0.02374 market mean return 0.18 0.2873 portfolio sensitivity 0 0.367 S &P 500 Jensen’s Alpha; 0.0167 Sharpe Ratio Optimal completed Risky portfolio Risk-free Asset Optimal Risky portfolio Overall portfolio Sharpe Ratio return 1.01 10.705 9.306 Risk-free rate 0 17.547 8.102 0.054 Std Dev 7.4754 S &P 500 Sharpe Ratio; 0.019 3. Bond Portfolio Immunization AVERAGE TOTAL RETURNS DATE ASSET 1 ASSET 2 ASSET 3 ASSET 4 ASSET 5 ASSET 6 ASSET 7 ASSET 8 ASSET 9 ASSET 10 Portfolio* 30.06.2014 8.6 25.7 48.0 1.1 1.5 33.6 40.8 85 64.2 72 37.8 30.12.2014 111 47.2 9.4 104 7.7 207 17.6 8 18.7 202 71.9 30.06.2015 39.3 52.0 32.8 59.4 53.7 65.2 32.7 56 63 71 41.9 30.12.2015 28.8 34.5 5.9 28.8 0.1 19.3 25.2 20 11.8 22 3.9 30.06.2016 17.4 1.5 10.8 4.8 29.3 5.0 36 15 10.4 31 7.7 30.12.2016 10.6 21 2.5 67 11.8 2.6 3.6 22 4.3 151.6 20.2 30.06.2017 59 4 24 12 32 30 36.0 11 28.2 18.4 8.8 AVERAGE TOTAL RETURNS 25 11 9 21 13 17 0.4 8 7.3 40.2 15.5 STDEV 45 30 22 48. 23 82 30 40 36.1 96.0 32.1 COVARIANCE MATRIX   ASSET 1 ASSET 2 ASSET 3 ASSET 4 ASSET 5 ASSET 6 ASSET 7 ASSET 8 ASSET 9 ASSET 10 ASSET 1 0.3734 0.1906 0.1469 0.4198 0.0087 0.4660 0.1218 0.1774 0.0924 0.4218 ASSET 2 0.1906 0.1393 0.0900 0.2753 0.0347 0.2896 0.0828 0.1145 0.0729 0.3392 ASSET 3 0.1469 0.0900 0.1089 0.1890 0.0034 0.1615 0.0896 0.1471 0.0848 0.1901 ASSET 4 0.4198 0.2753 0.1890 0.6197 0.0181 0.5850 0.1825 0.2109 0.0999 0.7017 ASSET 5 0.0087 0.0347 0.0034 0.0181 0.0564 0.0653 0.0015 0.0093 0.0334 0.1042 ASSET 6 0.4660 0.2896 0.1615 0.5850 0.0653 0.8745 0.2160 0.2160 0.1412 0.8469 ASSET 7 0.1218 0.0828 0.0896 0.1825 0.0015 0.2160 0.1212 0.1294 0.0617 0.2264 ASSET 8 0.1774 0.1145 0.1471 0.2109 0.0093 0.2160 0.1294 0.2238 0.1288 0.2147 ASSET 9 0.0924 0.0729 0.0848 0.0999 0.0334 0.1412 0.0617 0.1288 0.1177 0.1681 ASSET 10 0.4218 0.3392 0.1901 0.7017 0.1042 0.8469 0.2264 0.2147 0.1681 1.0912 PORTFOLIO CASE RISK(MINIMIZED) MAXIMIZED RETURN MIN LONG 0% to 25% 5% to 15% LONG 0% to 25% 5% to 15% WEIGHED VAR WEIGHTS WEIGHTS WEIGHTS WEIGHTS STOCK PORTFOLIO STOCK PORT PORT PORT PORT STOCK PORT PORT PORT ASSET 1 10.00 ASSET 1 43 0.00 0.0 5.0 ASSET 1 0.0 25.0 15.0 ASSET 2 10.00 ASSET 2 87 16.9 25.0 15.0 ASSET 2 0.0 0.0 15.0 ASSET 3 10.00 ASSET 3 7.72 0.0 0.0 15.0 ASSET 3 0.0 0.0 5.0 ASSET 4 10.00 ASSET 4 14 0.0 0.0 5.0 ASSET 4 0.0 25.0 15.0 ASSET 5 10.00 ASSET 5 70.7 59.6 25.0 15.0 ASSET 5 0.0 0.0 5.0 ASSET 6 10.00 ASSET 6 18.6 0.0 0.0 5.0 ASSET 6 0.0 25.0 15.0 ASSET 7 10.00 ASSET 7 28.9 0.0 25.0 15.0 ASSET 7 0.0 0.0 5.0 ASSET 8 10.00 ASSET 8 1.6 0.0 0.0 5.0 ASSET 8 0.0 0.0 5.0 ASSET 9 10.00 ASSET 9 5.1 23.3 25.0 15.0 ASSET 9 0.0 0.0 5.0 ASSET 10 10.00 ASSET 10 5.8 0.0 0.0 5.0 ASSET 10 100 25.0 15.0 WEIGHT(SUM) 100.00 WEIGHTS SUM 100.0 100 100.0 100.0 WEIGHTS SUM 100 100 100 RETURN EXPECTED 27.75 RETURN EXPECTED 7.5 15 14.3 21.5 RETURN EXPECTED 60.4 45.2 34.0 STDEV 44.51 STDEV 0.0 14 21.4 33.2 STDEV 104.4 78.4 56.7 Limitations of the analysis The input parameters are just reference points because the multivariate normal distribution randomly generates values in the normal standard distribution (Levine 2005). For simulation, the results are always seen as an extra source of information as opposed to other explains the framework (Levine 2005). Due to this, the entire results are treated with care and should be seen as a quantitative finance. The size of fund could influence the way managers transact in credit market as well as in global fixed income. In this case, large funds could gain access through derivatives contracts (Levine 2005). References Treynor Jack L., (1965)."How to Rate Management of Investment Funds", Harvard Business Review. Sharpe, William F. (1992). "Asset Allocation: Management Style and Performance Measurement", Journal of Portfolio Management, Winter Sharpe William F., Alexander Gordon J., Bailey Jeffery V. (1998). "Investments",Sixth Edition, Prentice Hall/Upper Saddle River, NJ Barras, L., O. Scaillet and R.Wermers. (2007). False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alphas, working paper Sornette, D., A. B. Davis, K. Ide, K. R. Vixie, V. Pisarenko, and J. R. Kamm (2007) Algorithm for Model Validation: Theory and Applications, Proc. Nat. Acad. Sci. USA 104 (16), 6562-6567. Fabozzi, F. J. (1998). Active equity portfolio management. New Hope, Pa, Frank J. Fabozzi Associates. Brentani, C. (2003). Portfolio Management in Practice. Burlington, Elsevier. http://www.123library.org/book_details/?id=33945. Levine, H. A. (2005). Project portfolio management a practical guide to selecting projects, managing portfolios, and maximizing benefits. San Francisco, Jossey-Bass. http://site.ebrary.com/id/10301234. Smithson, C. (2003). Credit portfolio management. Hoboken, N.J., John Wiley. http://public.eblib.com/choice/publicfullrecord.aspx?p=469922.. Read More