Applied Portfolio Management - Example

Applied portfolio management (Student’s Name) (University Name) 19-November-2013 Table of Contents Introduction 3 Uni-variate backtesting process 3 Optimization and construction of the final strategy 3 In-sample and out-sample 4 Constant proportional portfolio insurance 5 Results 5 Rebalancing the portfolio 5 Out of sample 7 Optimization 9 Aggregate score 11 Discussion 13 Conclusion 16 Reference 17 Introduction Portfolio contains risks which will cause the wealth value of an investor fluctuate time to time causing an investor unnecessary jittery. This requires proper asset allocation between risky assets and riskless assets. This is done using dynamic portfolio strategies which include constant mix, open based portfolio insurance, buy-and-hold and constant-proportion insurance. This strategy will help an investor make a decision that will make him achieve his objectives. In selecting a strategy, the investors risk tolerance plays an important role. An investor who is risky averse will definitely choose a strategy that will keep the returns at a constant value. Uni-variate backtesting process Uni-variate backtesting involves testing trading strategy or investment model using various factors. It estimates how good the strategy is in ensuring a investors wealth is maintained. It takes a certain investment period as well a number of indices. In our case, the first date of backtesting is 31/01/2005 and the last back testing is 31/12/2009 which gives an investment period of six years. The numbers of indices that have been considered are 10. Optimization and construction of the final strategy In constructing a final portfolio that is optimal various strategies are employed in order to reset the parameters in a manner that the wealth of the investor is maintained at a certain level. This is done with the assistance of financial analyst and the investor’s objectives. There are several styles or principles that determine the portfolio allocation when choosing types of different assets. The most popular method of determining allocation is to choose the assets depending on the age or goal of the client. If the client is young, then stocks that are poised for growth are chosen because the client still has plenty of working years ahead of him and very little bonds for the portfolio because he doesn’t need the slow but guaranteed income from bonds. The situation is different however if the client is old. In-sample and out-sample This helps in determining the investment by mitigating biasness. Out of sample is used to validate the model while in-sample is used in making the model. When one is testing the system, there must be information which will be optimized and tested using other information. In brief out of sample data is used in testing while in-sample is used for modeling. It is thus evident that a reliable means to ascertain the efficiency of different competitive models is to make assessment of the out of sample forecasting performances. It is felt that the In-sample proves to be an efficient proxy for the factual volatility due to several reasons. Firstly, it is well recognized that the estimate pertaining to the second moment is more specific with the enhancement of sampling frequencies. A basic problem associated with conducting back tests is that the volatility process has the inherent nature of being unobservable. This problem is surmounted by making use of an alternative for the monthly volatility that is ascertained by utilizing the day to day data. Different specifications have been entertained for the variation equations along with the pattern of mean equations and attempts have been made to examine in-sample, while out-of-sample testing has been done on most models. It is evident that a reliable means to ascertain the efficiency of different competitive models is to make assessment of the out of sample forecasting performances Constant proportional portfolio insurance This is a model that uses a multiplier and the assets that are invested whose wealth should not exceed a certain floor. It is up to the investor to choose a multiplier under floor that will be used in calculating the value of his investment. Usually the floor fluctuates based on riskless asset. In the case under consideration, the floor has been selected based on riskless rate. Such functions prove to be of immense use in applications related to stock return data in the context of option pricing, dynamic optimization and portfolio allocation. Results Rebalancing the portfolio Rebalancing the portfolio constant proportion portfolio insurance has been employed to address the problem of static approach. In the process of rebalancing the portfolio, the following graph has been made for stock price, the selected floor and the portfolio. In the rebalancing strategy, five year period has been selected where the initial investment was 100% equity and 0%bond. In February of the same year, bond increases to 8% because the stock price decreased therefore giving the bond a chance to be incorporate into investment. The investor has selected a floor where he does not want the value of the portfolio to fall beyond however in one occasion that is February 2009, the portfolio was almost equivalent to the floor From the graph below it can be noted that the investor had invested 100% stock and briefly in February the same year some bonds. This ceased up to the last years when investment in bond increased marginally. At one point he invested 20% in equity while bonds had 80%. When the market improved, the investment shifted towards equity. This strategy is important because it allows an investor to maintain a certain wealth as well as reduce exposure of risky assets to even to zero. However to maintain the selected floor one must rebalance his portfolio from time to time to avoid poor performance due to abrupt market crush. The selected market for this market is a pool market since the portfolio performed well from initial investment period to the last two years of the investment period. Out of sample From the graph and the tables below, it can be noted that the aggregate outperformed, the benchmark from May 2004 onward. The rebalancing was done in 1, 3 and 6 months and it appears that three month rebalancing performs better than the other months. The return for this month exceeds the return for the benchmark although between 2003 and 2004 the performance was poor. out of sample ( Jan 2003 - Dec 2006) Number 5 10 20 10 10 Rebalancing 3 3 3 1 6 Signals(18) agg agg agg agg agg Active Return 7.23% 5.03% 0.37% 4.73% 4.19% Information Ratio 61.15% 57.28% 7.58% 55.07% 50.64%   Monthly Annulaized Active Return 0.35% 4.19% Tracking Error 2.39% 8.27% Information Ratio 14.62% 50.64%   In Out Of   Sample Sample Active Return 2.92% 4.19% Information Ratio 35.56% 50.64% From the graph it can be noted that there is growth in active return as well as information ratio. If the market stock falls, it means investor’s value will decrease which will require him to sell some equity and purchase riskless asset. This will ensure the investor maintains at least a portfolio valued above the floor. Out-of-sample results show however less evidence of superior forecasting ability Optimization   Monthly Annualized Active Return 0.23% 2.76% Tracking Error 2.45% 8.48% Information Ratio 9.40% 32.56% Aggregate Signals Number 10 10 10 5 20 Rebalancing 1 3 6 3 3 Signals(18) Agg agg agg agg agg Active Return 3.04% 2.92% 2.76% 5.61% 2.01% Information Ratio 34.69% 35.56% 32.56% 55.31% 28.01% optimization aggregate singnals Aggregate Signals Number 10 10 10 5 20 Rebalancing 1 3 6 3 3 Signals(18) Agg agg agg agg agg Active Return 3.04% 2.92% 2.76% 5.61% 2.01% Information Ratio 34.69% 35.56% 32.56% 55.31% 28.01% In trying to optimize the score, it can be noted that the aggregate and the benchmark have lower scores than the optimized figure. It can be noted that the active return for optimized score performs better than aggregate score and benchmark. However active return for rebalancing 3 is lower than aggregate score. The information ratio for the 2 is higher than the optimized score. In the graph above, they show an upward trend up to the year 2001 when a down trend is experienced. Aggregate score   Monthly Annulaized Active Return 0.24% 2.92% Tracking Error 2.37% 8.22% Information Ratio 10.27% 35.56% Rebalancing Mom12 (singal 4) Wep12 (singal 8) Wroa (singal 10) Aggregate ( signal 18) Active Return 4.52% 3.07% 5.06% 5.61% Information Ratio 52.97% 27.40% 50.24% 55.31% Aggregate Signals Number 10 10 10 5 20 Rebalancing 1 3 6 3 3 Signals(18) Agg agg agg agg agg Active Return 3.04% 2.92% 2.76% 5.61% 2.01% Information Ratio 34.69% 35.56% 32.56% 55.31% 28.01% The graph above shows aggregate scoring results for various rebalancing strategies. It can be noted that in twelve months rebalancing that is signal 4 has a similar trend with signal 10 which has an active return of 5.06% and information ration of 50.24%. These rates are higher than annualized active return and information ratios. The aggregate signals have also performed better than the benchmark signal in all the period under consideration. The aggregate signal has an active return for rebalancing one of 3.04% with information ratio of 34.69% which is below the annualized information ration. From the graph it can be noted that the strongest performer is aggregate signal followed by signal 4. This performance is higher than signal 8 the benchmark. The graph plotted above indicates a increasing trend from start to end whereas a rising trend has been observed after that. However, in the later period seasonal fluctuations can also be noted which are in January 1999 and years on as it appears to increase significantly in the in the end of investment period. Discussion For both bonds and stocks however, there are common risks that should be dealt with by the investor. There shouldn’t be any excessive trading for stocks and excessive movements for bonds as well because they all incur a broker’s fee or management fee from the brokerage house that you are buying securities from. You earn your profit from choosing securities well and let time do its work on the growth aspect but financial firms derive their revenue from the constant activity of the financial market regardless of whether or not it is good for you. This is the reason why financial brokerage firms encourage day trading in the first place. For the investor however, the rules are different and you would be well advised not to follow what is being done by the majority of the market. The possibility of default is also present for both stocks and bonds asset class because the companies behind them are facing financial concerns always in the real world. It is for this reason that investors should be very wary and thorough when investigating potential assets to buy. Obvious financial weaknesses as well as operational risks should be fully evaluated before buying anything. It should be noted however that not all risks involving a security for investment can be gleaned just from reading their financial statements. The most significant risks are sometimes based in the future hence, there is no current data that will indicate this for you. The best way to deal with this risk aspect is simply to try to ascertain the future risks in addition to the thorough financial analysis. The results offered in the preceding section have some significant connotations for scorecard-type of measurement of performance. One of the essential factors for making investment decision is the return and risk of the risky assets. The importance of stock market volatility arises since it is one of the most significant parameter for forecasting future risk which is a basic element in investor’s portfolio construction. Financial market price volatility has a notable characteristic that is changing with time. The bigger fluctuation tends to centralize in certain periods of time, which is similar to smaller ones in other periods of time. This phenomena that is quite strong in holding that a financial variable varies when the market undulates, is quite common in financial time-series. Despite this difficulty, it is important to estimate and forecast the market volatility for investors and arbitrageurs; individual stock forecasting is also very important to personal investors. In spite of the strong evidence in regard to the two aspects of the data, most research efforts on predictability of stock returns do not directly take them into account. Such omissions can result under conditions when the techniques of estimation are not efficient, which largely lead to serious standard mistakes in regard to estimation of coefficients that relate to predictability and small t-statistics. Obviously such a situation results in failure to discard the null hypothesis since there is no predictability, which further leads to failures in detecting predictability even though the returns could be actually predictable. It is thus required to investigate if there is a predictable factor that are demonstrated amongst the CRSP values weighed monthly surplus rates as compared to the Treasury bill rate. Such distribution frameworks have been gainfully and effectively used in modeling returns in a number of research studies by different scholars. Multiple performance measures still have more problems considering that diversity of performance measure gives rise to more lenient ratings of performance in addition to having less differentiation among employees. Other scholars (Kaplan and Norton 2001) argue that, even though the Balanced Scorecard ought to be used as a part of the system of the strategic management, it can be connected to incentive compensation. They posit that ‘returns on incentives can be anchored on twenty five strategic measures’ without creating any troubles. Nonetheless, this is far in excess of the mean number of performance measures by more than five times and in fact this far exceeds 3 times the highest number of such measures employed in a typical research. For this reason, it could be questioned the effectiveness of using a balanced scorecard which comprises a large number of performance measures for measurement of performance as well as applying it in the reward system more so where the superior has prudence that would enable him to weight the measures. One great impediment however is that there would be bias in performance evaluation if subjectivity is applied. What this means is that in case subjectivity is applied in the evaluation and reward system for employees then there would be manipulations from the superiors where they set higher performance ratings while at same time compressing them. This would result in a complication where the firm would not be able to separate those employees who are highly skilled from those who are less skilled. It implies that in case the promotion decisions would be difficult tom make in the firm especially if the decisions determined by the skills and competencies of employees. Conclusion This paper has focused upon different aspects of the back testing stock market instability and their capability in delivering one or more periods ahead of forecasting of volatility. Such forecasts have been compared with proxies of actual volatility that were ascertained by making use of stock returns. It was found that the volatility outcomes derived from models are very smooth in capturing the complete variations of actual volatility. It was demonstrated that such outcomes are not to be understood as mere objects of choice in the monthly or daily frequencies but they are to be understood as being independent of the frequency selected. Reference Achour, D., Harvey, C., Hopkins, G. & Lang, C., 1999. Stock Selection in Mexico. Emerging Markets Quarterly,Fall edition, pp.1-38, ISSN: 1093-2666 Diebold F X & Mariano, R.S., 2006. Comparing predictive accuracy, Journal of Business & Economic Statistics, 13, 253-263. Read More