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Adaptive Asset Allocation: Which Is Better – Quarterly, Monthly, Or Weekly Trading?

Summary The performance of adaptive asset allocation is sensitive to the look back period, as well as to the frequency of market monitoring. The best performance is obtained by monthly monitoring, which significantly outperforms quarterly or weekly monitoring. For the SPY+TLT pair over the 2004-2014 time interval, the highest CAGRs are as follows: 14.70% for monthly monitoring, 12.93% for quarterly monitoring, and 11.74% for weekly monitoring. The best look back periods are 2 to 7 months, 10 to 20 weeks, and 1 quarter. The relative performance of the adaptive allocation strategy is consistent for ETFs and related mutual funds. We obtained similar effects on (SPY, TLT), (VTI, AGG), (FSTMX, FTBFX), and (VTSMX, VBMFX). In a couple of recent articles , we demonstrated that a very simple and well-diversified portfolio may be made up of two instruments – one representing the total stock market, and the other representing the total bond market. These portfolios are quite robust, and achieve decent returns using simple strategies such as rebalancing and momentum-based adaptive allocation. At the suggestion of some readers, we investigate the sensitivity of the adaptive allocation strategy to the frequency of market monitoring and the duration of the look back period. As in our previous articles, we considered the following four portfolios: one built with the SPDR S&P 500 Trust ETF ( SPY) and the iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ) , the second with iShares and Vanguard ETFs, the third with Vanguard mutual funds, and the fourth with Fidelity mutual funds. ETFs portfolio: iShares 20+ Year Treasury Bond ETF and SPDR S&P 500 Trust ETF. ETFs portfolio: iShares Core US Aggregate Bond Market ETF (NYSEARCA: AGG ) and Vanguard Total Stock Market ETF (NYSEARCA: VTI ). Mutual funds portfolio: Vanguard Total Bond Market Index Fund (MUTF: VBMFX ) and Vanguard Total Stock Market Index Fund (MUTF: VTSMX ). Mutual funds portfolio: Fidelity Total Bond Market Index Fund (MUTF: FTBFX ) and Fidelity Spartan Total Stock Market Index Fund (MUTF: FSTMX ). For purposes of comparison, we simulate these portfolios from December 2003 to December 2014, a total of eleven years. The time period of the study was selected based on the availability of historical data of the investment instruments; AGG was created in September 2003. The data for the study were downloaded from Yahoo Finance, using the Historical Prices menu for the eight tickers: SPY, TLT, AGG, VTI, VBMFX, VTSTX, FTBFX, FSTMX. We use the weekly and monthly price data from September 2003 to December 2014, adjusted for stock splits and dividend payments. The article has two parts. In the first part, we discuss the effect of the frequency of market monitoring. The second part presents the effect of varying the look back period. Part I: Quarterly, Monthly, and Weekly Market Monitoring The first study was done on the SPY+TLT. We compare the results obtained by monitoring the market quarterly, monthly, or weekly in the following manner. Quarterly monitoring is done at market closing on the last trading day of each quarter. Monthly monitoring is done at market closing on the last trading day of each month. Weekly monitoring is done at market closing on the last trading day of each week. The portfolio is at all times invested 100% in either SPY or TLT. All the funds are invested in the instrument with the highest return over the current look back period. The following look back periods were utilized in our simulations: 1 to 4 quarters for quarterly monitoring; 2 to 20 months for monthly monitoring; 5 to 50 weeks for weekly monitoring. The data below show the best investment results over 11 years, from January 2004 to December 2014. The first line is for quarterly monitoring with a 1-quarter look back period; the second is for monthly monitoring with a 3-month look back period; the third for weekly monitoring with a 13-week look back period. It is apparent that monthly monitoring delivers significantly better results than weekly or quarterly monitoring. Table 1. SPY+TLT quarterly, monthly, and weekly monitoring of portfolios January 2004-December 2014 Total Return% CAGR% Max DD% Number of trades Quarterly 281.1 12.93 -19.59 22 Monthly 347.0 14.70 -17.13 29 Weekly 141.1 11,74 -17.37 60 Part II: The Effect of the Look Back Period The effect of the look back period is presented separately for quarterly, monthly, and weekly monitoring. For quarterly monitoring , the look back period was varied from 1 quarter to 4 quarters. The results obtained for the SPY+TLT portfolio are shown in Table 2. It is apparent that a look back of one quarter is significantly better than any other period. Table 2. SPY+TLT quarterly, look back periods from 1 to 4 quarters January 2004-December 2014 Look back [quarters] Total Return% CAGR% Max DD% Number of trades 1 281.1 12.93 -19.59 22 2 77.2 5.20 -29.80 17 3 77.6 5.21 -31.54 14 4 56.4 4.15 -36.75 12 For monthly monitoring , the look back period was varied from 2 months to 20 months. The first two figures show the scatter of the compound annual growth rate (CAGR). A few observations can be made from analyzing these results: The SPY+TLT portfolio is the most sensitive to a change in the look back period. A look back period between 2 and 4 delivers the highest returns. VTI+AGG, as well as the mutual fund portfolios are little sensitive to changes in the look back period. Still, a look back period in the 2-6 month range delivers higher returns. (click to enlarge) Figure 1. CAGR for monthly monitoring with look back periods from 2 to 20 months. Source: This chart is based on Excel calculations using the adjusted monthly closing share prices of securities. (click to enlarge) Figure 2. CAGR for monthly monitoring with look back periods from 2 to 20 months. Source: This chart is based on Excel calculations using the adjusted monthly closing share prices of securities. (click to enlarge) Figure 3. Maximum drawdown (DD) for monthly monitoring with look back periods from 2 to 20 months. Source: This chart is based on Excel calculations using the adjusted monthly closing share prices of securities. (click to enlarge) Figure 4. Maximum drawdown for monthly monitoring with look back periods from 2 to 20 months. Source: This chart is based on Excel calculations using the adjusted monthly closing share prices of securities. For weekly monitoring , the look back period was varied from 5 weeks to 50 weeks. The first two figures show the scatter of the compound annual growth rate . A few observations can be made from analyzing these results: The SPY+TLT portfolio is the most sensitive to a change in the look back period. A look back period between 10 and 21 weeks delivers the highest returns. VTI+AGG, as well as the mutual fund portfolios are not very sensitive to changes in the look back period. (click to enlarge) Figure 5. CAGR for weekly monitoring with look back periods from 5 to 50 weeks. Source: This chart is based on Excel calculations using the adjusted weekly closing share prices of securities. (click to enlarge) Figure 6. CAGR for weekly monitoring with look back periods from 5 to 50 weeks. Source: This chart is based on Excel calculations using the adjusted weekly closing share prices of securities. (click to enlarge) Figure 7. Maximum drawdown for weekly monitoring with look back periods from 5 to 50 weeks. Source: This chart is based on Excel calculations using the adjusted weekly closing share prices of securities. (click to enlarge) Figure 8. Maximum drawdown for weekly monitoring with look back periods from 5 to 50 weeks. Source: This chart is based on Excel calculations using the adjusted weekly closing share prices of securities. Conclusions The performance of adaptive asset allocation is sensitive to the look back period, as well as to the frequency of market monitoring. The best performance is obtained by monthly monitoring, which significantly outperforms quarterly or weekly monitoring. The optimal look back period varies with the type of assets that make up the portfolio. For the assets considered in this study, the best look back periods are 2 to 7 months, 10 to 20 weeks, and 1 quarter. The author prefers a look back period of 3 months in conjunction with monthly monitoring.

Adaptive Asset Allocation: Which Day Of The Month Is Best To Trade?

Summary The performance of adaptive asset allocation is sensitive to the day of the month when transactions are executed. The performance is better if the trades are executed around the end/beginning of the month than close to the middle of the month. The day of month effect is consistent for ETFs and related mutual funds. We obtained similar effects on (SPY, TLT), (VTI, AGG), (FSTMX, FTBFX), and (VTSMX, VBMFX) pairs. In a couple of recent articles , we demonstrated that a very simple and well-diversified portfolio may be made up of two instruments, one representing the total stock market and the other the total bond market. These portfolios are quite robust and achieve decent returns using simple strategies such as rebalancing and momentum-based adaptive allocation. At the suggestion of some readers, we investigate the effect of the day of month on the performance of the momentum-based adaptive asset allocation strategy. From many possibilities, I selected the following four portfolios: one built with SPY and TLT, the second with iShares and Vanguard ETFs, the third with Vanguard mutual funds, and the fourth with Fidelity mutual funds. ETFs portfolio: iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ) and SPDR S&P 500 Trust ETF (NYSEARCA: SPY ). ETFs portfolio: iShares Core Total US Bond Market ETF (NYSEARCA: AGG ) and Vanguard Total Stock Market ETF (NYSEARCA: VTI ). Mutual funds portfolio: Vanguard Total Bond Market Index Fund (MUTF: VBMFX ) and Vanguard Total Stock Market Index Fund (MUTF: VTSMX ). Mutual funds portfolio: Fidelity Total Bond Market Index Fund (MUTF: FTBFX ) and Fidelity Spartan Total Stock Market Index Fund (MUTF: FSTMX ). For purposes of comparison, we simulate these portfolios from December 2003 to December 2014, a total of eleven years. The time period of the study was selected based on the availability of historical data of the investment instruments; AGG was created in September 2003. The data for the study were downloaded from Yahoo Finance on the Historical Prices menu for the eight tickers, SPY, TLT, AGG, VTI , VBMFX , VTSTX , FTBFX and FSTMX. We use the monthly price data from September 2003 to December 2014, adjusted for stock splits and dividend payments. The article has two parts. In the first part, we present general results for the four portfolios. The second part presents the effect of varying the day of the month when the trading is done. Part I. General Results The first study was done on the SPY + TLT. In it, we compare the results obtained with the following two strategies: (1) A portfolio with 50% SPY and 50% TLT without rebalancing. This portfolio is called “fixed allocation”. (2) A portfolio that is, at all times, invested 100% in either SPY or TLT. The switching, if necessary, is done monthly at the closing of the last trading day of the month. All the funds are invested in the instrument with the highest return over the previous 3 months. This portfolio is called “adaptive allocation”. The data below shows the investment results over 11 years (132 months). The first line is a buy-and-hold on SPY, the second is a buy-and-hold on TLT, the third is buy-and-hold of an initial investment of 50% in SPY and 50% in TLT, while the fourth line is adaptive allocation on SPY and TLT based on a look back of 3 months. Table 1. SPY + TLT portfolios January 2004-December 2014 Total Return% CAGR% Max DD% SPY 130.4 7.88 -50.79 TLT 126.6 7.72 -21.81 Fixed Allocation 128.5 7.76 -18.68 Adaptive Allocation 347.0 14.58 -17.13 The equity curves for the fixed and adaptive allocation of the SPY + TLT portfolios are shown in Figure 1. (click to enlarge) Figure 1. Equities of SPY + TLT portfolios Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities. The second study compares the four pairs using the momentum-based adaptive allocation. The trading is done at the month’s closing prices. The results are given in Table 2. Table 2. Adaptive allocation of four portfolios January 2004-December 2014 Total Return% CAGR% Max DD% SPY + TLT 347.0 14.58 -17.13 VTI + AGG 241.6 11.82 -13.03 VTSMX + VBMFX 243.4 11.87 -13.81 FSTMX + FTBFX 214.8 10.99 -20.29 The equity curves for the three portfolios with adaptive allocation are shown in Figure 2. The Vanguard mutual fund was omitted because it virtually overlaps with the Vanguard ETF portfolio. (click to enlarge) Figure 2. Equities of portfolios with adaptive allocation Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities. Part II. Day of Month Trading Results The study was done using the daily historical prices of the eight instruments. Because the results were very similar for the four pairs, we report mostly the results for the SPY + TLT pair only. The switching between bond and stock funds was done, if necessary, on the same day of the month. The look back period was three months, comparing prices on the same day of the month, but for three months apart. The day of the month is indicated by a variable called “shift”. Shift takes values between -16 and 6. Here shift=6 means the 6th trading day of the month, shift=0 means the last trading day of the month, shift=-1 means the trading day before the last trading day, etc. The equity curves for the SPY + TLT portfolio for three different trading days and with adaptive allocation are shown in Figure 3. As can be seen, the trading day of the month has a significant effect on the results. Trading on the last day of the month is better than trading on the 6th day of the month, but a little worse than trading seven days before the end of the month. These results are related to the specific historical data and cannot be generalized. (click to enlarge) Figure 3. Equities of the SPY + TLT portfolios with adaptive allocation Source: This chart is based on EXCEL calculations using the adjusted daily closing share prices of securities. To illustrate better the variability of the performance of adaptive allocation with the trading day of the month, we show the scatter plots of CAGR and DD versus the shift values from -16 to 6. (click to enlarge) Figure 4. CAGR% of the SPY + TLT portfolios with adaptive allocation Source: This chart is based on EXCEL calculations using the adjusted daily closing share prices of securities. As can be seen in Figure 4, CAGR varies very little for shift values from -5 to 5, but decreases substantially for shift values outside this range. (click to enlarge) Figure 5. DD% of the SPY + TLT portfolios with adaptive allocation Source: This chart is based on EXCEL calculations using the adjusted daily closing share prices of securities. As can be seen in Figure 5, DD varies very little for shift values from -16 to 4, but increases somewhat for shift=6. Conclusions The day of the month when the trading is done affects the performance obtained applying the adaptive asset allocation strategy. The performance is better if the trades are executed around the end/beginning of the month, than close to the middle of the month. The day of month effect is consistent for ETFs and related mutual funds. It may be useful to extend this study to various portfolios with instruments from other asset classes.

Momentum And Rebalancing Of Retirement Income Portfolios

Summary Robust investment portfolios can be constructed with just two ETFs: one representing the total stock market and another representing the total bond market. From November 2003 to December 2014, the ETF portfolio with fixed allocation allowed a safe 4% annual withdrawal rate and achieved a 28.95% increase of the capital. Better returns were achieved by rebalancing the portfolio at 25% deviation from the target weights. Capital increased by 43.66%, average annual return of 3.35%. Radically better performance is achievable using adaptive asset allocation. With a safe 4% withdrawal rate, the capital increased by 164.93%, average annual return of 9.26%. ETF portfolio performs essentially the same as its mutual fund counterparts. The comparison of their performance is evident in the tables included in the article. In a couple of recent articles , we demonstrated that a very simple and well diversified portfolio may be made up of two instruments, one representing the total stock market, and the other the total bond market. These portfolios are quite robust and achieve decent returns using simple strategies as rebalancing and momentum based adaptive allocation. At the suggestion of some readers, we investigate the suitability of these portfolios as retirement investments for income generation and capital appreciation. From many possibilities, I selected the following three portfolios: one built with iShares and Vanguard ETFs, the second with Vanguard mutual funds, and the third with Fidelity mutual funds. ETFs portfolio: iShares Core US Aggregate Bond Market ETF (NYSEARCA: AGG ) and Vanguard Total Stock Market ETF (NYSEARCA: VTI ). Mutual funds portfolio: Vanguard Total Bond Market Index Fund (MUTF: VBMFX ) and Vanguard Total Stock Market Index Fund (MUTF: VTSMX ). Mutual funds portfolio: Fidelity Total Bond Market Index Fund (MUTF: FTBFX ) and Fidelity Spartan Total Stock Market Index Fund (MUTF: FSTMX ). For purposes of comparison we simulate these portfolios from November 2003 to December 2014, a total of eleven years. The time period of the study was selected based on the availability of historical data of the investment instruments; AGG was created in September 2003. In this article, three different strategies will be considered: Portfolio is 50% stocks and 50% bonds without rebalancing. Portfolio is created with 50% stocks and 50% bonds; it is rebalanced when the allocation deviates by 25% from the 50 target, when the allocations become 62.5% and 37.5%. Portfolio is at all times invested 100% in either stocks, or bonds. The switching, if necessary, is done monthly at closing of the last trading day of the month. All the funds are invested in the instrument with the highest return over the previous 3 months. The data for the study were downloaded from Yahoo Finance on the Historical Prices menu for the six tickers. We use the monthly price data from September 2003 to November 2014, adjusted for stock splits and dividend payments. The time selection is restricted by the availability of data; AGG was created in September 2003. Portfolios with fixed weights with withdrawals, no rebalancing Assume that we have $1,000,000 to invest for income in retirement. We plan to withdraw 4% annually plus a 2% inflation adjustment. The withdrawals are done monthly. Over the 11 years from 2003 to 2014, a total of $488,000 was withdrawn. The first table shows the results of the portfolios created with 50% AGG and 50% VTI, and their Vanguard and Fidelity mutual fund counterparts. The monthly withdrawal is done such a way that the weights of the two components are brought back toward the target of 50-50. Below, we show the hypothetical behavior of these equal weight portfolios from November 2003 to December 2014. The maximum drawdowns of the portfolios are larger than that of the same portfolios without income withdrawals, because the withdrawals decrease the equity. On the average the returns are greater than the withdrawals, so the total capital is increasing . The CAGR columns give the cumulative average growth rate of the capital. Table 1. Fixed allocation portfolios without rebalancing CAGR% Max DD % Final Equity AGG + VTI 2.40 -28.29 1,298,500 VTSMX + VBMFX 2.40 -28.34 1,298,100 FSTMX + FTBFX 3.05 -32.75 1,392,100 The plots of the portfolios are shown in figure 1. The values are shown in percentages of the initial investment. (click to enlarge) Figure 1. Equities of portfolios with 4% annual withdrawal without rebalancing. Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities. Portfolios with fixed weights with withdrawals and rebalancing As before, we assume that we have $1,000,000 to invest for income in retirement. We plan to withdraw 4% annually plus a 2% inflation adjustment. Over the 11 years from 2003 to 2014, a total of $488,000 was withdrawn. The only difference of the strategy is that we rebalance the portfolio when the allocation between stocks and bonds deviates by 25% from the 50% target. The rebalance happens when the allocations become 62.5% and 37.5%. During the 11 years of our study there was only one rebalancing. But, as can be seen in Table 2, the rebalance contribute to a substantial increase in returns. Table 2. Fixed allocation portfolios with rebalancing CAGR% Max DD % Final Equity AGG + VTI 3.35 -28.29 1,436,600 VTSMX + VBMFX 3.31 -28.34 1,430,800 FSTMX + FTBFX 3.45 -32.75 1,451,700 The plots of the portfolios are shown in figure 2. The values are shown in percentages of the initial investment. (click to enlarge) Figure 2. Equities of portfolios with 4% annual withdrawal and rebalancing. Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities. To appreciate the improvement obtained by rebalancing, in figure 3 are shown the equities for the ETF portfolio with and without rebalancing. (click to enlarge) Figure 3. ETF portfolios with fixed allocations Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities. Adaptive Asset Allocation What we presented so far is a robust example from which one can infer that portfolio rebalancing has some positive effect in improving returns of a retirement investment. Another approach, with significant better results is to apply an adaptive asset allocation based on price momentum. We consider again the ETF portfolio of VTI and AGG by switching between two allocations: 100% AGG and 0% VTI 0% AGG and 100% VTI The switching is done monthly, on the last trading day of the month, using the following rule: invest fully in the asset with the highest return during the most recent 3 months. From November 2003 to November 2014, there were 25 reallocations of the ETF portfolio. The system was invested 88 months in VTI, and 44 months in AGG. The adaptive allocation system based on momentum achieved much higher return and lower drawdown than the fixed allocation system with or without rebalancing. Similar results were obtained with the Vanguard and Fidelity mutual funds. Those portfolios required 27 reallocations during the 11 years of the study. The Vanguard portfolio was invested 87 months in VTSMX, and 45 months in VBMFX. The Fidelity portfolio was invested 87 months in FSTMX, and 45 months in FTBFX. Table 3. Adaptive allocation portfolios CAGR% Max DD % Final Equity AGG + VTI 9.26 -18.18 2,649,300 VTSMX + VBMFX 8.22 -18.67 2,384,300 FSTMX + FTBFX 7.61 -24.97 2,241,700 The plots of the portfolios are shown in figure 1. The values are shown in percentages of the initial investment. (click to enlarge) Figure 4. Adaptive Allocation Portfolios Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities. Conclusion The adaptive allocation algorithm performed substantially better than the fixed allocation algorithms regardless of the type of market. It generated much higher returns with lower risk. For a comparison see figure 5. (click to enlarge) Figure 5. ETF portfolios with monthly withdrawals 2003-2011. Source: This chart is based on EXCEL calculations using the adjusted monthly closing share prices of securities.