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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.

The Idiot’s Guide To Asset Allocation

The finance industry constantly strives to confuse investors with new, more sophisticated and increasingly complex ways to manage risk and generate returns. But these new products and strategies generate their own risks – for example, falling prey to data mining or extrapolation. But there are simple ways to invest that can produce superior investment outcomes with a fraction of the time and effort. This article focuses on investment techniques that are so simple, it is surprising how well they work – a phenomenon that Brett Arends of MarketWatch has called “dumb alpha.” A Simpler Way to Think about the Future Let’s assume you are in your thirties or forties. You need to finance your retirement with your savings. Creating a portfolio to build retirement wealth is no easy feat, given the fact that retirement may be 30-40 years in the future. A lot can happen in that time. Who can say what the next 30 years will look like? Since it is impossible to predict which investments will do well during the next three decades, there are only two logical ways to invest. One is to keep all your savings in cash or the safest short-term bills and bonds. The problem with this approach is that you will find it impossible to keep pace with inflation once taxes and other expenses are taken into account. The alternative is to invest an equal amount of your money in every asset class that’s available in the marketplace. This makes sense, because you don’t know how stocks will do compared with bonds or real estate investments, or how Apple (NASDAQ: AAPL ) stock will do compared to Amazon (NASDAQ: AMZN ). The simplest example of this naive equal-weighted approach would be a portfolio split 50/50 between stocks and bonds. Another approach would be to invest one-quarter of your assets in cash, one-quarter in bonds, one-quarter in equities, and one-quarter in precious metals. Similarly, instead of investing in a common stock index, such as the cap-weighted S&P 500 Index, you could evenly spread your precious funds across all 500 stocks of the index. The Advantages of a Naive Asset Allocation As it turns out, this way of investing tends to work extremely well in practice. In their 2009 article ” Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy? ” Victor DeMiguel, Lorenzo Garappi, and Raman Uppal tested this naive asset allocation technique in 14 different cases across seven different asset classes and found that it consistently outperformed the traditional mean-variance optimization technique. None of the more sophisticated asset allocation techniques they used, including minimum-variance portfolios and Bayesian estimators, could systematically outperform naive diversification in terms of returns, risk-adjusted returns, or drawdown risks. Unfortunately, naive asset allocation does not work all the time. Over the last several years, only one asset class has generated high returns: stocks. So, a naive asset allocation will not keep up with the more equity-concentrated portfolios during such periods. But it is interesting to note how well a naive approach works over an entire business cycle. Practitioners should compare their portfolios with a naive asset allocation to check whether they really have a portfolio that delivers more than an equal-weighted portfolio. You can create a better (“more sophisticated”) portfolio than the equal-weighted (“dumb”) one, but it is surprisingly hard to do. As a check, you can create an equal-weighted portfolio from the assets or asset classes used in your current portfolio. Then test whether the current portfolio is superior to this equal-weighted benchmark over time in terms of returns, risks, and risk-adjusted returns. If that is the case, congratulations: You have a good portfolio. If not, you should think of ways to improve the performance of your existing portfolio. It is also pretty clear why this dumb alpha works. Within stock markets, putting the same amount of money in every stock systematically prefers value and small-cap stocks over growth and large-cap stocks. These two effects conspire to create outperformance. There is a second effect at play, however. After all, the value and small-cap effect cannot explain why a naive asset allocation also works in a multi-asset-class portfolio. The key reason for its strong showing is its robustness to forecasting errors. Most asset allocation models, like mean-variance optimization, are very sensitive to prediction errors. Unfortunately, even financial experts are terrible at forecasting, and one follows forecasts at one’s peril. By explicitly assuming that you cannot predict future returns at all, an equal-weighted asset allocation is well suited for unexpected surprises in asset class returns – both positive and negative. Since unexpected events happen time and again in financial markets, in the long run an equal-weighted asset allocation tends to catch up with more “sophisticated” asset allocation models whenever an event happens that the latter are unable to reflect. In other words, if a naive asset allocation outperforms a more sophisticated portfolio, it might provide a hint as to why this is the case. Are there too many risky assets in the sophisticated portfolio that directly or indirectly create increased stock market exposure? What are the implicit or explicit assumptions that led to the more sophisticated portfolio that have not materialized and have led to an underperformance relative to a less sophisticated naive asset allocation? In this sense, the naive asset allocation can act as a more practical alternative to a sophisticated portfolio, and as a more easily managed risk management tool.

The Risks Of Selling The Rally

Summary Investors that were fortunate to buy into the hole in either August or September have now been rewarded with a double digit gain on most broad-based indices. If you had the tenacity or good luck to buy the dip, you may question the risks of overstaying your welcome on the upside. Below are some bullet points that may provide a road map to making this difficult decision a little easier to digest. Investors that were fortunate to buy into the hole in either August or September have now been rewarded with a double digit gain on most broad-based indices. What began with some skepticism as just a short-covering binge has now morphed into the notion of a full blown recovery. There is even quite a bit of debate on whether or not we could take out the prior all-time highs on the S&P 500 Index before the year is out. Of course, if you had the tenacity or good luck to buy the dip, you may question the risks of overstaying your welcome on the upside. Those that took a more active approach in loading up on stocks near the lows are likely just as leery of a blow off top that ends in a swift and pernicious drop. Below are some bullet points that may provide a road map to making this difficult decision a little easier to digest. Evaluate your time horizon and investment goals. If you are short-term trader with defined risk parameters, then taking off some of your long positions into this run higher may be a prudent decision. It will free up cash to evaluate other opportunities and offer the flexibility to deploy capital when needed. Conversely, long-term investors may not be as concerned with these daily machinations and are willing to ride out additional volatility in order to stick with their plan. Here is a short guide to some of the key differences between being an investor and a trader . Consider making changes in small increments. If you took an above-average risk by loading up on stocks at the lows, then you have more flexibility to bank profits on the way higher. That may include breaking trades up into two or three pieces in order to slowly reduce your stock allocation over time. That way you can still participate in additional upside momentum if the market continues on the current course, but don’t have as much to lose if it turns lower. Don’t count on timing the market perfectly. There was a risk of buying on the way down that the market continues falling even further and compounds your losses. Similarly, there is an even greater risk that selling on the way up will leave you underinvested as the market continues to march higher. No one knows exactly where and when inflection points will form. Hanging on to some token long exposure may allow you to avoid the FOMO (fear of missing out) syndrome that leads to poor decision making at inopportune times. Analyze the risk profile of your exposure. If you loaded up on high beta sectors of the market such as technology or consumer discretionary stocks, it may be prudent to switch to a more defensive approach . That could include a low volatility index such as the PowerShares S&P 500 Low Volatility Portfolio (NYSEARCA: SPLV ) or individual sectors exhibiting less relative price sensitivity. That way you are still able to participate in some measure of upside potential with the intent of reducing downside risk. The Bottom Line There is always an opportunity cost when you make a change to your portfolio that your intended actions lead to more harm than good. Nevertheless, with a well-thought out game plan and sound portfolio management principles, you can enhance the odds of a favorable outcome.