TECHNICAL ANALYSIS OF ETF PORTFOLIO REBALANCING STRATEGY by Nina Bao B.COMM, University of Northern British Columbia, 2009 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION UNIVERSITY OF NORTHERN BRITISH COLUMBIA May 2013 © Nina Bao, 2013 UMI Number: 1525698 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI Dissertation PiiblishMiQ UMI 1525698 Published by ProQuest LLC 2014. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 ABSTRACT Portfolio rebalancing strategy is of great importance to minimize the risk taken so as to ensure profitable investments. Regular rebalancing keeps the portfolio developing as it was planned and achieved initial invest goals. The relevant literature of the technical analysis on rebalancing strategy is scarce. After elaborating the four traditional rebalancing strategies and a set of risk measurements, the thesis proposes the multiplier rebalancing strategy, which combines the traditional periodically rebalancing strategy with the interval rebalancing strategy, and Relative Strength Index (RSI) rebalancing strategy based on technical analysis. In order to evaluate the effectiveness of the multiplier and RSI rebalancing strategies, the thesis conducts an experiment to compare the performances of two proposed strategies with the other four traditional strategies in terms of the rewards and risk measurements by using nineteen years Canadian stock and bond Indices and Exchange Traded Funds data from 1983 to 2010. Key Words: Portfolio Rebalancing Strategy; Technical Rebalancing Strategy; Risk Measurements; Traditional Rebalancing Strategies; Exchange Traded Funds. Table of Contents Acknowledgement................................vii C hapter I Introduction................................................................................................................... 1 Section 1.1 The Importance of Portfolio Rebalancing..................................................................3 Section 1.2 Technical Analysis..................................................................................................... 7 Section 1.3 Modem Portfolio T heory.......................................................................................... 8 Section 1.4 Exchange Traded Funds............................................................................................9 Section 1.5 Objective of the Research .........................................................................................9 Section 1.6 Structures................................................................................................................. 10 C hapter II Literature Review...................................................................................................... 11 Section 2.1 Traditional Rebalancing Strategies.......................................................................... 11 Section 2.2 Technical Trading Strategies................................................................................... 13 C hapter HI Rebalancing Approaches and Strategies ..............................................................16 Section 3.1 Buy and Hold Strategy........................................................................................... 18 Section 3.2 Periodic Rebalancing (Quarterly and Annually)....................................................19 Section 3.3 Interval Rebalancing (Threshold and Range rebalancing ..................................... 19 Section 3.4 Multipliers Rebalancing.........................................................................................20 Section 3.5 RSI Rebalancing..................................................................................................... 23 C hapter IV Technical Analysis of ETF Rebalancing S trateg y ............................................... 26 Section 4.1 Data, Measurements of Risk and Experiments.......................................................26 Section 4.1.1 Data Source s ................................................................................................ 26 Section 4.1.2 Average Annualized Return ........................................................................27 Section 4.1.3 Number of Rebalancing E vents...................................................................28 Section 4.1.4 Maxi Drawdown.......................................................................................... 28 Section 4.1.5 Standard Deviation ...................................................................................... 29 Section 4.1.6 B e ta .............................................................................................................. 30 Section 4.1.7 Sharpe R atio................................................................................................. 31 Section 4.1.8 Rolling Window Approach....................... 32 Section 4.1.9 Experiments............................................... 32 Section 4.2 Empirical and Experimental Results......................................................................33 Section 4.2.1 Average Annualized Return ..................................................................... 36 Section 4.2.2 Dollar Amount R eturn...............................................................................38 Section 4.2.3 Number of Rebalancing E vents................................................................ 39 Section 4.2.4 Maximum Drawdown............................................................................... 41 Section 4.2.5 B e ta ............................................................................................................42 Section 4.2.6 Standard Deviation ....................................................................................43 Section 4.2.7 Sharpe R atio...............................................................................................45 Section 4.3 Summary................................................................................................................ 46 Chapter V Conclusion and R em arks......................................................................................... 49 BIBLIOGRAPHY........................................................................................................................ 53 LIST OF TABLES Table 1: Examples of How Risks Can Affect Wealth................................................................ 6 Table 2: Examples of Risk and Losses........................................................................................ 6 Table 3: The Resulting Classification of All Implemented Rebalance Strategies..................... 18 Table 4 and 5: Examples of Average Annualized Return......................................................... 27 Table 6 : 10-Year Annual Compounded Returns of Six Rebalancing Strategies.......................38 Table 7: Six Rebalancing Strategies' Dollar Amount Returns at End of Every Period.............39 Table 8: Number of Trades in 10 Years..................................................................................... 40 Table 9: Maximum Drawdown in 10-Year Periods of Six Rebalancing Strategies...................42 Table 1 0 :10-Year Beta of Six Rebalancing Strategies.............................................................. 43 Table 11: 10-Year Standard Deviations of Six Rebalancing Strategies.....................................45 Table 12: 10-Year Sharpe Ratios of Six Rebalancing Strategies...............................................46 List of Figures Figure 1: Maximum Drawdown..............................................................................................29 Figure 2: Accumulative Returns of Six Rebalancing Strategies............................................. 39 A bbreviations AAR: Average Annualized Return ARB: Annual Rebalancing Strategy B&H: Buy-and-Hold Rebalancing Strategy ETF: Exchange Traded Fund MDD: Max Drawdown MPT: Modem Portfolio Theory Multiplier: Multiplier Rebalancing Strategy QRB: Quarterly Rebalancing Strategy RSI: Relative Strength Index Rebalancing Strategy Threshold: Threshold Rebalancing Strategy vii ACKNOWLEDGEMENT Time passes very quickly, Master graduate student learning is coming to an end, three years of my life learning benefit. Through the years, master’s thesis was finally completed. Looking back on the process of collection, collation, years of thinking, stagnation, modify until finally finished, I got a lot of care and help, to express my sincere gratitude to them. In writing this paper in a year, and has also experienced a huge test. To subject confusion, then is the literature structure tired, research question is again on the paper to solve the proposed reference point of reasonable when encountered bottleneck, thinking at the same time, their knowledge of precipitation to be accumulated and enriched the discovery in the process, both in the theory and the text of the control needs to be improved and sublimation, finally forming, feels gratified. But all the knowledge can only support them write this level and height, hope in the future continue to process, can improve even more and deeper insights. I have a grateful heart to face all around the professors, classmates, friends and family. Don’t know "thank you" two words can express my heart that the most deep affection. First of all, I want to thank my supervisor Professor Baotai Wang. Professor Baotai Wang is modest, amiable and easy of approach. An erudite scholar, a gracious elders, one can talk with friends, I learn from you enough for my benefit for life. In the paper, data collection and writing process, Dr. Wang has devoted a lot of care and encouragement. In the process of writing, whenever I have questions, Dr. Wang will put down the busy work, not to mind taking the trouble to show me; in my following the completion of the first draft, Dr. Wang for taking the time to check on my thesis, put forward many pertinent guidance, make me not to get lost in the process of and in writing. In the course of my paper to each modification, Dr. Wang help me develop research ideas, carefully taught, warmly encourage; it causes me to be able to click into place in the face of various problems. Professor Baotai Wang and rigorous style and the cause of the pursuit will influence and motivate my life; he cares for me and teaches me more forever. Take this opportunity; I would like to express my deep gratitude to Dr. Wang! Secondly, I would also like to thank teacher, Dr. Ajit Dayanandan, Dr. Jing Chen, Zaidong Dong, and Dr. Kuma Penash, thank you for my training, and education, are you a rigorous and realistic attitude, the spirit of earth not wasted the learning time makes me, get a life important wealth. Because there are strict, and the cultivation of high quality education, I can learn professional knowledge and enhance the ability of rapidly in the learning process in recent years. I want to thank my thesis reviews and defense in the teachers, they gave me a look at recent years learning opportunity, let me be clear development direction in the future, they help to me is an asset price. I will redouble our efforts in the future work, learning, in order to achieve more return them, repay the society. Thank them again, and wish them a lifetime of happiness, Ankang! viii At the same time, also thanks to Shu Xu, you support me, with great enthusiasm to help me, encourage me. It is such a good friend, so I am full of strength in the difficult years, thank you and I the same sense of happiness and sadness, had important moments in life, hope the next day everyone can be happy. Finally, thank mom and dad always love me like that, my love, understand me, and support me. I will be graduated now, to become parents rely on; let them rest assured, peace of mind, happy to spend every day! Thank you very much. I could not have it without you! Want to say to yourself, the end of learning master is also the beginning of a new life, in the years ahead, no matter what you do, must be carefully, efforts; continue to dream of their own achievements and more wonderful life! CHAPTER I: INTRODUCTION It is prevailing for companies and individuals to hold at least one tax deferred long term investment account(s) for assets appreciation nowadays. However, what leave much to be desired is that the investments may not create as much premium as investors expected, which may lead to panic if there is huge loss in the society. A good management of these long term investments is vital. Portfolio rebalancing not only plays a significant role in individual investments, but also demonstrates remarkable effectiveness in secure institutional investments, especially in the long term, such as investments from mutual fund and insurance companies. Picking the right investment vehicles is far away from sufficient. The compounding power requires further on-going monitors and adjustments. Therefore, portfolio rebalancing presents deeper influential for long-term investments. Like “exercise regularly” and “physical exam yearly”, portfolio rebalancing indicates better advice for your investment, the ignorance may do no harm to your portfolio instantly, but in the long run, serious loss may be suffered on your portfolio. The volatility of the rebalanced portfolio is smaller than these have never been rebalanced. The thesis intends to find out how the rebalancing strategies work under technical analysis compared with traditional rebalancing strategies. Firstly, the thesis will explain the importance of portfolio rebalancing and the backgrounds about technical trading strategies, modem portfolio theory, and Exchange Traded Funds. Secondly, the thesis will utilize technical 1 analysis to propose two rebalancing strategies, as well as the advantages and disadvantages of all rebalancing strategies. Thirdly, give a comparison results on the proposed methods with other traditional rebalancing strategies. The last part of this thesis is the conclusion. Portfolio management (PM), to be brief, the management of basket of stocks and (or) bonds, is the art of selecting the right investment policy for the investor in terms of maximum return at a given risk level. Investment policy which is prepared by portfolio manager provides the general investment goals and objectives of the investor and the investment strategies that the manager would apply to meet investor’s expectation. That includes specific information such as asset allocation, risk tolerance level, expected performance, and other requirements. PM contains three stages: asset allocation, security selection, and rebalancing strategy. Asset allocation of a portfolio, which is a key factor in investment performance, mainly determines a portfolio’s riskand-retum characteristics1. Studies has suggested that up to 80% or more of the variability in the portfolio performance is explained by asset allocation, with the rest determined by security selection, market timing, and other factors. By analyzing the expected returns and risks of different securities within various asset classes, portfolio managers can seek to construct portfolios that will yield the highest possible return for a given level of risk. However, investors should have in-depth understanding about asset allocation. It is a dynamic process. Due to the prices of different securities change over time, change in original target allocations might lead to increasing risk or lower returns and hence make it impossible for investors to achieve initial investment aims. Portfolio managers would monitor their portfolios frequently and have procedures in place to restore their original target allocations, so that the portfolio performance is in line with the investment policy which addressed investors’ objectives 1 Buraschi, A., Porchia P., Trojani, F. "Correlation risk and optimal portfolio choice*. J. Finance (2010).Vol. 65(1): pp. 393-420. 2 and risk tolerance level2. This dynamic process is called portfolio rebalancing and cannot be ignored during investments. Portfolio rebalancing is accomplished by occasionally resetting the proportions of each asset class back to their original weights. 1.1 The Importance of Rebalancing Portfolio rebalance is crucial because it can make investors to maintain their target asset allocation. Periodically rebalancing can benefit the maintenance of target allocation of the portfolio. As a result, the exposure to risk relative to target asset allocation can be deducted. By this means, the rebalance of portfolio will bring it back to its original target allocation and reset its routes. Therefore, the primary goal of a rebalancing strategy is to minimize risk of the portfolio relative to a target asset allocation, rather than to maximize returns of the portfolio. The importance of portfolio rebalancing can be explained from following three aspects: firstly, Investors need effective and efficient disciplines to manage their investment portfolio rationally from behavioral finance perspective; Secondly, risk management and diversification is the foundation to offset over risky assets for asset management; Thirdly, as portfolio rebalancing is an inherently contrarian process, additional value for the portfolio can be added. First, from behavioral finance perspectives, people tend to have “status quo bias” when dealing with their investment portfolios. Market force drives dramatically changes in stock price even every single second and correspondingly leads to a fluctuated financial market over time. It is investors’ decision to let the portfolio drift or adjust the portfolio weights to its target asset allocation when come across these changes. A survey of among 1200 pension fund participants from a mutual-fimd institute shows that only 25% participants had made some changes to the * Busse, J. A., Goyal A., Wahal. S. "Performance and persistence in institutional investment management". J. Finance (2010). Vol. pp. 65(2) 765-790. 3 allocation of their portfolio; one or two small changes had been made regarding to the rest3. The finding of this survey also recommended that the participants who seldom made any changes in their portfolio tended to be more risk-averse than those who did; as they think the change is dangerous. Investors’ actions through letting their portfolio drift with the prevailing current towards avoid risk often end up with the opposite direction - increasing risk. As the lead or lag characters of the returns on different assets, their portfolios will be transformed accordingly over the long run. The automatic mechanism may raise the allocated weights to the outperforming asset classes while shrink the weight of underperforming asset classes, then the profits made by outperformers can offset the loss resulted from underperformers. In the short run, this automatic change mechanism can enhance a better portfolio performance by elevating the outperforming assets’ allocated weight automatically4. However, there is no free lunch in investment field. In the long run, the risk level increases as the portfolio grow and concentrate on the outperforming assets. The portfolio becomes more vulnerable to a sea change in the markets. A great lesson could be learned from Japanese market during the 1980s. Japan experienced one of most dramatic stock-market bubbles in financial history. The Nikkei 225 index was at least trebled from 1984 to 1989. On the contrary, the stock market experienced a great shock and the index dropped nearly 60% over following three years since 1990. If an investor had a portfolio in Japan during 1984 to 1994 without a rebalancing policy, since the equity prices had been raised significantly as years’ lifting in the big market, then the losses 3 John O'Brie. Rebalancing: A Tool for Managing Portfolio Risk. Journal of financial service professionals. (2006) Vol.60(3): PP 191-209 4 This automatic adjustm ent system can only apply to short term portfolio. When it comes to long term , th e precious outperforming assets may turn unsuccessful, rebalancing should intervene. Gary Brinson, P; Randolph Hood, L; Gilbert Beebower, L. "Determinants of Portfolio Performance". Financial Analysts Journal. Vol. 42 (4): pp. 39 - 44. 4 during the subsequent bear market would be magnified as well. Therefore, a rational management of the long term investment and portfolio is essential. Second, from risk management perspective, rebalancing is necessary. A hypothetical diversified portfolio over 10 year period from May 1994 to May 2004 without rebalancing shows how quickly an untended portfolio can drift into risky zone. Assuming the portfolio contains 50% of Canadian short term bond and 50% of S&P/TSX 60 on May 1994, the weight on equity portion would grow to 66.68% on August 2000, and then changed to 56.24% on May 2004. The portfolio is heavily concentrated on equity market and thus higher risk due to the volatile of the equity market. If the initial invest $100,000 was made on May 2004, the portfolio value in ten years will be $190,147.22 without rebalancing, and its value is $198,244.53 with quarterly rebalancing. That means the value would increase by 4.26% compared to the untended portfolio, and the volatility of the rebalanced portfolio is much lower than the one without rebalancing. Investors could reduce portfolio volatility by keeping up with the target weights. This could also allow the compound growth works more quickly and boosting long term returns. Thus, rebalancing is necessary for risk management and assets diversification for long term investment. The example below will show you how risks can affect investor’s wealth. I use the 15year S&P/TSX60 total return from January 1995 to February 2010 as an example to show how market volatility can impact the risk and the investment. (Table 1) Assuming I invest $100,000 on January 1995, the returns and risks in the four scenarios below show that the level of risk can be reduced while maintaining stable returns if I can avoid the “market extremes”. 5 Table 1: Examples of How Risks Can Affect Wealth Value %Changes Beta(Risk) (Return) Scenario 1: Buy & Hold $418,156.03 0 1 6 best months removed 3 best months removed 1 best months removed $226,261.09 $298,270.97 $371,462.46 -45.89% -28.67% -11.17% 0.85 0.909 0.966 Scenario 3: Worst months 6 worst months removed 3 worst months removed 1 worst months removed $1,139,326.31 $828,873.71 $589,039.18 172.46% 98.22% 40.87% 0.701 0.779 0.901 $549,105.13 $526,619.39 $466,075.86 31.32% 25.94% 11.46% 0.551 0.688 0.867 With no months removed Scenario 2: Best months Scenario 4: Extremes 6 best and 6 worst months removed 3 best and 3 worst months removed Best and worst month removed Risks can be very harmful to the investment because the more money you lose the harder to make up your initial investment. As the examples shown on Table 3 below, if the investor invest $100 initially, when he lose $75 or 75% of the investment, 300% return will be required to grow back to principal investment value. However, it is unlikely investor can 300% return investment very often. Table 2: Examples of Risk and Losses 1 2 3 $100 15% $85 $100 50% $50 $100 75% $25 17.65% 100% 300% Scenario Principal Invested Percent loss Total Percent Gain Required to return to principal value 6 Thirdly, the counterintuitive rebalancing process can provide a better understanding of the market force and implement policies to deal with the changing. The rebalancing procedures invite rational consideration to increase the weight of well performed stocks and decrease that of risky ones regarding to the changing market. Investors sell the winners and buy the losers, but it also push investors to buy low and sell high in practice. It also makes big part of the benefit. Rebalancing also can promote return. If there is a long term upwards market trend, the capital injection into undervalued asset class from current outperforming asset class can lift the return. Even in a down market, rebalancing does help reduce losses. 1.2 Technical Analysis Technical analysis focuses on the price of a share of its stock relative to a company. A technical analyst buys or sells the stock based on the stock past behavior. The differential between market price and underlying value is very elastic. Technical analysis deals with problems posed by changes in investor confidence more efficiently than conventional “fundamental” value analysis. Therefore, technical analysis and fundamental analysis can be regarded as mutually complementary and interdependent. A technical indicator is a series of data points that are derived by applying a formula to the price data of a security. In our study, the price data used in the formula and calculation is the monthly closing prices. For instance, the average of 3 closing prices is one data point ((15+19+16) / 3 = 16.67 ). However, one data point does not have sufficient much information. A series of data points over a period of time is needed to create valid reference points to enable analysis. Different technical indicators analyze the price action from different perspectives. Two proposed technical rebalancing methods are based on leading technical indicators which are designed to lead price movements. More specifically, both methods are based on the theory of price momentum indicators. The first method is inspired by a practitioner in the financial service company who manages portfolio for clients. He calculates the average gains and average losses of the securities in the portfolio, and then finds the best selling and buying points by multiplying the average gains and average losses to the multipliers accordingly. This method will be discussed thoroughly in section Three. The other one is Relative Strength Index (RSI) developed by J. Welles Wilder. RSI is one of the most popular momentum indicators. Momentum measures the acceleration or deceleration of a security's price. As the price of a security rises, price momentum increases. The larger the period-over-period price change, the greater the change in momentum. Once the price change decelerates, momentum would also decelerate. The RSI rebalancing method will be explained in details in section three. 1.3 Modern Portfolio Theory Modem Portfolio Theory (MPT) assumes that investors are risk-averse. The theory uses standard deviation of return as a proxy for risk, which is valid if asset returns are jointly normally distributed. Under the mathematic model of MPT, portfolio return is the proportion weighted combination of the assets returns in the portfolio; portfolio volatility is a function of the correlation py of the component assets, for all assets pair (i, j). For simplicity, only two-assetportfolio will be explained in this study as follows. Portfolio return: E(Jip) = wA E(flU) + vjb E = wA E(Ra) + (1 - wA) E(RB). 8 Where Rp is the return on the portfolio, R a and Rb are the return on asset A and B; and waand Wb are the weighting of component asset A and B. Portfolio variance: measures the rate of return of the portfolio benchmark (in this case, the buy-and-hold strategy), and cov(r„,rb) is the covariance between the rates of return. 4.1.7 Sharpe Ratio Sharpe ratio is named after Nobel laureate William F. Sharpe21. It measures risk-adjusted performance or excess return per unit of deviation in an investment asset or a trading strategy. The Sharpe ratio describes performance of an asset compensated by the risk investors taken. Sharpe ratio can be evaluated as the asset with a higher ratio shows better return than the other when the two assets share the same benchmark (i.e. risk free rate). Higher Shape Ratio means the same return for a lower risk as well. A negative Sharpe ratio indicates that even a risk-free asset (or the benchmark asset) would perform better than the security being analyzed. The Sharpe ratio is calculated by subtracting the risk-free rate (such as Government 90 day bond rate) from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns22. The Sharpe ratio indicates whether the preferable return of an investment derives from excess risks or informed investment decisions. In terms of Sharpe ration, higher rate of return does not mean a well performed portfolio, only these demonstrate a higher return rate at a relevant lower risk or no additional risk to be paid can be regarded as good ones. The formula of the ratio is: ** _ '± F —1 r Where: rP » Expected porfblio return fir a Risk free rate «■ Portfolio standard deviation 21 He was the winner of die 1990 Nobel Memorial Prize in Economic Sciences. He was one of the originators of die Capital Asset Pricing Model, created the Sharpe ratio far risk-adjusted investment performance analysis, contributed to the development of die binomial method for die valuation of options, the gradient method for asset allocation optimization, and retums-based style analysis for evaluating the style and performance of investment funds. Sharp Ratio eliminates the risk free return and focuses more on die risk investors took. Ross A. Mailer; Robert B. Durand; Hediah Jafarpour. “Optimal portfolio choice using the maximum Sharpe ratio". The Journal o f Risk. Vol.l2(4), 2010pp. 49-73 31 Consider the Rf =1.5%, asset A has an expected return Rp=5%, and the Standard Deviation is 0.06. While asset B’s Rp equals 15%, Sd = 0.5. Calculated with Shape Ratio, asset A’s ratio is 0.58, while that of B is 0.27. From the first sight, asset B has a really attractive expected return, but with deeper analysis according to Shape Ratio, asset A presents a higher return rate at the same risk, or asset B has higher return rate with excess risk taken. Risk lover may choose asset B, but I assume prudent investors will choose asset A. 4.1.8 Rolling Window Approach The 10-year rolling window approach constitutes the proposed rebalancing strategy. For a 10-year investment horizon of the proposed rebalancing strategy, it requires previous 120 monthly returns observations into the rolling window for the simulation algorithm. The multipliers calculated from the previous 120 monthly returns are used to set the trading boundaries for the individual security in the portfolio. Then, the out-of-sample tests are conducted for the future 10-year investments. This process repeats every 10-year period from January 1992 to December 2010 based on the simulation algorithm from January 1991 to December 2000. 4.1.9 Experiments For empirical testing, a portfolio with 70% equity, 25% fixed income, and 5% treasury bills have been constructed for all rebalancing strategies. In practice, 70% equity and 30% fixed income mix is preferred by majority of investors based on their risk tolerance level in practice. Moreover, long-term investments are normally chosen younger investors who have sufficient investment horizon to tolerance the risks. All strategies tested in ten periods from January 1992 to December 2010 with an initial investment of $10,000. Every tested period is with 10 years 32 monthly returns. For example, January 1992 to December 2001 is one signal tested period; and the next tested period is from January 1993 to December 2002, and so on. Following four rebalancing strategies are compared: ■ Buy-and-hold strategy ■ Periodic rebalancing strategy (Annual Rebalancing) ■ Interval rebalancing strategy (+/-5% Threshold Rebalancing) ■ Multiplier rebalancing strategy ■ RSI rebalancing strategy As for periodic rebalancing strategies, both annual rebalancing and quarterly rebalancing are tested. +1-5% threshold is applied for interval rebalancing strategy. For the multiplier rebalancing strategy, all multipliers are calculated from previous 10-year returns. For example, period January 1992 to December 2001 simulations are based on the multipliers calculated from January 1991 to December 2000, and period January 1993 to December 2002 simulations are based on the multipliers calculated from January 1992 to December 2001, and so on. 4.2 Empirical and Experimental Results This section presents the main results of the simulation analyses. In order to proof that the rebalancing strategy using technical analysis could generate superior performance to long-term investment, I start the discussion by comparing the returns of the buy-and-hold, periodic, interval, and the proposed rebalancing strategies, which is annual returns by percentage. The costs of the rebalancing strategy will be briefly presented. Then, risk management of different rebalancing strategies will be discussed. Finally, Sharpe ratio which incorporates both the return and the volatility of the investment strategy will be explained. 33 A Returns (%) and number of transactions Selling of a fraction of the better performing security and investing the proceeds in the less performing or low risk security are generally required by all rebalancing strategies. One would expect that buy-and-hold strategy outperform rebalancing strategies with increasing investment horizons. However, it is not reflected in real world data. In the financial market, there are time periods in which equity market returns substantially outperform fixed income market returns, and other time periods vice versa. The following nineteen 10-year historical data will show you what happen in the real world. Table 6 illustrates the 10-year annual compound returns in percentage of every strategy. In fifteen out of nineteen periods, buy-and hold strategy gives the lowest returns except for period 1983 to 1992, period 1984 to 1993, period 1985 to 1994, and period 1986 to 1995. Also, the quarterly rebalancing is almost always performing better than annual rebalancing strategy at the expense of more frequent transactions. Threshold rebalancing strategies perform better than periodic rebalancing strategy in most of the cases. The multiplier rebalancing strategy and RSI rebalancing strategy give superior returns in most of the cases except for the first and last two periods. For the first one period, the RSI rebalancing performs the same as the buy-and- hold strategy and the multiplier rebalancing strategy outperform all other strategies, but both technical rebalancing strategies still outperform other three traditional rebalancing strategies. For the last two periods, threshold rebalancing strategy performs much better than other strategies; however, it has the highest standard deviations which will be discussed later in this section. This might due to the financial crisis and sudden drop in the financial market, so that the previous trend cannot capture it. Even though the proposed rebalancing strategy gives higher return, dynamic portfolio strategies will produce different risk and return characteristics showed by Perold and Sharpe (1988). Therefore, an appropriate 34 strategy is subject to the investor’s risk preference. Even though the proposed rebalancing strategies give higher returns, I cannot say it is a good strategy until its risk is taken into account carefully. Table 7 shows the dollar amount return in 10 years with initial investments of $100,000 for every strategy. Figure 2 gives the stacked line graph of the 10-year returns for all strategies. Table 8 shows the number of trades of every strategy in every 10-year periods. The quarterly rebalancing strategies give the highest number of trades required, whereas annual rebalancing strategy and threshold rebalancing strategy gives the lowest number of trades. The number of trades required for the multiplier and RSI rebalancing strategies are similar, which are slightly higher than annual rebalancing strategy and threshold rebalancing strategy, but far lower than quarterly rebalancing strategy. B. Volatility (Standard Deviation, Beta, Maximum Drawdown) The returns of both technical rebalancing strategies are relatively higher than the returns of traditional rebalancing strategies, but the returns of threshold rebalancing strategy, quarterly rebalancing strategy, multiplier rebalancing strategy, and RSI rebalancing strategy are close to one another. The rebalancing strategy with lower volatility gives better risk management. Table 9,10, and 11 present the annualized standard deviation, beta, and maximum drawdown classified by strategy. Buy-and-hold strategy clearly has the highest volatility in most of the tested periods after period 1990 to 1999. This illustrates that the rebalancing strategies can reduce volatility of the portfolio in most of the cases. Quarterly rebalancing strategy seems to produce lower volatility than the threshold rebalancing strategy. Both quarterly and threshold rebalancing strategies have lower maxi-drawdown than annual rebalancing strategy. Quarterly rebalancing strategy has relatively lower risk than annual rebalancing strategy. That shows frequent rebalancing can actually reduce drawdown rate except for the last tested period. The multiplier 35 and RSI strategy produces the lowest risk for the long-term investments as its standard deviation, beta, and maximum drawdown are almost always lower than other strategies except for periods 1988 to 1999. It might due to it is not fully invested in the whole time as part of the money stays in treasury bills. However, the number of transactions is higher than threshold and annual rebalancing strategies. If the investor is in the annual fee based and registered accounts (tax deferred), the proposed strategy may work better. If not, the transaction costs have to be taken into account. C. Sharpe Ratio In order to appropriately evaluate portfolio performance, it is necessary to apply a performance measure that incorporates both the rewards and the volatility of the underlying strategies. The Sharpe ratio as a risk-adjusted performance measure is widely applied in practice. The proposed multiplier and RSI rebalancing strategy generates the highest the Sharpe ratio presented on Table 12. From this table, I can see the quarterly rebalancing has higher riskadjusted returns than annual rebalancing strategy. Threshold rebalancing strategy works better than periodic rebalancing strategy on the risk-adjusted bases. Overall, the simulations give a clear idea that most of the rebalancing strategy can generate value or lower risks to the portfolio compared to buy-and- hold strategy. The proposed multiplier and RSI rebalancing strategy generate superior returns on the risk-adjusted basis while the volatility of the portfolio was well controlled. From the tests, I found the threshold rebalancing strategy and annual rebalancing strategy produce lowest number of transactions, and quarterly rebalancing strategy, threshold, and technical rebalancing methods give lower risks. 4.2.1 Average Annualized Return 36 The 10 year annual compounding return rate was calculated for the five mentioned rebalancing strategies. As mentioned earlier, compounding return shows a conductive advice on investment, higher compound return will bring higher return on portfolio investment. From Table 6 , 1can see the proposed multiplier presents the highest annual compounded returns in the 16 rounds out of nineteen 10-year-periods than buy-and-hold, quarterly, and annual rebalancing methods, which in turn means, a higher performance of the portfolio. The annual compounded return of the multiplier rebalancing strategy was lower buy-and-hold strategy in one period only which is from year 1984 to 1993, but its returns were still higher than buy-and-hold and two periodic rebalancing strategies in all periods. However, the returns of technical rebalancing strategies were higher than threshold rebalancing strategy in only 16 rounds out of 19 periods, because the threshold rebalancing methods outperformed all rebalancing strategies in the last two periods which were period 2000 to 2009 and 2001 to 2010. In the 19 10-year investments, the returns of buy-and-hold rebalancing were lowest in 15 rounds out of 19 periods from periods 1987 to 2010; and its returns are higher than two periodic and threshold rebalancing strategies for the first four periods. In this test, the quarterly rebalancing strategy and threshold rebalancing strategies were outperforming annual rebalancing strategy in all periods. 37 Table 6 : 10-Y ear A nnual C om pounded Returns o f S ix R ebalancing Strategies Year Multiplier QRB ARB Threshold B&H RSI Jan 1983 - Dec 1992 Jan 1984 - Dec 1993 Jan 1985 - Dec 1994 Jan 1986 - Dec 1995 Jan 1987 - Dec 1996 Jan 1988 - Dec 1997 Jan 1989 - Dec 1998 Jan 1990 - Dec 1999 Jan 1991 - Dec 2000 Jan 1992 - Dec 2001 Jan 1993 - Dec 2002 Jan 1994 - Dec 2003 Jan 1995 - Dec 2004 Jan 1996 - Dec 2005 Jan 1997 - Dec 2006 Jan 1998 - Dec 2007 Jan 1999 - Dec 2008 Jan 2000 - Dec 2009 Jan 2001 - Dec 2010 7.45% 7.91% 8.54% 11.27% 9.01% 9.92% 9.43% 10.03% 11.81% 9.13% 8.03% 8.52% 8.57% 8.76% 7.69% 6.95% 3.76% 3.64% 3.62% 7.45% 7.03% 7.00% 8.15% 7.78% 7.76% 7.74% 7.68% 7.63% 7.35% 7.23% 7.19% 8.77% 8.88% 8.84% 9.76% 9.80% 9.86% 9.22% 9.36% 9.29% 9.62% 9.88% 9.85% 11.42% 11.62% 11.50% 8.67% 9.01% 8.84% 7.61% 8.04% 7.83% 7.00% 7.42% 7.22% 8.07% 8.46% 8.27% 8.44% 8.66% 8.49% 7.42% 7.63% 7.46% 6.58% 6.78% 6.61% 3.25% 3.69% 3.70% 3.00% 3.44% 3.44% 3.16% 3.54% 3.58% 7.22% 7.81% 7.66% 7.21% 8.97% 9.93% 9.45% 9.91% 11.55% 8.65% 8.36% 7.25% 8.30% 8.72% 7.73% 6.84% 3.69% 5.15% 5.81% 7.61% 8.13% 7.97% 7.50% 9.10% 10.02% 9.47% 9.94% 11.68% 9.18% 8.18% 7.58% 8.59% 8.91% 8.03% 6.91% 3.81% 3.65% 3.75% 4.2.2 Dollar Amount Returns Assuming the initial investments are $100,000, the dollar amount returns of every strategy for nineteen periods (Table 7) are more intuitive way to show the reward differences among six rebalancing strategies. Figure 2 gives the accumulative returns of six different rebalancing strategies of 19 tested periods. Both technical rebalancing strategies clearly have the highest rewards compared with other strategies. The returns of threshold rebalancing strategy are lower than the returns of technical rebalancing strategies, but higher than the returns of both periodic rebalancing strategies. Buy-and-hold rebalancing strategy gives the lowest cumulative returns after all. 38 Table 7: S ix R ebalancing Strategies' D ollar A m ount Returns at End o f Every Period End of 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 B&H QRB ARB THRESHOLD MULTIPLIER RSI $205,159 $218,893 $210,796 $203,263 $231,772 $253,856 $241,466 $250,597 $294,787 $229,665 $208,303 $196,797 $217,359 $224,788 $204,562 $189,102 $137,750 $134,380 $136,510 $197,283 $196,730 $211,049 $208,654 $200,168 $233,237 $256,208 $243,122 $255,946 $2%,933 $233,190 $212,507 $200,839 $221,272 $225,816 $205,325 $189,649 $143,806 $140,231 $142,100 $200,792 $212,051 $209,221 $200,659 $236,020 $257,808 $246,687 $257,180 $298,331 $229,284 $223,257 $201,408 $221,945 $230,735 $210,584 $193,761 $143,660 $165,237 $175,833 $208,186 $218,442 $215,266 $206,195 $238,827 $259,733 $247,196 $257,863 $301,874 $240,662 $219,508 $207,614 $227,888 $234,716 $216,557 $195,093 $145,339 $143,097 $144,458 $205,150 $214,092 $226,944 $290,980 $236,856 $257,461 $246,165 $257,180 $305,231 $239,530 $216,452 $226,597 $227,523 $231,679 $209,714 $195,724 $144,623 $143,031 $142,678 $211,489 $209,663 $200,933 $234,045 $254,623 $244,652 $256,634 $300,338 $237,001 $216,682 $204,485 $225,169 $229,373 $208,647 $192,690 $143,617 $140,209 $141,578 Figure 2: Accumulated Returns of Six Rebalancing Strategies $4,300,000 $4,200,000 ■ $4,100,000 • $4,000,000 $3,900,000 • $3,800,000 4.2.3 Number of Trades The number of trades of all rebalancing strategies is shown on table 8. It is a proxy for transaction costs of investments. The 5% threshold rebalancing strategy clearly has the lowest number of trades. The quarterly rebalancing strategy has the highest number of trades. Two 39 technical rebalancing strategies and annual rebalancing strategy have moderate numbers of trades. Even though the transaction costs of the annual rebalancing strategy and threshold rebalancing strategy are relatively lower, but both strategies have higher volatility as well. Therefore, if the investor is paying a flat fee, the more profitable technical rebalancing strategies should be considered. Otherwise, if the transaction costs are higher than profits, the annual rebalancing method and threshold rebalancing method should be considered. However, if the benefits from the rebalancing strategy are higher than the transaction costs, the better rebalancing strategy should be considered as rebalancing can reduce portfolio risk. In this case, the technical rebalancing strategies are recommended as both strategies give higher return and moderate number of trades. | Table 8: Number of Trades in 10 Years Year Jan 1983 - Dec 1992 Jan 1984 - Dec 1993 Jan 1985 - Dec 1994 Jan 1986 - Dec 1995 Jan 1987 - Dec 1996 Jan 1988 - Dec 1997 Jan 1989 - Dec 1998 Jan 1990 - Dec 1999 Jan 1991 - Dec 2000 Jan 1992 - Dec 2001 Jan 1993 - Dec 2002 Jan 1994 - Dec 2003 Jan 1995 - Dec 2004 Jan 1996 - Dec 2005 Jan 1997 - Dec 2006 Jan 1998 - Dec 2007 Jan 1999 - Dec 2008 Jan 2000 - Dec 2009 Jan 2001 - Dec 2010 B&H QRB 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 ARB 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 Threshold 12 9 6 6 9 9 9 12 9 6 12 6 6 15 15 15 15 12 12 Multiplier 29 38 37 28 36 38 33 27 40 28 39 34 37 39 35 64 27 38 29 RSI 34 30 38 38 40 38 36 38 38 48 50 44 44 56 58 56 62 54 44 4.2.4 Max Drawdown Regarding to the analysis of evaluating the max drawdown, the larger the drawdown (smaller rate) is, the more difficult for it to recover the investment to its previous value and the greater the risk of ruin, which discussed the thoroughly on chapter one. What I can see from Table 9 is that fourteen out of nineteen drawdown rates for the proposed multiplier and twelve out of nineteen drawdown rates for RSI rebalancing are the lowest, which means the drawdown is smaller than other four traditional strategies. For RSI rebalancing strategy, other five max drawdown rate is slightly higher than quarterly rebalancing strategy, but still lower than annual rebalancing strategy and threshold rebalancing strategy in the rest seven periods. That is to say, it is easier for investors to recover to the initial investment from the first largest shock when rebalancing with multiplier strategy than others. Except for the last period, annual rebalancing strategy was the worst in respect to max drawdown analysis as its max drawdown rates are highest in all periods. The max drawdown rate of buy-and-hold strategy was lower than annual rebalancing strategy, but higher than all other rebalancing strategies. This result shows the longer the periods to avoid rebalancing the portfolio, the higher the portfolio risks are. 41 Table 9: M axim um D raw dow n in 10-Y ear Periods o f S ix R ebalancing Strategies Year B&H QRB ARB Jan 1983 - Dec 1992 Jan 1984 - Dec 1993 Jan 1985 - Dec 1994 Jan 1986 - Dec 1995 Jan 1987 - Dec 1996 Jan 1988 - Dec 1997 Jan 1989 - Dec 1998 Jan 1990 - Dec 1999 Jan 1991 - Dec 2000 Jan 1992-Dec 2001 Jan 1993 - Dec 2002 Jan 1994-Dec 2003 Jan 1995 - Dec 2004 Jan 1996 - Dec 2005 Jan 1997 - Dec 2006 Jan 1998 - Dec 2007 Jan 1999 - Dec 2008 Jan 2000 - Dec 2009 Jan 2001 - Dec 2010 -16.98% -16.71% -17.76% -17.75% -18.30% -12.94% -19.47% -19.19% -20.53% -33.75% -40.43% -39.76% -39.50% -39.89% -38.67% -37.95% -38.72% -36.04% -34.28% -16.99% -16.99% -16.99% -16.99% -16.99% -13.28% -19.74% -19.74% -19.74% -30.74% -36.15% -36.15% -36.15% -36.15% -36.15% -36.15% -36.15% -36.15% -32.59% -18.30% -18.30% -18.30% -18.30% -18.30% -12.84% -20.21% -20.21% -20.21% -31.11% -36.80% -36.80% -36.80% -36.80% -36.80% -36.80% -36.80% -36.80% -32.22% Threshold Multiplier -16.97% -17.98% -17.76% -17.75% -16.98% -12.94% -19.56% -20.54% -20.26% -31.58% -36.79% -36.79% -36.79% -36.79% -36.14% -36.20% -35.98% -35.98% -35.72% -14.67% -14.92% -14.74% -15.37% -17.61% -13.33% -19.84% -19.86% -19.86% -30.81% -35.81% -35.70% -35.51% -35.51% -35.70% -36.02% -35.99% -35.23% -32.50% RSI -16.99% -17.06% -15.25% -16.91% -16.90% -13.26% -19.49% -19.49% -19.46% -30.57% -36.36% -36.36% -35.63% -36.11% -36.15% -36.00% -35.90% -35.60% -32.83% 4.2.5 Beta Beta is the number to evaluate the risk an asset taken. The higher beta means higher risk investors taken to get excess return. In this test, I used buy-and-hold rebalancing strategy as the benchmark asset for calculating beta. As a key element to evaluate the portfolio, the computed data in the below table 10 briefly illustrates the multiplier has the lower beta compared to periodic and threshold rebalancing strategies in fifteen out of nineteen periods, its betas were higher than the benchmark in two periods which were periods of 1983 to 1992 and 1990 to 1999; and in the rest of four periods, its betas were either equal or slightly higher than other traditional rebalancing strategies. The betas of RSI rebalancing strategies were lower than the traditional 42 rebalancing strategies in thirteen out of nineteen periods; and in the rest of six periods, its betas were either equal or slightly higher than other traditional rebalancing strategies. The beta of both technical rebalancing strategies is still lower than periodic and threshold rebalancing strategies in most of the case. This is to say, portfolio will become less risky with technical rebalancing strategies and will positively give more profitable space for the investment. Table 10: 10-Year Beta of Six Rebalancing Strategies Year Jan 1983 - Dec 1992 Jan 1984 - Dec 1993 Jan 1985 - Dec 1994 Jan 1986 - Dec 1995 Jan 1987 - Dec 1996 Jan 1988 - Dec 1997 Jan 1989 - Dec 1998 Jan 1990 - Dec 1999 Jan 1991 - Dec 2000 Jan 1992 - Dec 2001 Jan 1993 - Dec 2002 Jan 1994 - Dec 2003 Jan 1995-Dec 2004 Jan 1996 - Dec 2005 Jan 1997 - Dec 2006 Jan 1998 - Dec 2007 Jan 1999 - Dec 2008 Jan 2000 - Dec 2009 Jan 2001 - Dec 2010 B&H 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 ARB 1.04 1.07 1.04 1.04 1.03 1.04 1.04 1.06 0.99 0.96 0.93 0.95 0.95 0.94 0.96 0.98 0.93 0.99 0.99 QRB 1.03 1.06 1.02 1.02 1.01 1.04 1.04 1.05 0.98 0.96 0.93 0.94 0.94 0.93 0.96 0.97 0.93 0.99 0.99 Threshold 1.03 1.06 1.02 1.03 1.00 1.05 1.03 1.07 0.99 0.97 0.95 0.97 0.97 0.95 0.97 0.98 0.94 1.02 1.03 Multiplier 1.00 0.98 0.96 0.95 1.02 1.05 1.05 1.04 0.97 0.97 0.92 0.94 0.93 0.93 0.96 0.97 0.92 0.98 0.99 RSI 1.00 1.06 1.00 0.99 1.01 1.05 1.03 1.05 0.97 0.95 0.92 0.95 0.94 0.93 0.96 0.97 0.93 0.99 1.01 4.2.6 Standard Deviation It is known that the higher standard deviation means a higher dispersion from the mean and that means more volatile of the portfolio. In other words, the more risky the portfolio was taken. From the table 11 below, the data describes a lower standard deviation of the multiplier 43 and RSI rebalancing strategies in most of the periods which reflects less volatile when using this rebalancing strategy than other four traditional strategies. The standard deviations of buy-andhold strategy were the lowest in first eight periods covering years 1983 to 1999, but its standard deviations were highest from year 1991 to 2010. The standard deviations of annual rebalancing strategy were the highest in fifteen out of nineteen periods, and the standard deviations of quarterly rebalancing strategy were lower than annual rebalancing strategies in all periods. It illustrates frequent rebalancing portfolios can actually reduce volatility of the portfolio. The standard deviations of the multiplier rebalancing strategy were the lowest in fourteen out of nineteen periods; and its standard deviations were slightly lower than the quarterly rebalancing and threshold rebalancing strategies in the rest five periods. The standard deviations of RSI rebalancing strategy were lower in eight out of nineteen periods; and in the rest of eleven periods, seven of its standard deviations were slightly higher than the standard deviations of the quarterly and threshold rebalancing strategy during the periods 1985-1994 and 1985 to 1995. In period 1989 to 1998, the standard deviation was only higher than buy-and-hold strategy, and lower than all other strategies. Although the standard deviations of both technical rebalancing strategies were higher in some cases, it may not represent they are bad strategies; because the risk-adjusted performances should always take into consideration in portfolio management. The nest section, Sharpe ratio, will show the risk adjusted performances of all rebalancing strategies. Therefore, the multiplier and RSI rebalancing strategies provides a better way to secure the investment as well as generating more investment incomes as they are less volatile in most of the cases. 44 | Table 1 1 : 10-Y ear Standard D eviation s o f S ix R ebalancing Strategies Year B&H QRB ARB Threshold Multiplier 10.61% 10.31% Jan 1983 - Dec 1992 10.31% 10.62% 10.79% Jan 1984 - Dec 1993 10.51% 9.75% 9.89% 10.47% 10.63% Jan 1985 - Dec 1994 10.30% 10.49% 10.68% 9.99% 10.53% 9.51% Jan 1986 - Dec 1995 10.42% 10.26% 9.97% 10.23% 10.57% Jan 1987 - Dec 1996 10.42% 10.35% 10.43% 10.63% 9.44% Jan 1988 - Dec 1997 9.43% 8.99% 9.36% 9.36% 11.00% Jan 1989 - Dec 1998 10.45% 10.84% 10.86% 10.82% Jan 1990 - Dec 1999 11.17% 10.75% 11.32% 11.35% 11.46% Jan 1991 - Dec 2000 11.53% 11.86% 11.63% 11.76% 11.77% 12.72% 12.65% Jan 1992-Dec 2001 13.05% 12.48% 12.56% 12.61% Jan 1993-D e c 2002 13.01% 13.67% 12.68% 12.73% Jan 1994-Dec 2003 12.53% 12.58% 12.87% 12.47% 13.29% Jan 1995-Dec 2004 12.08% 12.92% 12.21% 12.26% 12.52% Jan 1996-Dec 2005 13.15% 12.25% 12.32% 12.18% 12.49% Jan 1997-Dec 2006 12.14% 12.05% 12.52% 12.01% 12.07% Jan 1998-Dec 2007 11.60% 11.97% 11.65% 11.71% 11.78% Jan 1999-Dec 2008 11.62% 12.56% 11.64% 11.65% 11.79% Jan 2000 - Dec 2009 11.88% 11.78% 11.78% 12.97% 11.67% Jan 2001 - Dec 2010 10.85% 10.99% 10.93% 10.85% 12.50% RSI 10.31% 10.52% 10.95% 11.43% 10.50% 9.41% 10.82% 11.35% 11.57% 12.47% 12.62% 12.82% 12. 11% 12.27% 12.00% 11.68% 11.67% 11.78% 11. 10% 4.2.7 Sharpe Ratio From the analysis above, the greater Sharpe Ratio is the higher return rate of the portfolio at the same risk. Compared with the buy-and-hold and periodic rebalancing strategies, data in table 12 shows that the proposed multiplier and RSI rebalancing strategies present relevant higher ratio in the nineteen 10-year-period analyses; and Sharpe ratios of both technical rebalancing strategies were higher than threshold rebalancing strategies in fifteen out of nineteen periods. However, their Sharpe ratios are lower than the one with threshold rebalancing strategy in four periods. For the data of Jan 1999- Dec 2008 and Jan 2000- Dec 2009, the Sharpe Ratio of multiplier and RSI rebalancing strategies even double that of the buy-and-hold rebalancing 45 strategy. For the period 1985 to 1994 and the period 1986 to 1995, the Sharpe ratios of RSI rebalancing strategy were much higher than the Sharpe ratio of the buy-and-hold strategy. The negative Sharpe ratios in earlier years were the results of higher treasury-bill rates. The significance of the proposed technical rebalancing strategies can be proved clearly by the table below. Under the same risk taken, the multiplier and RSI rebalancing strategy achieve better return for the portfolio; or with the same rate of return, multiplier rebalancing strategy undertook lower risk. Table 12: 10-Year Sharpe Ratios of Six Rebalancing Strategies Year Jan 1983 - Dec 1992 Jan 1984 - Dec 1993 Jan 1985 - Dec 1994 Jan 1986 - Dec 1995 Jan 1987 - Dec 1996 Jan 1988 - Dec 1997 Jan 1989 - Dec 1998 Jan 1990 - Dec 1999 Jan 1991 - Dec 2000 Jan 1992 - Dec 2001 Jan 1993 - Dec 2002 Jan 1994 - Dec 2003 Jan 1995 - Dec 2004 Jan 1996 - Dec 2005 Jan 1997 - Dec 2006 Jan 1998 - Dec 2007 Jan 1999 - Dec 2008 Jan 2000 - Dec 2009 Jan 2001 - Dec 2010 QRB B&H -14.62% -17.60% -7.37% -4.89% -2.81% -3.11% -4.60% -5.38% 12.98% 13.87% 28.84% 28.37% 25.62% 26.29% 35.01% 35.91% 52.31% 54.71% 33.02% 36.45% 27.73% 31.96% 25.32% 29.12% 35.80% 40.02% 41.09% 44.79% 35.15% 37.76% 28.81% 30.89% 4.51% 7.46% 5.51% 9.05% 10.81% 14.13% ARB Threshold Multiplier RSI -13.23% -14.62% -17.39% -15.96% -7.03% -5.35% -6.11% -7.27% -1.15% 4.74% -3.25% -3.30% -3.82% 28.93% -5.44% -5.45% 14.68% 15.76% 14.99% 13.50% 30.34% 29.55% 29.45% 29.03% 27.02% 27.10% 26.89% 25.69% 35.80% 36.66% 37.03% 35.60% 55.54% 53.64% 56.33% 53.25% 37.34% 33.41% 37.36% 35.02% 33.10% 31.96% 30.36% 33.77% 30.42% 36.78% 27.62% 27.53% 41.12% 38.21% 41.33% 38.48% 46.87% 45.57% 44.65% 43.35% 40.78% 38.25% 38.20% 36.30% 32.04% 31.16% 32.19% 29.44% 8.07% 7.54% 8.48% 7.58% 10.77% 10.74% 21.98% 9.06% 16.02% 14.78% 31.15% 14.49% 4.3 Summary In this chapter, the experiment applied 19-year market returns of ETFs from 1983 to 2010 in Canadian market. The portfolio in this experiment is the balanced portfolio, which includes 5% 46 treasury-bills, 25% fixed income security, and 70% equity security. The reason I choose this asset mix is because this mix is widely applied by average investors, and it is easier to detect how the rebalancing strategy impact the portfolio performances as there are more assets on equity markets and thus more volatile. This study compares the returns, risks, and rebalancing cost proxy of all rebalancing strategies to the index, which is the buy-and-hold strategy in this case, and traditional rebalancing strategies to show that the proposed technical rebalancing methods would be better to manage the long term ETF investment portfolios. There are two parts in this chapter. The first part introduces the performance and volatility measurements in various perspectives as well as the experiment methodology. The second part of the chapter gives empirical and experimental results. Average annualized return and dollar amount return would be used to measure portfolio performances; number of rebalancing events would be used as a proxy for measurement of rebalancing costs; maximum drawdown, standard deviation, and beta would be used to measure volatility or portfolio risk; and finally Sharpe ratio would be used to measure risk-adjusted performances of the portfolio. The AAR is the arithmetic mean of a series of rates of return. It is a helpful guide for measuring the long-term performance of portfolios. The average annualized returns of both technical rebalancing strategies were highest in all periods compared to quarterly and annual rebalancing strategies; their AARs were higher than threshold rebalancing strategies in seventeen out of nineteen periods and higher than buy-and-hold strategy in eighteen out of nineteen periods. The percentage figure of AAR might not be intuitive enough. The dollar amount returns of all rebalancing strategies are illustrated in the following section. Assuming the initial investments are $ 100,000, the accumulative returns of all rebalancing strategies in 10 years are presented on Figure 2. Moreover, the numbers of rebalancing events of both technical rebalancing strategies 47 are moderate, which are lower than quarterly rebalancing strategy, higher than threshold rebalancing strategy, and similar to annual rebalancing strategy. With respect to volatility measurements, three types of measurements (max drawdown, standard deviation, and beta) give slightly different results. The MDDs of multiplier rebalancing strategy are lower than the MDDs of traditional rebalancing strategies in thirteen out of nineteen periods; and the MDDs of RSI rebalancing strategy are lower than traditional rebalancing strategies in twelve out of nineteen periods. The betas of multiplier rebalancing strategy are lower than all traditional rebalancing strategies in fifteen out of nineteen periods; and the betas of RSI rebalancing strategy are lower than traditional rebalancing strategies in thirteen out of nineteen periods. The standard deviations of multiplier rebalancing strategy are lower than traditional rebalancing strategies in fourteen out of nineteen periods; the standard deviations of RSI rebalancing strategy are lower than annual rebalancing and threshold rebalancing strategies in thirteen out of nineteen periods but higher than threshold rebalancing strategy in seven periods. The volatilities of annual rebalancing and buy-and-hold strategies appear to be higher compared to other strategies in this test. However, the risk adjusted performance should always be taken into consideration when evaluating a portfolio. The last section of the test results are the Sharpe ratios of all rebalancing strategies. The Sharpe ratio generally evaluates how well the return of the portfolio compensates the investor for the risk taken. The Sharpe ratios of both technical rebalancing strategies are the highest compared to periodic rebalancing strategies and buy-and-hold strategy in all nineteen tested periods; but they are lower than the threshold rebalancing strategy in five tested periods. In general, the technical rebalancing strategies outperform all other strategies according to riskadjusted performance. 48 CHAPTER V: CONCLUSION AND REMARKS Benjamin Graham wrote in the Intelligent Investors than, “The essence of Investment Management is the management of risks, not the management of returns. Well-managed portfolios start with this precept.” Nowadays, institutional investors often employ mean-variance optimization analysis, also known as modem portfolio theory, to determine optimal portfolio weights. However, the portfolio can drift away from the optimal target weights as the asset price changes over a period of time. Thus, a profitable portfolio rebalancing strategy is significant in this case, because it impacts the returns and risks associated with the portfolio. Most investors apply the traditional rebalancing strategies which are based on the calendar basis (ex: monthly, quarterly, and annually). This study firstly addresses the question why institutional investors prefer rebalancing even though these strategies require the selling of a fraction of the better performing assets and investing the proceeds in the treasury bills and later in the less performing assets. First of all, investors need disciplines to avoid “status quo bias”. Secondly, minimizing risk (defined as return volatility) with respect to a given asset allocation is the primary objective of any rebalancing strategy. The diversification of investment leads to the risk reduction. Rebalancing the portfolio back to the original target allocation prevents the portfolio drifted away from the worse performing security with lower volatility towards the better performing security with higher volatility, thereby increasing risk and reducing diversification. Thus, rebalancing to the less risky security ultimately leads to a reduced volatility. Risk control is especially important for long-term investment because of the compounding powers. The less the 49 investor loses, the faster the money could grow in the long-run. Thirdly, portfolio rebalancing adds value due to its contrarian process in natural. In contrast to prior rebalancing studies, this study proposed technical analysis to form rebalancing strategy for long-term investments. The portfolio performance can be optimized by using technical analysis or proposed rebalancing strategies. The proposed multiplier and RSI rebalancing strategies combine the periodically rebalancing with the interval rebalancing strategy. By specifying the trading range for every individual security in the portfolio, it improves the portfolio performance while minimizing portfolio volatility in the long run compared to other traditional rebalancing strategies for various risk preferences. The tests are based on two asset-class portfolio. Monthly return data of a stock index, a bond index, and treasury bills are used for the simulation. As for the proposed rebalancing strategy, out-of-sample tests from January 1983 to December 2010 are conducted based on the simulation algorithms of 10-year rolling returns from historical data of period from January 1982 to December 2000. Buy-and-hold, interval, range, multiplier, and RSI rebalancing strategies are compared in terms of performance, volatility, and number of transactions. The different risk and return measurements represent different aspects investors take into consideration when evaluate a portfolio. The compounding rate demonstrates a more accurate return of rate and the higher rate means a better performance. Maximum drawdown is used to measure the risk of the portfolio. It is more appropriate for the long term investments as the deeper the drawdown the harder for the investment to recover. The standard deviation presents the dispersion from the average returns and the higher standard deviation means more risky of a portfolio. Moreover, the Sharpe Ratio is used to measure portfolio performance as it incorporates 50 both the return and the risk of any given portfolio strategy. The findings indicate that the rebalancing methods based on technical analysis give lower level of risks and superior returns in most of the cases during the sample periods. In addition, the proposed multiplier and RSI rebalancing strategies allow a better recovery from the Maximum drawdown. This implies that technical analysis could add value for well diversified portfolio under normal conditions, but it could not work when big events affect financial market such as financial crisis in 2008. Therefore, using technical analysis to manage portfolio does not mean to leave fundamentals alone. Technical analysis is to deal with problems posed by changes in investor confidence more efficiently than conventional “fundamental” value analysis. Therefore, technical analysis and fundamental analysis are mutually complementary and interdependent. The study also exhibits that all other rebalancing strategies generate a significantly lower volatility compared to the corresponding buy-and-hold strategy. The findings of the thesis lead to in-depth studies in many aspects. This study is focus on Canadian market, which is relative small and less volatile. The technical rebalancing strategies could work more significant in bigger and more volatile markets such as China or US. The technical rebalancing strategies in this study may be calculated by other methods so that the trading range can be better defined for every security in the portfolio. In addition, the proposed method can be improved by adding relative algorithms. There are many other technical analysis indicators that can be tested into rebalancing strategies such as moving average convergence or divergence (MACD), point and figure charting, and so on. Moreover, why the multiplier and RSI rebalancing strategy relatively work better than other rebalancing strategies might be explained by behavior economics or behavior finance’s point of view, which focus on the effects of social, cognitive, and emotional factors on the economic decisions of individual and institutions and 51 consequences for market prices, returns, and the resources allocation. 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