Tag Archives: etfs

Combining Volatility, Momentum, And Trend In Asset Allocation

Summary Risk-based portfolio strategies are popular in the asset management industry. Three common strategies are Minimum Variance (MV), Equal Risk Contribution (ERC) and Maximum Diversification (MD). These strategies do not depend on asset returns’ forecasts and they are based on a single criterion: risk. With higher returns and lower risk, risk-based portfolios that use moving averages have higher Sharpe ratios than initial risk-based portfolios. High momentum risk-based portfolios, by contrast, have higher risk, which is largely compensated for by higher returns. By Gregory Guilmin The Effective Combination of Risk-Based Strategies with Momentum and Trend Following Abstract: The Efficient Market Hypothesis (EMH) has been widely called into question in the investment literature, through two main anomalies: timing and low-volatility anomalies. In this paper, we aim to combine the predictive power of timing and low-volatility strategies to deliver better risk-adjusted portfolio performance. We adopt a two-step approach for a constant dataset composed of 18 country MSCI stock market indices over the 1975-2014 period. First, we use different timing strategies: moving averages and momentum. We select stock market indices based on different moving averages (6, 8, 10, and 12 months), while the momentum strategy ranks the different stock market indices into momentum subsets (low, medium, and high momentum). After the first step using the different timing strategies, the second step consists in building risk-based portfolios (MV, ERC, and MD) as well as 1/N benchmark portfolios for each of these timing strategies. Our results highlight the effectiveness, the relevance and the robustness of our approach. First, risk-based portfolios using relevant timing strategy indeed provide better returns, lower volatilities, higher Sharpe ratios, and lower Value-at-Risk (VaR) and Expected Shortfall (ES) than traditional risk-based portfolios. The second contribution of our approach features that risk-based strategies provide better risk-adjusted returns and lower VaR and ES than the 1/N portfolio within a context in which the first step is dedicated to the application of a relevant timing strategy. Finally, among these risk-based portfolios using relevant timing strategies, the MD and MV portfolios usually obtain the best risk-adjusted performance. Alpha Highlight: Risk-based portfolio strategies are popular in the asset management industry. Three common strategies are Minimum Variance (MV), Equal Risk Contribution (ERC) and Maximum Diversification (MD). These strategies do not depend on asset returns’ forecasts and they are based on a single criterion: risk. The interest in estimation procedures relying on a risk measure could be explained by three major factors: Reconsideration of the importance and the relevance of portfolio risk management. Better predictability of security variance and covariance risks by comparison with expected returns. The outperformance of the “low-volatility anomaly.” Details here . In addition to the low-volatility anomaly, a large number of authors have talked about the “momentum anomaly.” The momentum effect has been emphasized by Jegadeesh and Titman (1993). Momentum strategies are profitable in most major stock markets worldwide and this outperformance of momentum strategies is consistent over time. Linked to this concept of cross sectional momentum, time-series momentum, such as trend following strategies, have been identified. Several academic papers show that moving average trading rules have predictive power for future returns, and that trend following strategies with moving averages are effective in practice (Among others, see Brock et al., 1992; Clare et al., 2014; Faber, 2007, 2013; Hurst et al., 2010 and ap Gwilym et al., 2010). Methodology: Given this backdrop, in which risk-based strategies and timing strategies have been developed in the literature, the purpose of this paper is to combine the two strategies. This two-step approach consists in applying a timing strategy (either a moving average or a momentum strategy in the first step) followed by risk-based portfolio optimization procedures (second step). We compute risk-based and equally weighted (as a benchmark) portfolios with and without timing strategies in the first step for a constant empirical dataset composed of 18 country MSCI stock market indices. The estimation period ranges from January 1975 to December 2014. To the best of our knowledge, this paper is the first to shed light on the combination of timing and risk-based strategies. First Step: Selection of the stock market indices The methodology consists of two steps. In the first step, moving averages are used to select stock market indices that perform well (by exhibiting an upward trend) and that are used in the second step of our analysis (i.e., in the risk-based and 1/N portfolio optimization). Stock market indices exhibiting a negative trend are not selected as an input in the portfolio optimization procedure. If the price of the stock market index is above its x − month moving average, then this index is selected for the portfolio optimization procedure. Conversely, if it crosses below its x − month moving average, then the stock market index is not selected for the second step. We use moving averages of varying lengths: 6, 8, 10, and 12 months. To add an additional timing strategy, we also select stock market indices in accordance with the concept of momentum, in which a stock market’s performance relative to its peers predicts its future relative performance. As long-term investors, the momentum strategy involves ranking stock market indices based on their past 12-month performance and splitting them into three subsets, depending on the value of their momentum compared with one of their peers. The three subsets are the low, medium and high momentum subsets, respectively. Second Step: Portfolio optimization After selecting stock market indices following the different timing strategies of the first step, the second stage consists in applying different portfolio optimization procedures to find the optimal weights of the selected stock market indices. Selection (1st step) and weighting (2nd step) are adjusted simultaneously, i.e., on a monthly basis (end of month). We apply three risk-based portfolio strategies (Minimum Variance, Equal Risk Contribution and Maximum Diversification) as well as the 1/N benchmark portfolio strategy, usually considered a relevant benchmark in the literature. First, the Minimum Variance portfolio aspires to minimize the global variance of the portfolio. Second, the Equal Risk Contribution portfolio is the portfolio in which the risk contribution is the same for all assets in the portfolio. Finally, the Maximum Diversification portfolio (also called the Most Diversified Portfolio), introduced by Choueifaty (2006), is the portfolio that maximizes diversification. Diversification is computed using the diversification ratio. The diversification ratio is defined as the ratio of its weighted average volatility to its portfolio volatility. Main Findings: The table below summarizes results based on a constant dataset composed of 18 country MSCI stock market indices between 1975 and 2014. We can see that all portfolios that employ moving averages in the first step perform better than initial risk-based portfolios . Regarding momentum, high momentum risk-based strategies offer better annual performance than initial risk-based portfolios. Table 1: Portfolio performances with the constant country MSCI Indices sample (1975-2014) Annualized Annual Annualized Sharpe VaR (1%) ES (1%) returns (%) returns (%) Volatility (%) Ratio (%) (%) Initial Portfolios 1/N 8.931 10.013 16.723 0.599 -13.118 -18.531 MV 8.152 8.866 14.017 0.632 -10.987 -14.785 ERC 8.785 9.781 16.131 0.606 -12.550 -18.116 MD 8.624 9.655 16.275 0.593 -14.254 -17.890 With timing strategies 6 months 1/N 10.032 10.732 14.965 0.717 -11.946 -15.482 MV 9.987 10.472 13.439 0.779 -10.238 -13.884 ERC 9.605 10.256 14.387 0.713 -11.592 -15.107 MD 10.515 11.166 14.882 0.750 -11.966 -15.843 8 months 1/N 10.401 11.062 14.897 0.743 -11.946 -15.363 MV 10.626 11.056 13.419 0.824 -10.212 -13.961 ERC 10.107 10.694 14.218 0.752 -11.592 -15.000 MD 11.079 11.650 14.664 0.794 -11.966 -15.787 10 months 1/N 9.832 10.534 14.842 0.710 -11.665 -15.258 MV 9.299 9.853 13.499 0.730 -10.871 -14.453 ERC 9.486 10.119 14.170 0.714 -11.311 -15.026 MD 10.191 10.855 14.744 0.736 -11.966 -16.022 12 months 1/N 10.612 11.229 14.725 0.763 -11.904 -15.220 MV 10.523 10.957 13.358 0.820 -10.602 -14.488 ERC 10.494 11.020 14.021 0.786 -11.621 -15.066 MD 11.206 11.766 14.671 0.802 -12.325 -16.304 Low momentum 1/N 5.359 7.021 18.821 0.373 -14.322 -19.843 MV 5.533 6.855 17.063 0.402 -13.632 -17.501 ERC 5.162 6.704 18.127 0.370 -14.152 -19.464 MD 5.773 7.233 17.884 0.404 -13.852 -19.023 Medium momentum 1/N 8.919 9.997 16.747 0.597 -12.766 -17.035 MV 9.245 10.101 15.602 0.647 -11.012 -15.796 ERC 9.069 10.087 16.456 0.613 -12.456 -16.953 MD 9.247 10.309 16.770 0.615 -14.402 -18.084 High momentum 1/N 11.896 13.022 18.266 0.713 -14.637 -20.915 MV 12.583 13.446 17.231 0.780 -11.539 -18.729 ERC 12.16 13.178 17.834 0.739 -13.770 -20.125 MD 12.092 13.218 18.356 0.720 -13.443 -20.719 Market-cap weighted benchmarks MSCI World 8.016 8.839 14.782 0.598 -11.073 -14.564 MSCI World Momentum 11.432 12.130 15.817 0.767 -11.517 -14.965 The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request. Trend following and high momentum strategies are effective for 1/N portfolio optimization but also for risk-based portfolios because they produce better annual returns compared with initial risk-based portfolios. With respect to risk measures such as volatility, Value-at-Risk (VaR) and Expected Shortfall (ES), risk-based portfolios that employ moving averages exhibit lower volatility than initial risk-based portfolios as well as lower VaR and ES. This finding is important because it enables investors to reduce the risk to which they are exposed. With higher returns and lower risk, risk-based portfolios that use moving averages have higher Sharpe ratios than initial risk-based portfolios. High momentum risk-based portfolios, by contrast, have higher risk, which is largely compensated for by higher returns. Therefore, such portfolios are characterized by higher Sharpe ratios than initial risk-based portfolios. This paper documents the effectiveness, in terms of risk and return, of the use of these relevant timing strategies combined with risk-based portfolio strategies. In addition to that, robustness checks were also conducted with different other datasets, different estimation periods as well as different parameters of the variance-covariance matrix. Original Post

Lower Risk Versions Of A Dual Momentum Fixed Income Strategy

Summary This article presents the performance and risk of Lower Risk Versions (LRVs) of a dual momentum fixed income strategy as compared to a High Risk Version (HRV) presented previously. The difference between the LRVs and HRV is the number of assets per month; the HRV selects one asset per month, while the LRVs select multiple assets per month. The LRV-3 (3 assets per month), backtested to 1994 using mutual fund proxies, has a CAGR of 10.2%, a standard deviation of 6.3%, and a maximum drawdown of -6.1%. The minimum annual return of LRV-3 is -2.4% in 1994. All other annual returns are positive. The LRVs are more robust than the HRV, and should be used by more conservative investors, who desire reasonable growth with less volatility and drawdown. In a recent article on Seeking Alpha, I discussed a simple tactical bond ETF strategy employing relative strength momentum. This strategy is explained in detail here . I will call the original strategy the High Risk Version (HRV) of the fixed income strategy, since only one ETF is selected each month (out of a basket of five ETFs). This article presents Lower Risk Versions (LRVs) of the same momentum strategy. For LRVs, a multiple number of ETFs are selected each month in order to reduce volatility and drawdown compared to the HRV, while still maintaining a CAGR greater than an equalweight portfolio holding all five assets. My basic objectives of the LRVs are: 1. A CAGR > 10%; 2. A standard deviation (SD) that is less than the SD of an equalweight portfolio of all assets; 3. No negative years of return; and 4. A maximum drawdown based on monthly returns of less than 7%. I started out by making a slight modification to the original HRV strategy in order to turn the strategy into a dual momentum strategy. The original methodology only used relative strength (no absolute momentum) to determine what asset to select. But, in a way, the original HRV that selected only one asset each month was really a dual momentum strategy, because a short-term treasury was included in the basket of assets. In order to determine the effect of selecting multiple assets each month rather than just one asset, I needed to use a true dual momentum approach instead of a relative strength strategy. So I have switched to the dual momentum technique in this study. Dual momentum strategies have been popularized by Gary Antonacci and are well-known to many investors. Dual momentum means relative strength momentum is first used to select the top-ranked asset(s) each month, and then the top-ranked asset(s) have to pass an additional absolute momentum test (must have positive momentum) in order to be selected in any given month. I selected a basket of five fixed income assets that have relatively low correlation to each other. A major challenge in developing fixed income strategies is the short history of fixed income ETFs. This results in rather limited backtesting for the ETFs. To extend the backtesting, mutual fund proxies are used that have longer histories; this permits backtesting of the strategy to the 1990s. Shown below are the assets in the basket, both the ETF and the mutual fund proxy. Convertible Bonds: SPDR Barclays Capital Convertible Bond ETF (NYSEARCA: CWB ) – Vanguard Convertible Securities Fund (MUTF: VCVSX ) High Yield Bonds: SPDR Barclays Capital High Yield Bond ETF (NYSEARCA: JNK ) – Fidelity Advisor High Income Advantage Fund (MUTF: FAHDX ) Long Term Treasury: iShares 20+ Year Treasury Bond ETF (NYSEARCA: TLT ) – Vanguard Long Term Treasury Fund (MUTF: VUSTX ) Short Term Treasury: iShares 1-3 Year Treasury Bond ETF (NYSEARCA: SHY ) – Vanguard Short Term Treasury Fund (MUTF: VFISX ) Emerging Market Bonds: PowerShares Emerging Markets Sovereign Debt Portfolio ETF (NYSEARCA: PCY ) – Fidelity New Markets Income Fund (MUTF: FNMIX ) In the original article, I used CNSAX as proxy for CWB and PREMX as proxy for PCY. But based on comments by EquityCurve in the original article, in order to get backtesting to 1994 instead of 1998, I changed to VCVSX instead of CNSAX and FNMIX instead of PREMX. So backtesting of the mutual funds now goes back to 1994. 1994 turns out to be a difficult year for bonds and I’m glad I could include it in the analysis. (All of this work was performed using the free Portfolio Visualizer software. Any investor can go online and trade the strategies in this article without any cost.) It turns out that the dual momentum strategy using this basket of assets is very robust, and good results are seen if one, two, three, four or all five ETFs are selected each month. There is the usual tradeoff between growth and drawdown depending on the number of assets selected each month. The greater the number of assets selected, the less the risk and growth. I will now present the results of the HRV that selects only one asset each month. These results are similar to the results presented in the original article, and are presented here just to be consistent with the results of the LRVs shown later in this article. The basket of mutual funds is used, and the backtesting timeframe is 1994-present. Two relative strength timing periods are employed to rank the funds: 4-months and 2-months. A 51% weighting on the 4-month ranking and a 49% weighting on the 2-month ranking is used. The 51%/49% weighting split is a good way to ensure that the 4-month timing period determines the better-ranking asset if there is a tie. The total return curves of the HRV, the equalweight portfolio (buy and hold all five assets, rebalanced annually), and the S&P 500 are shown below, together with a table of their relevant parameters and annual returns. Total Return Curve of HRV: (click to enlarge) Tabular Summary of HRV Results: (click to enlarge) Annual Returns: (click to enlarge) It can be seen that the HRV has a CAGR of 15.0%, an SD of 10.4%, and a maximum drawdown (based on monthly returns) of -13.0%. In terms of a risk-adjusted return on investment, the CAGR/SD is 1.44. This compares with holding an equalweight portfolio that has a CAGR of 7.8%, an SD of 7.0%, a maximum drawdown of -17.6%, and a CAGR/SD of 1.11. It can be seen that the HRV substantially increases growth at the expense of volatility (standard deviation). Yet the maximum drawdown is actually better for the HRV than the equalweight portfolio holding all five assets. For the LRVs, I systematically looked at various combinations of timing periods and number of assets selected each month. Overall, when two or more assets are selected each month, the strategy tends to be very robust in terms of what timing periods are used for relative strength ranking. This means the strategy works well for various sets of timing periods and results do not change dramatically when timing periods are varied slightly. With some flexibility in what timing periods to choose, I decided to use the same timing periods that I employed for the HRV in my previous article, namely 4-months and 2-months. I first show graphical results when one, two, three, four and five assets are selected each month. A logarithmic scale of total return is employed. One asset (HRV): (click to enlarge) Two assets (LRV-2): (click to enlarge) Three assets (LRV-3): (click to enlarge) Four assets (LRV-4): (click to enlarge) Five assets (LRV-5): (click to enlarge) The results of LRV-5, compared to the equalweight portfolio, identify the effect of absolute momentum. It can be seen that absolute momentum mainly plays a role in reducing drawdown, and does not significantly affect growth in the years when drawdown does not occur. The beneficial effect of absolute momentum continues to be seen as the number of assets is reduced using relative strength. When the number of assets is reduced using relative strength, higher portfolio growth is seen as expected. The highest growth, of course, comes when only one asset is selected each month corresponding to the HRV. The tabular form of the overall results is shown below: (click to enlarge) The tradeoff between performance and risk is seen in the table above. Based on the objectives stated previously, the best LRV is LRV-3 (three assets each month). LRV-3 has a CAGR of 10.2%, an SD of 6.3%, a maximum drawdown of 6.1%, and CAGR/SD of 1.62. This compares well against the equalweight portfolio that has a CAGR of 7.8%, an SD of 7.0%, a maximum drawdown of -17.6%, and a CAGR/SD of 1.11. Thus, the LRV-3 has significantly higher CAGR, lower SD, and substantially lower drawdown and higher risk-adjusted return on investment than the equalweight portfolio. The equalweight portfolio also has three negative years: 1994 (-6.4%), 1998 (-0.3%), and 2008 (-11.6%), while the LRV-3 only has one year with negative returns: 1994 (-2.4%). In comparison to the HRV, the LRV-3 has lower growth (CAGR of 10.2% versus 15.0%), but the SD (6.3% versus 10.4%) and maximum drawdown (-6.1% versus -14.5%) are greatly improved. And the risk-adjusted return on investment of LRV-3 is significantly better (CAGR/SD of 1.62 versus 1.44). And for 1994, the LRV-3 has a -2.4% return, while the HRV has a -5.4% return. One negative aspect of the LRV-3 is that more trades are required each year compared to the HRV. However, the costs will still be minimal for an account value over $100K. Based on backtest results, the average number of annual trades (buys and sells) is approximately 20 for LRV-3. In a Schwab account, this amounts to a cost of 20 x $9 = $180 per year. So, the cost is about 0.18% for a $100K account. In addition, PCY and CWB are commission-free ETFs on Schwab (and the commission-free SCHO is a good substitute for VFISX). So, the commission costs of trading LRV-3 (neglecting any other costs) are quite minimal. A final step in this study is to ensure the ETF version of the strategy gives similar results as the mutual fund version. The ETF version can only be backtested to 2010, so the 2010-present timeframe is used for comparison. The backtest results for the ETFs and the mutual funds for LRV-3 are shown below. LRV-3 Results Using ETFs (2010 – Present) (click to enlarge) LRV-3 Results Using Mutual Funds (2010 – Present) (click to enlarge) Good agreement is seen between using ETFs and mutual funds. Using ETFs, the CAGR is 7.9%, the SD is 6.2%, and the maximum drawdown is -4.5%. Using mutual funds, the CAGR is 8.3%, the SD is 5.3%, and the maximum drawdown is -4.2%. It should be noted that the performance of the mutual funds from 2010-present is less than the performance between 1994-present. This is probably caused by the Federal Reserve holding short-term rates near zero from 2009-present. When short-term rates are increased, performance should eventually increase (after, perhaps, a short time of reduced performance). Also to be noted is that LRV-3 has gone to all cash (money market) since July 2015. So, for July, August and September, the top three assets based on relative strength have not passed the absolute momentum test. In summary, the LRV-3 should be used by more conservative investors, who desire solid growth (10%) with lower risk, while HRV should be used if more growth is desired (15%) at the expense of higher risk. For those investors, who desire even lower risk than LRV-3 as well as higher risk-adjusted return on investment, LRV-5 might be a better choice. For 1994-present, LRV-5 has a CAGR of 9.0%, a maximum drawdown of only -4.4%, and a CAGR/SD of 1.80. It should be mentioned that this strategy using fixed income ETFs is best employed in non taxable retirement accounts that avoid tax issues. I would also like to thank Terry Doherty for reading over this article and making a number of excellent suggestions.

The Cash Is King Playbook

We’re seeing something really unusual in the financial markets this year. As I’ve noted recently , there’s almost nothing that’s working this year. No matter where you’ve diversified your savings you’ve likely lost money with the exception of cash. If we look at the two primary asset classes, stocks and bonds, cash has only outperformed both in the same year 10 times in the last 90 years. So this is a pretty unusual event. But there’s some potential good news on the horizon. When this occurs both stocks and bonds tend to bounce back very strong. In the 10 times this has occurred in the last 90 years stocks have followed up with average 1, 2, and 3 year returns of 14.34%, 18.76% and 16.72%. Bonds have done a bit worse with a 1, 2 and 3 year average return of 10.24%, 7.7% and 6.17%. A balanced portfolio has also generated abnormally high returns with a 1, 2 and 3 year average return of 12.29%, 13.23% and 11.44%. As is often the case with diversification, it’s not timing the market that counts. It’s time in the market. So, while cash looks particularly smart today the historical figures say that cash won’t be king for long. Share this article with a colleague