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Mean-Variance-Optimization Applied To Portfolios Using QQQ During Bear Markets

Summary Portfolios using QQQ and bond mutual funds achieved high returns with low risk from 1999 to 2015. The parameters of the mean-variance optimization (MVO) algorithm can be easily adapted to the risk tolerance of the investors. MVO strategy is very robust, and it may continue to perform well in the future. The idea of writing this article came from a comment by Varan, a frequent contributor on Seeking Alpha. Varan suggested that I investigate the performance of a portfolio using the PowerShares QQQ Trust ETF (NASDAQ: QQQ ) during the 2000 to 2003 period. Since two funds in the portfolio, the iShares 1-3 Year Treasury Bond ETF (NYSEARCA: SHY ) and the iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ), were created in July 2002, Varan suggested that I use two mutual funds with similar holdings, the Vanguard Long Term Treasury Fund (MUTF: VUSTX ) and the Fidelity Limited Term Government Fund (MUTF: FFXSX ). In the articles on the simple ETF portfolio the simulations did not cover the 2000-03 bear market when QQQ had a maximum drawdown of -82.96%. We frequently hear investors saying that tactical asset allocation using bond funds will not work anymore because everybody expects a secular bond bear market. So, it is relevant to ask how tactical asset allocation worked using an asset that suffered a severe bear market. In that respect, QQQ is a prime example, having suffered such deep and prolonged losses during the 2000-03 bear market. It has taken twelve years for QQQ to recover and reach the level it had at its top in March 2000. The new portfolio is made up of the following four assets: SPDR S&P MidCap 400 ETF (NYSEARCA: MDY ) PowerShares QQQ Trust ETF Vanguard Long Term Treasury Fund Fidelity Limited Term Government Fund Basic information about the funds was extracted from Yahoo Finance and marketwatch.com and it is shown in table 1. Table 1. Symbol Inception Date Net Assets Yield% Category MDY 5/04/1995 14.23B 1.41% Mid-Cap Blend QQQ 3/03/1999 36.93B 0.96% Large Growth VUSTX 5/19/1986 3.27B 2.75% Long Term Treasury Bond FFXSX 11/10/1986 385M 0.68% Short Term Treasury Bond The data for the study were downloaded from Yahoo Finance on the Historical Prices menu for MDY, QQQ, VUSTX, and FFXSX. We use the daily price data adjusted for dividend payments. For the adaptive allocation strategy, the portfolio is managed as dictated by the Mean-Variance Optimization (MVO) algorithm developed on the Modern Portfolio Theory (Markowitz). The allocation is rebalanced monthly at market closing of the first trading day of the month. The optimization algorithm seeks to maximize the return under a constraint on the portfolio risk determined as the standard deviation of daily returns. The portfolios are optimized for three levels of risk: LOW, MID and HIGH. The corresponding annual volatility targets are 5%, 10% and 15% respectively. In Table 2 we show the performance of the strategy applied monthly from June 1999 to September 2015. Table 2. Performance of MVO algorithm applied monthly versus 100% in QQQ. TotRet% CAGR% VOL% maxDD% Sharpe Sortino 2015 return LOW risk 268.91 8.32 5.51 -5.51 1.51 2.19 3.60% MID risk 553.49 12.18 10.3 -10.55 1.18 1.68 3.10% HIGH risk 824.31 14.59 15.11 -16.12 0.97 1.36 -0.24% QQQ 124.69 5.08 29.43 -82.96 0.17 0.23 -1.22% In table 2 we see that all MVO portfolios had stellar performance over the 16 years of this study, even though QQQ had a very rocky ride. Also, notice that the realized volatilities of the MVO strategies are well correlated with the maximum drawdown and the realized annual returns. The 2015 returns column reports the results during 2015 to the end of September. It shows that all MVO strategies performed better than QQQ. The LOW and MID risk portfolios achieved a positive return of over 3% while QQQ lost 1.33%. The HIGH risk portfolio lost a minute 0.24%. The equity curves for all portfolios are shown in Figure 1. (click to enlarge) Figure 1. Equity curves of the portfolios with MVO monthly optimization versus QQQ over the whole time interval from June 1999 to September 2015. Source: All charts in this article are based on calculations using the adjusted daily closing share prices of securities. In figure 2 we show the equity curves during a shorter period that includes the 2000-03 bear market, specifically, we show the June 1999 to December 2003 interval. During the first nine months there was a steep increase in QQQ price followed by a three year bear market. We also included a nine month period of recovery. (click to enlarge) Figure 2. Equity curves of the portfolios with MVO monthly optimization versus QQQ over the time interval from June 1999 to December 2003. We see that all MVO portfolios increased at a slow pace during the bear market. The HIGH risk portfolio was basically flat from March 2000 to March 2003, while the LOW and MID risk portfolios achieved small but steady gains. The details of their performance are given in table 3. Table 3. Returns of QQQ and MVO portfolios during the 2000-03 bear market. Time Interval QQQ LOW_Risk MID_Risk HIGH_Risk 6/10/1999-3/28/2000 123.95% 13.32% 23.93% 53.15% 3/29/2000-3/11/2003 -79.79% 26.21% 22.72% 6.65% 3/12/2003-12/31/2003 53.25% 10.59% 17.86% 34.09% In figure 3 we show the equity curves of the MVO portfolio during the 2008-09 bear market. We included nine months of recovery from April to December 2009. (click to enlarge) Figure 3. Equity curves of the portfolios with MVO monthly optimization versus QQQ over the time interval from October 2007 to December 2009. In figure 3 we see that QQQ suffered a large loss from October 2007 to March 2009. During the same interval, the HIGH risk portfolio lost 8.40%, the MID portfolio was flat, and the LOW risk portfolio gained 7.29%. The exact numbers are given in table 4. Table 4. Returns of QQQ and MVO portfolios during the 2008-09 bear market. Time Interval QQQ LOW_Risk MID_Risk HIGH_Risk 10/1/2007-3/09/2009 -50.27 7.29 0.37 -8.40 3/10/2009-12/31/2009 78.72 8.71 19.35 42.54 Finally, in figure 4 we show the equity curves from September 2014 to September 2015. (click to enlarge) Figure 4. Equity curves of the portfolios with MVO monthly optimization versus QQQ over the time interval from September 2014 to September 2015. In figure 4 we see that QQQ as well as all the MVO portfolios were very volatile, but their equity was bound in a narrow range. Still, the LOW and MID risk portfolios outperformed by realizing modest gains. The exact gains and losses are given in table 5. Table 5. Returns of QQQ and MVO portfolios during the latest one year and the first nine months of 2015. Time Interval QQQ LOW_Risk MID_Risk HIGH_Risk 9/30/2014-9/30/2015 3.63 8.18 9.17 3.58 12/31/2014-9/30/2015 -1.22 3.60 3.10 -0.24 To give the reader more insight into how the MVO strategy succeeds in making gains even when an asset of the portfolio suffers extremely large losses, we present in the following three figures the monthly allocations during the period from June 1999 to December 2003. We decided to display the allocations over a short time interval in order to get graphs that are easy to read. (click to enlarge) Figure 5. Monthly allocations of the portfolios LOW risk strategy over the 2000-03 bear market. In figure 5 we see that the LOW risk strategy allocated, on average, over 60% of the money to the short term bond fund. QQQ was not allocated any funds between March 2000 and November 2002. The long term bond fund was allocated substantial funds during the bear market. (click to enlarge) Figure 6. Monthly allocations of the portfolios MID risk strategy over the 2000-03 bear market. The MID risk strategy allocated more funds to the long term bond fund than to the short term during the bear market. Again, QQQ was allocated the smallest amount of funds during the bear market. (click to enlarge) Figure 7. Monthly allocations of the portfolios HIGH risk strategy over the 2000-03 bear market. The HIGH risk portfolio allocated very little money to the short term bonds. During the bear market most money went alternately to the long term bonds and the mid cap MDY. QQQ was still not allocated any significant funds from April 2000 to November 2002. In table 6 we show the October 2015 allocations for all the strategies. Table 6. Current allocations for October 2015. MDY QQQ FFXSX VUSTX LOW risk 0% 0% 70% 30% MID risk 0% 0% 31% 69% HIGH risk 0% 0% 0% 100% Conclusion The Mean-Variance Optimization strategy applied to a well-constructed portfolio of stocks and bonds performs quite satisfactorily during deep bear markets. It also offers a very simple mechanism of adaptation to the risk tolerance of the investors by trading off risk and returns. The illustrations of this article give us confidence that MVO strategy is very robust, and it may continue to perform well in the future. Additional disclosure: The article was written for educational purposes and should not be considered as specific investment advice.

Simple ETF Portfolio Performance With Monthly Reallocation By Mean-Variance-Optimization

Summary The simple ETF portfolio with monthly reallocation performed better than the equal weight portfolio in 2015. The low and mid risk portfolios had good positive returns, while the high risk portfolio had a very small loss. Even the high risk portfolio performed better than the equal weight portfolio. The simple ETF portfolio was introduced in an article published in August 2015. Since then the markets suffered a mini crash and a correction associated with high volatility and very negative market sentiment. Investors all over the world moved large amount of money out of the stock market and into other “perceived safer” asset classes such as bonds. It is appropriate, therefore, to ask ourselves how an adaptive strategy is dealing with this kind of market environment. In this article we analyze the performance of the simple ETF portfolio, emphasizing its results during the latest period of high market turbulence. For completeness, we will review the historical performance of the portfolio since January 2003, but will discuss in more detail its performance during the first nine months of 2015. The portfolio is made up of the following four ETFs: SPDR S&P MidCap 400 ETF (NYSEARCA: MDY ) PowerShares QQQ Trust ETF (NASDAQ: QQQ ) iShares 1-3 Year Treasury Bond ETF (NYSEARCA: SHY ) iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ) Basic information about the funds was extracted from Yahoo Finance and marketwatch.com and it is shown in table 1. Table 1. Symbol Inception Date Net Assets Yield% Category MDY 5/04/1995 14.23B 1.41% Mid-Cap Blend QQQ 3/03/1999 36.93B 0.96% Large Growth SHY 7/22/2002 13.11B 0.48% Short Term Treasury Bond TLT 7/22/2002 6.41B 2.62% Long Term Treasury Bond The data for the study were downloaded from Yahoo Finance on the Historical Prices menu for MDY, QQQ, SHY and TLT. We use the daily price data adjusted for dividend payments. For the adaptive allocation strategy, the portfolio is managed as dictated by the mean-variance optimization algorithm developed on the Modern Portfolio Theory ( Markowitz ). The allocation is rebalanced monthly at market closing of the first trading day of the month. The optimization algorithm seeks to maximize the return under a constraint on the portfolio risk determined as the standard deviation of daily returns. The portfolios are optimized for three levels of risk: LOW, MID and HIGH. The corresponding annual volatility targets are 5%, 10% and 15% respectively. In Table 2 we show the performance of the strategy applied monthly from January 2003 to September 2015. Table 2. Performance of MVO algorithm applied monthly versus an equal weight portfolio. TotRet% CAGR% VOL% maxDD% Sharpe Sortino 2015 return LOW risk 167.65 8.03 5.60 -5.59 1.43 1.99 3.16% MID risk 399.09 13.45 10.61 -10.34 1.27 1.68 3.60% HIGH risk 697.85 17.70 16.40 -17.18 1.08 1.52 -0.33% Equal weight 204.71 9.14 9.58 -24.50 0.95 1.29 -1.33% Please notice that the realized volatilities are well correlated with the target values. In fact, the realized volatilities are just slightly greater that the target values. Also, as expected, the realized annual returns are also well correlated to the volatility targets. All the values in the CAGR% column are a little greater than the realized volatilities in the VOL% column. The 2015 returns column shows that all MVO strategies performed better than the equal weight portfolio. The LOW and MID risk portfolios achieved a positive return of over 3% while the equal weight portfolio lost 1.33%. The HIGH risk portfolio lost a minute 0.33%. The equity curves for all portfolios are shown in Figure 1. (click to enlarge) Figure 1. Equity curves of the portfolios with MVO monthly optimization and equal weight allocation. Source: All charts in this article are based on calculations using the adjusted daily closing share prices of securities. We see in figure 1 that the equity of the LOW risk portfolio had a constant, very stable, rate of increase over the entire time of the simulation. It was almost unaffected by any market event. By contrast, the equity of the equal weight strategy with rebalancing shows the highest variability and the highest loss during the 2008-09 crises. The equal weight strategy worked quite well during long bullish periods of the market such as during 2003-07 and 2009-14. The MID and HIGH risk strategies worked extremely well during the 2009-14 period with a very brief periods of mild correction in 2011. All strategies show a flattening of their equity curves during 2015. In Figures 2, 3 and 4 we show the time allocation for all MVO strategies from January 2014 to September 2015. We decided to display the allocations over a shorter most recent time interval in order to get graphs that are easy to read. (click to enlarge) Figure 2. In figure 2 we see that the LOW risk strategy allocated, on average, over 60% of the money to the bond funds. About 30% to 40% was allocated alternately to QQQ or MDY. (click to enlarge) Figure 3. In figure 3 we see that in 2014 the money was allocated alternately between TLT and QQQ. The first half of 2015 the allocation went to MDY and TLT. In July and August of 2015 the money was allocated to QQQ and SHY, switching all to TLT and SHY in September and October. (click to enlarge) Figure 4. In figure 4 we see that the HIGH risk strategy allocates the money to a single asset at any time. Since January 2014 it simply alternated between QQQ and TLT. This strategy worked very well most of the time, but in the first nine months of 2015 it suffered a very small loss. In table 4 we show the current allocations for all the strategies. Table 3. Current allocations for October 2015. MDY QQQ SHY TLT LOW risk 0% 0% 69% 31% MID risk 0% 0% 35% 65% HIGH risk 0% 0% 0% 100% As seen in table 3 all portfolios are invested only in bond funds, regardless of risk level. The low risk portfolio in mostly invested in the short term, while the high risk is 100% in long term treasuries. Conclusion The simple ETF portfolio with monthly reallocation performed better than the equal weight portfolio in 2015.The low and mid risk portfolios had good positive returns, while the high risk portfolio had a very small loss. Additional disclosure: The article was written for educational purposes and should not be considered as specific investment advice.

Fidelity Select Funds Portfolio Optimized For Low Volatility Performed Well In 2015

Summary LOW volatility portfolio: FIBIX, FSBIX, FSPHX, FSELX, FSCHX, FBMPX. MID volatility portfolio: FLBIX, FSBIX, FSPHX, FSELX, FSCHX, FBMPX. HIGH volatility portfolio: FLBIX, FIBIX, FSPHX, FSELX, FSCHX, FBMPX. The LOW volatility portfolio had a positive return so far in 2015 despite the interest rate uncertainty. In a previous article we presented the performance of a portfolio made up of five Fidelity select mutual funds. That portfolio had a stellar performance over the whole 27 year period starting in 1987. Back in July we decided to replace the GNMA fund (MUTF: FGMNX ) with two high quality government bonds. The performance of the two portfolios was discussed in the July article, the conclusion being that the new portfolio performed slightly better than the old one. In the first article I used a Relative Strength (RS) strategy based on a three-month look back evaluation period. In the second article I used a Mean-Variance Optimization (MVO) algorithm with 65-day look back evaluation period. While the MVO algorithm may approximate the RS algorithm if one selects the proper volatility target, the MVO strategy is very flexible, and it allows the investor to adapt it to the variable market environment. It turns out that during the first nine months of 2015 the RS strategy, as well as the Dual Momentum (DM) one, has performed poorly with a return of -15.22% for a 3-month look back, or -10.15% for a 12-month look back. The interested reader may verify the performance of Dual Momentum and Relative Strength on the portfoliovisualizer.com site. In this article we shall use only the MVO strategy and we want to emphasize the performance of the new portfolio during the first three quarters of 2015. We shall present three versions of this new portfolio for three levels of volatility: low, mid and high. The three versions are meant for investors with different risk tolerance. They also are meant for investors who may want to vary their risk level based on their evaluation of the markets. The portfolios are made up of the following funds: Fidelity Select Multimedia Portfolio (MUTF: FBMPX ) Fidelity Select Chemicals Portfolio (MUTF: FSCHX ) Fidelity Select Electronics Portfolio (MUTF: FSELX ) Fidelity Select Health Care Portfolio (MUTF: FSPHX ) Fidelity Spartan Long Term Treasuries Fund (MUTF: FLBIX ) Fidelity Spartan Intermediate Term Treasuries Fund (MUTF: FIBIX ) Fidelity Spartan Short Term Treasuries Fund (MUTF: FSBIX ) With the seven funds above, we created three portfolios to be used at three volatility levels: low, mid and high. All portfolios include the same four equity funds, but each one includes only two of the three treasury funds. The high risk uses FLBIX and FIBIX, the mid risk includes FLBIX and FSBIX, while the low risk has FIBIX and FSBIX. The data for the study were downloaded from Yahoo Finance on the Historical Prices menu for FBMPX, FSCHX, FSELX, FSPHX, FLBIX, FIBIX and FSBIX. We use the daily price data adjusted for dividend payments. The portfolio is managed as dictated by a variance-return optimization algorithm developed on the Modern Portfolio Theory ( Markowitz ). The allocation is rebalanced monthly at market closing of the first trading day of the month. In table 1 we present the performance of the portfolio for three levels of risk. Table 1. Portfolio performance from January 2007 to October 2015 TotRet% CAGR% VOL% maxDD% Sharpe Sortino 2015 return LOW risk 109.22 8.80 5.49 -7.50 1.60 2.10 1.75 MID risk 287.58 16.75 13.37 -16.97 1.25 1.69 -0.49 HIGH risk 569.16 24.26 20.22 -16.97 1.20 1.70 -2.45 The realized volatilities of the portfolios are in agreement with their names; the LOW risk had 5.49% annualized volatility, the MID had 13.37%, while the HIGH had 20.22%. Also, please notice the strong correlation between the returns CAGR and volatility of the portfolios. On the other hand, during 2015 the LOW volatility portfolio produced a positive return of 1.75%, while the MID and HIGH risk portfolio suffered negative returns. In figure 1 we show the graphs of the portfolio equities for the period from January 2007 to October 2015. (click to enlarge) Figure 1. Equity curves for three portfolios adaptively optimized for low, medium and high risk targets. Source: All charts in this article are based on EXCEL calculations using the adjusted daily closing share prices of securities. In figure 2, 3 and 4 we show the time variation of the percentage allocation of the funds for the period since January 2014 to October 2015. We opted for this shorter time period to get graphs that are easily readable. We are mostly interested in the allocations during 2015. (click to enlarge) Figure 2. Percentage allocation of the funds for low risk portfolio January 2014 to October 2015. One can see in figure 2 that most of the time the portfolio was invested about 50% in the short term treasury fund FSBIX. In figure 3 we show the time variation of the percentage allocation of the funds for mid risk. (click to enlarge) Figure 3. Percentage allocation of the funds for MID risk portfolio January 2014 to October 2015. (click to enlarge) Figure 4. Asset allocations for the portfolio adaptively optimized for the HIGH risk target January 2014 to October 2015.. Since July 2015 the high risk portfolio was invested 100% in treasuries; in FSLBX in July and August, and in FIBIX in September and October. The current fund allocations are shown in table 3. Table 3. Asset allocations for October 2015 FSELX FBMPX FSPHX FSCHX FLBIX FIBIX FSBIX LOW risk 0% 0% 0% 0% 0% 0% 100% MID risk 0% 0% 0% 0% 88% 0% 12% HIGH risk 0% 0% 0% 0% 0% 100% 0% Conclusion The low risk Fidelity select portfolio performed better than the mid and high risk portfolios. While the return of 1.75% is relatively modest, it is better than many other choices. The losses of the mid risk portfolio are very small at -0.49%, while the high risk portfolio lost the most at -2.45%. In hindsight, investing in a low risk portfolio was the better choice due to the fact that the market environment was very difficult since the beginning of 2015.