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Beware The Death Cross?

Summary A most ominous event came to pass this week. For the first time in four years, we witnessed a “death cross” in the broader U.S. stock market. It’s worthwhile to consider the death cross in historical context to determine its significance if any to investors today. A most ominous event came to pass this week. For the first time in four years, we witnessed a “death cross” in the broader U.S. stock market. The mere name alone may cause investors to think that they should be taking action. After all, if we are reading about a death cross in the business news headlines, it certainly can’t be a good thing, right? While a death cross is widely considered a bearish signal that stocks are about to break lower, this is not necessarily the case when examining these episodes from a historical perspective. This does not mean that it should be completely ignored, but at a minimum it must be taken in context. Dissecting The “Death Cross” So what exactly is the death cross? It takes place when the average closing price of the U.S. stock market over the last 50 days (a shorter term trend reading) falls below the average closing price over the last 200 days (a longer term trend reading). To many investors, the fact that the shorter-term trend in the 50-day moving average has crossed below the longer term trend in the 200-day moving average is a signal that the overall market trend may be reversing to head much lower. As a result, some investors are inclined to use the death cross as a signal that it may be time to start exiting stock positions to protect against portfolio losses. Before going any further, it’s important to make a key distinction about the recent death cross that we have been hearing about. It took place on the Dow Jones Industrial Average (NYSEARCA: DIA ). And while I appreciate the historical significance and its well-known status among the broader general public, the Dow is not a U.S. stock market index to which I pay much attention. This is due to the fact that it’s an index that’s not only limited in its number of holdings at just 30 stocks, but it also is a price weighted index instead of being market cap or equal weighted. As a result, price movements in Goldman Sachs (NYSE: GS ) trading at $200 per share has a disproportionately larger impact on the Dow on any given day than General Electric (NYSE: GE ) or Cisco (NASDAQ: CSCO ) that are trading in the $20s despite the fact that both are meaningfully larger in terms of market cap. Instead, I prefer to monitor the S&P 500 Index (NYSEARCA: SPY ), which consists of a much broader universe of 500 stocks and is market cap weighted, along with a variety of other indices. And to date, the S&P 500 Index is still trading with a 50-day moving average that’s still nearly 1% above its 200-day moving average. In other words, while we have witnessed a death cross on the Dow, it has yet to take place on the broader S&P 500. This is not to say that we won’t see a death cross in the S&P 500 Index soon, but it should be noted that we have not yet seen one to date. Moreover, the uptrend in U.S. stocks remains very much intact despite the extended period of sideways trading that has taken place since late 2014. (click to enlarge) But given the fact that the S&P 500 is as close to a death cross as it has been in years, it’s still worthwhile to consider the implications of such an event. To begin with, the death cross is a fairly uncommon occurrence for the U.S. stock market. Over the last 85 years, stocks as measured by the S&P 500 Index have experienced a Death Cross on 44 separate occasions. The last such instance took place in 2011, which is shown in the chart below. (click to enlarge) The death cross is a fairly rare experience. But do they matter? Not nearly as much as the name might suggest. First, it’s important to note that a fair amount of stock market downside has typically been absorbed by the time the death cross takes place. Historically, this supposedly bearish crossover has historically occurred 74 trading days on average following a market peak for an average decline of -10.66%. In short, investors are already down double-digits on average before the death cross alarms have been triggered. With that being said, it’s worth noting that today’s market is setting up a bit differently. Through Friday, August 14, we are now 59 trading days removed from our most recent market S&P 500 peak on May 20 (although it should be noted that we came extremely close to a new high just 18 trading days ago on July 20). And if a death cross were to take place today, it would only have stocks down less than -3% from their peaks. As a result, it could be argued that such a signal this time around might provide some protection against more meaningful downside that might follow this time around. Exploring this point in more detail, stocks have continued lower for another 77 days on average after a Death Cross before bottoming with an average decline of -12.21%. As a result, if average historical precedence held, taking action might protect an investor from absorbing a mid to high single digit portfolio decline on average. But the risk may outweigh the reward by undertaking such an approach for the stock market has shown the propensity on a meaningful number of instances to be at or near a bottom by the time a death cross has taken place. For example, in eight of the 44 past Death Crosses in the last 87 years, the stock market has bottomed immediately on the day that this bearish crossover has taken place. In other words, an investor using the death cross as an exit signal would have them selling at the exact bottom of the market 18% of the time. And a one in five chance of bottom ticking a stock market pullback is a risk that investors should take into consideration. Taking this a step further, the potential for bottom picking on a death cross signal becomes measurably worse when incrementally expanding the time horizon. For in another 12 of the 44 past death crosses, or another 27% of the time, the stock market bottomed within 10 trading days after the bearish crossover occurred. And four more, or an additional 9% of the time, stocks bottomed within 25 trading days, or roughly a month, after the death cross took place. Putting this all together, at 24 out of 44 instances, or 55% of the time, the death cross is more likely to signal that a short-term bottom is imminent for investors than that a long-term correction is underway. As a result, despite its ominous sounding name, investors should not be quick to react upon hearing that a death cross has taken place. What About The Other 45% Of The Time? None of this means, however, that the death cross should be completely ignored. For it does provide some useful leading signals that investors should consider in protecting against any future market correction or outright bear market. First, while the actual crossover of the 50-day moving average below the 200-day moving average comes too late to be useful from a trading perspective in many instances, the spread between the 50-day and 200-day moving average can serve as a useful leading indicator about the continuing strength of the stock market going forward. Over time, a spread between the 50-day and 200-day moving average between 5% and 10% is considered strong. But what we have seen since the market peak in early 2013 is that the strength of the U.S. stock market has been gradually but steadily fading in the two plus years since. What this suggests is that the third longest bull market in history is increasingly running out of gas. Could it reverse to the upside? Absolutely, but we have seen nothing to suggest a revival in stock market strength in this regard for more than two years running. (click to enlarge) Another consideration is the average amount of time between death crosses. While as suggested above that most such crossovers have often been better predictors of short-term market bottoms than long-term market reversals, nine out of 44 past instances, or 20% of the time, have been followed by extended market corrections if not full blown bear markets. And each of these nine instances has taken place following what have been far longer than normal periods of time between death crosses. For example, when U.S. stocks have gone more than 500 trading days between death crosses, the probability that it’s followed by an outright bear market including a decline greater than -20% increases to roughly half. And given the fact that we are now at 1,007 trading days and counting since the last death cross in 2011, we are operating today with risk levels considerably elevated in this regard. Bottom Line While the death cross is an ominous sounding event that we are likely to hear more about if the market continues to grind, it’s not nearly the bearish indicator that the name suggests. More often than not, it serves as a signal that a short-term bottom in stocks may be imminent. But with that being said, it’s still useful for long-term investors that are viewing the information in the right context. And while a death cross in stocks should not be viewed in isolation as anything that requires urgent portfolio action, it does hold more meaningful significance in the current environment when considered in the context of the market environment that we are operating in today. Disclosure : This article is for information purposes only. There are risks involved with investing including loss of principal. Gerring Capital Partners makes no explicit or implicit guarantee with respect to performance or the outcome of any investment or projections made. There is no guarantee that the goals of the strategies discussed by Gerring Capital Partners will be met. Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Facts, Opinions, And Risk Management

Editor’s note: Originally published at tsi-blog.com on August 14, 2015. Commentators on the financial markets often make statements like “it’s a bull market” and “the trend is up” as if these were indisputable facts, but such statements are always opinions. A statement of fact could reasonably be phrased along the lines of “the market was in an upward trend between date X and date Y,” because if a sequence of rising lows and rising highs occurred between two dates then the trend was, by definition, up during that period. However, it is impossible to know the direction of a market’s current price trend with absolute certainty, let alone the direction of its future price trend. The reason is that even if a market has just made a new high/low, there will be some chance that this will turn out to be the ultimate high/low. For example, it’s a fact that gold was in a bear market in US$ terms from its peak in September of 2011 through to 24th July 2015 (when it hit a 4-year low of $1072), but it is a matter of opinion as to whether gold is now in a bear market. The bear market could obviously still be in progress, but there is also a possibility that it ended on 24th July 2015. At the time of writing, nobody knows for sure. Some market participants and commentators will draw a line on a chart and then make a statement such as “I will consider the trend to be up (or down) unless the market proves otherwise by moving below (or above) my line”. Fine, but there’s a big difference between claiming to know the direction of the price trend and working under the assumption that the trend is in a particular direction unless/until proven otherwise by some predetermined event. The valley of shattered financial dreams is littered with traders who were determined to stay ‘long’ or ‘short’ because they thought they KNEW the direction of the price trend. The impossibility of knowing whether a bull/bear market or an up/down trend is going to continue, or even whether the market is currently in bull or bear mode, makes risk management essential. Someone who knew the future would never have to bother with risk management; they could, instead, risk everything on a particular outcome because for them it wouldn’t be a risk at all. But ordinary mortals always face a degree of uncertainty when making investment decisions and, as a result, always need to face the reality that these decisions could prove to be wrong. Be wary, then, of advisors who claim that there is only one possible direction for the future price of an investment. But while unwillingness to acknowledge the possibility of being wrong is a defect in the approach of some investors, other investors suffer from the opposite problem in that they have a hard time maintaining a bullish or bearish view unless that view is continually being validated by the price action. That is, they are incapable of remaining confident in any opinion that doesn’t happen to conform to the current opinion of the manic-depressive mob. As a result, they routinely get ‘sucked in’ following large price rises and ‘blown out’ following large price declines, as opposed to taking advantage of the mob’s proclivity to be wrong. Therefore, as investors, the challenge we all face is to strike a balance between staying the course in rough weather and preparing ourselves for the possibility that there could be unseen rocks up ahead.

Avoiding The Big Drawdown: Is Downside Protection Helpful Or Heresy?

By Wesley R. Gray, Ph.D. Chasing the Investing Unicorn: Give me “High Returns with Limited Risk” Having your cake and eating it too is a great way to go. It’s great to have the cake, and it’s also great to eat the cake. But you can’t have it both ways. This trend continues when we speak with fellow investors: “Give me high, after-tax, net of fee returns, but with limited risk and volatility.” Now, we certainly love high returns with low risk. We also love high reward with low effort and high calories with low weight gain. Unfortunately, this brings us to our first problem with the investing unicorn: Problem #1: Unicorns don’t exist, and neither do high returns with low risk. Unless you are my youngest daughter, age 3, unicorns don’t exist. Sadly, high-return assets with low-risk profiles don’t exist either. Assets that earn high returns, such as equities (e.g., an S&P 500 index fund), come with a lot of risk (i.e., you can lose over half your wealth). The only way to earn high returns, but limit the risk, is to develop a timing methodology that identifies how to sell the high-returning asset before it decides to jump off a fiscal cliff. Which brings me to another kink in the high-reward, low-risk paradox: Problem #2: Market-timing is extremely difficult. Let’s start this conversation with a concise summary of a 55-page academic analysis of a variety of systems that claim to have perfect market-timing ability: Trying to perfectly time the market is a waste of time. There you go. You no longer need to read this classic academic paper in which Ivo Welch and Amit Goyal assess market timing variables. Our own research over several years confirms this sad reality. We’ve reviewed hundreds of different concepts, and the results are not promising. Most signals never “survive” intense empirical scrutiny, and we are generally skeptical of ANY system that purports to work all the time. Simply stated: Nothing works ALL the time . If unicorns don’t exist (high returns, low risk), is there any good news? There is a glimmer of light at the end of this investing tunnel. Specifically, academic research indicates that investors who can stomach short-term volatility, avoid benchmark comparison, and follow a model can systematically outperform over long periods of time. We find the same conclusion with what we call “downside protection.” Historically, two elements provide downside protection: Focus on Strong Absolute Performance Focus on Strong Trending Performance Of course, past performance is certainly no guarantee of future performance ; nonetheless, historically, these methodologies have worked. They haven’t eliminated short-term volatility, and one can be sure they will underperform a buy-and-hold index at some point; however, they have protected portfolios from the most extreme loss situations. Let’s explore a simple downside protection tool and what the evidence to-date can show us. Rule 1: If weak absolute performance appears, go to cash. In the illustration below, the white line represents an asset class with poor absolute performance. In general, avoid assets with poor absolute performance. (click to enlarge) For illustration purposes only. Rule 2: If weak trending performance appears, go to cash. In the illustration below, the purple line represents a long-term trend line (e.g., a moving average) and the white series represents real-time prices. The red circle highlights a point where the real-time price falls below the long-term average. In general, avoid assets with poor trending performance. For illustration purposes only. Do these simple tools work? Let’s look at the data. Moskowitz, Ooi, and Pedersen, in a formal academic paper, highlight that technical rules don’t work all the time, but they have been effective at providing downside protection, historically: “We document significant ” time series momentum ” in equity index, currency, commodity, and bond futures for each of the 58 liquid instruments we consider… … A diversified portfolio of time series momentum strategies across all asset classes delivers substantial abnormal returns with little exposure to standard asset pricing factors and performs best during extreme markets.” – Moskowitz, Ooi, and Pedersen (2012) While market timing systems that work 100% of the time are impossible, we see that some systems, if followed over long periods, can work over time. It all gets back to model discipline and exploiting the behavioral biases of the market (something we love). Let’s simplify the complex analysis presented in formal academic research and focus on replicating these 2 simple rules. Let’s call our system, the “Downside Protection Model”: The Downside Protection Model ((NYSE: DPM )) follows two simple rules: Time Series Momentum Rules (TMOM) Simple Moving Average Rules (MA) Let’s review the details of our simple rules: Absolute Performance Rule: Time Series Momentum Rule (TMOM) Excess return = Total return over past 12 months less return of T-Bills If Excess return > 0, go long risky assets. Otherwise, go long alternative assets (T-Bills) Trending Performance Rule: Simple Moving Average Rule (MA) Moving Average (12) = Average 12-month prices If Current Price – Moving Average (12) > 0, go long risky assets. Otherwise, go long alternative assets (T-Bills). We need a way to combine these two principles in a simple way. We find that complexity does not add value , and simple models beat experts. We extend this belief to downside protection by keeping it simple: We create a Downside Protection Model (DPM) rule, which is 50 percent Absolute Performance (TMOM) and 50 percent Trending Performance (MA): DPM Rule: 50% TMOM, 50% MA Below is a figure that illustrates the basic trading rules we apply to provide downside protection on portfolios: (click to enlarge) The rule is simple: Trigger one rule = go to 50% cash. Trigger both rules = go to 100% cash. No rules triggered = go long. How has the Downside Protection Model performed? We provide a series of tests on the Downside Protection Model, applied to generic market indices. Our core samples includes 5 asset classes, assessed over the 1973-2014 time period: SPX = S&P 500 Total Return Index EAFE = MSCI EAFE Total Return Index LTR = The Merrill Lynch 10-year U.S. Treasury Futures Total Return Index REIT = FTSE NAREIT All Equity REITS Total Return Index GSCI = S&P GSCI Total Return CME Results are gross, no fees are included. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Data sources include Bloomberg. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Comparison #1: Looking at these basic rules individually: Absolute Performance (TMOM) vs. Trending Performance (MA) Before we compare the system as a whole, let’s compare each rule against the other to see if one is particularly more effective. From January 1, 1976 through December 31st, 2014, here is what we find: TMOM wins 60% of the time, MA wins 40% of the time (Win = better Sharpe and Sortino; Loss = Sharpe and Sortino worse; Tie = a combination of some sort) TMOM triggers around 20% less than MA does (number of triggers refers to the number of times the rule breaks out of the asset class and goes to T-Bills) Bottom Line: Both rules have been effective at providing downside protection. Below are the stats. (click to enlarge) The results are hypothetical, 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. Comparison #2: Assess the Downside Protection Model (DPM): Absolute Performance (TMOM) plus Trending Performance (MA) Now, let’s combine the rules into our simple Downside Protection Model ( DPM ) and see if any incremental improvement occurs. Here is what we find: Downside Protection Model (DPM) wins overall (Win = better Sharpe and Sortino; Loss = Sharpe and Sortino worse; Tie = combination of some sort). Bottom Line: Combining the rules into a single Downside Protection Model (DPM) appears to work. (click to enlarge) The results are hypothetical, 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. Note: Additional robustness tests are available in the appendix. Are these results sustainable? The basic results above highlight that DPM significantly reduces the realized maximum drawdown on a portfolio. But perhaps the entire exercise above is an example of data mining and over-optimization. Nobody can ever prove, beyond any doubt, that a Downside Protection Model works. There is always a chance that any historical finding is driven by randomness, and thus, past performance will not reflect future performance. In the Appendix section below, we stress test this system across numerous time periods and different markets, all of which present similar conclusions. However, we believe there is a behavioral story underlying the success of our simple downside protection rules. Consider the concept of dynamic risk aversion, which is the idea that human beings don’t stick to a set risk/reward behavior – their appetite for risk can change depending on their recent experience. For example, imagine we are making a decision to build a new house in California along the San Andreas Fault. If we just lived through an earthquake, taking on the risk of building a new house on the San Andreas Fault is probably scarier, even though the probability of another earthquake may not have changed. In contrast, when there hasn’t been an earthquake in fifty years, building a new house along a fault is not a big deal. As this example shows, our perception of risk is not constant, and can change based upon recent experience (if you doubt this example, kindly look at a picture of San Francisco’s skyline). In terms of market crashes, we will likely overreact to extreme times and underreact to peaceful times, despite the statistical probability to the contrary. Another assumption economists sometimes make is that risk, often measured in terms of standard deviation, or “volatility,” is relatively constant. These assumptions are challenged when extreme stock market drawdowns occur. Let’s look at another example: a 50% market correction, when fundamentals imply a 20% correction is sufficient. As market prices drop below the twenty percent threshold, an economist assumes that the new price is a bargain. Expected returns have gone up after prices have moved down, while volatility and risk aversion are assumed to be relatively constant. Implicitly, investors should swoop in to buy these cheap shares and bring the market to equilibrium (which, in our example, is their so-called fundamental value). But this doesn’t happen. Stocks can – and have – gone down over fifty percent, and these movements are much more volatile than the underlying dividends and cash flows of the stocks they represent! Remember 2008/2009? How many investors swooped in to buy value versus threw the baby out with the bathwater and kept selling? One approach to understanding this puzzle is by challenging the assumption that investors maintain a constant aversion to risk. Consider the possibility that investors change their view on risk after a steep drawdown (i.e., they just lived through an earthquake). Even though expected returns go up dramatically, risk aversion shoots up dramatically as well. This change means prices have to go down a lot further to justify an investment in these “cheap” stocks. This heightened aversion to risk – following a steep price drop – leads to more selling, and more selling leads to even more hate for risk, which leads to more selling, and so forth. What you end up with is a stampede for the exit and an intense sell-off in the marketplace – below fundamental value, and well beyond what a traditional economist would consider “rational.” The discussion above is a simplified story of investor psychology in the context of a stock market drawdown. For exposition purposes, we are leaving out many potentially important details. However, if one believes that investors rethink their tolerance for risk during a market debacle and tend to sell shares at any price, this might help explain why long-term trend-following rules, which systematically get an investor out of a cliff-diving bear market before everyone has jumped ship, have worked over time. Of course, technical rules will only work if the massive bear market doesn’t happen in a short time period before the long-term trend rules can signal an exit. Technical rules will not save an investor from a 1987-type “flash” crash, but they can save an investor from a 1929- or a 2008-type crash, which can take a few months to develop. In the end, if one believes in a price dynamic that involves steep and relatively sharp declines, followed by slow grinding uphill climbs, simple technical rules will, by design, improve risk-adjusted performance. Conclusion Simple timing rules, focused on absolute and trending asset class performance, seem to be useful in a downside protection context. Our analysis of the downside protection model (DPM), applied on various market indices, indicates there is a possibility of lowering maximum drawdown risk, while also offering a chance to participate in the upside associated with a given asset class. Important to note, applying the DPM to a portfolio will not eliminate volatility, and the portfolio will deviate (perhaps wildly) from standard benchmarks. For many investors, these are risky propositions and should be considered when using a DPM construct. Note: We will be implementing a version of our downside protection model with our new automated advisor offering, Alpha Architect Advisor . Appendix Robustness test of the DPM model across time periods and markets Subperiod: 01/01/1976-12/31/1995 DPM is 50% invested in a TMOM strategy and 50% invested in an MA strategy. Strategies invest in T-bills when a trading rule triggers. DPM wins 3/5, B&H wins 1/5, DPM ~ B&H 1/5 (Win = Sharpe & Sortino; Loss = Sharpe & Sortino; Tie = other) Bottomline: TMOM and MA provide downside protection. (click to enlarge) The results are hypothetical, 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. Subperiod: 01/01/1996-12/31/2014 Bottom Line: DPM holds and provides better protection. (click to enlarge) The results are hypothetical, 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. Out of Sample Test #1-> U.S. Market (01/01/1928-12/31/1975) Our core sample includes 1 asset class, assessed over the 1928-1975 time period: SPX = S&P 500 Total Return Index Results are gross, no fees are included. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Data sources include Bloomberg. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Both TMOM and MA work well for downside protection, significantly lowering total drawdowns. Strategies invest in T-bills when a trading rule triggers. Bottomline: TMOM and MA provide downside protection and have similar results to the Downside Protection Model. (click to enlarge) The results are hypothetical, 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. Drawdown Comparison Both TMOM and MA significantly lower downside risk when the top drawdowns of the buy-and-hold benchmark occurs. MA and TMOM provide similar drawdown protection during buy-and-hold drawdowns. TMOM and MA protect capital at different times (see bold text below). Bottomline: Downside Protection Model diversifies risk management by combining the rules. (click to enlarge) The results are hypothetical, 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. Out of Sample Test #2 -> Japanese and German Stock Markets Our robustness samples include 2 global markets (Japan and Germany): NKY = Nikkei 225 Index (1971 to 2014) DAX = Deutsche Boerse AG German Stock Index (1961 to 2014) Results are gross, no fees are included. All returns are price returns and DO NOT include the reinvestment of distributions (e.g., dividends). Data sources include Bloomberg. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. We use zero as the alternative asset return when a trading rule is triggered. Nikkei Summary Results (1971-2014): Both TMOM and MA work well on drawdown protection. TMOM works slightly better overall. TMOM has the highest return during this period. DPM lowers the sum of total drawdowns by a material amount. NKY_DPM (TMOM and MA): Equal weight on NKY_TMOM and NKY_MA; portfolio earns zero returns when flat. NKY_TMOM: Times series momentum applied on NKY with 12-month formation window, and earns zero returns when flat. NKY_MA: 1-month and 12-month MA rule applied on NKY and earns zero returns when flat. NKY_B&H: Buy and hold on Nikkei 225 price-only series. (click to enlarge) The results are hypothetical, 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. Drawdown Comparison (Nikkei) Both TMOM and MA significantly lower downside risk during the top drawdowns of the buy-and-hold benchmark. MA and TMOM provide similar drawdown protection during buy-and-hold drawdowns. TMOM and MA protect capital at different times (see bold). The Downside Protection Model is diversifying risk management. (click to enlarge) The results are hypothetical, 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. DAX Summary Results (1961-2014) Both TMOM and MA work well on drawdown protection. TMOM has higher CAGR and lower drawdown. The Downside Protection Model is roughly equivalent to TMOM with lower Max Drawdown. DAX_50,50 (TMOM and MA): Equal weight on DAX_TMOM and DAX_MA; portfolio earns zero returns when flat. DAX_TMOM: Times series momentum applied on DAX with 12-month formation window and earns zero returns when flat. DAX_MA: 1-month and 12 month MA rule applied on DAX and earns zero returns when flat. DAX_B&H: Buy and hold on DAX 40 price-only series. (click to enlarge) The results are hypothetical, 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. Drawdown Comparison (NASDAQ: DAX ) Both TMOM and MA significantly lower downside risk during the top drawdowns of the buy-and-hold benchmark. MA and TMOM provide similar drawdown protection during buy-and-hold drawdowns. TMOM and MA protect capital at different times (see bold). The Downside Protection Model is diversifying risk management. (click to enlarge) The results are hypothetical, 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. Statistics Definitions CAGR: Compound Annual Growth Rate Standard Deviation: Sample standard deviation Downside Deviation: Sample standard deviation, but only monthly observations below 41.67 bps (5%/12) are included in the calculation. Sharpe Ratio (annualized): Average monthly return minus Treasury bills divided by standard deviation Sortino Ratio (annualized): Average monthly return minus Treasury bills divided by downside deviation Worst Drawdown: Worst peak-to-trough performance (measured based on monthly returns) Mathematical Relationship Between TMOM and MA (click to enlarge) The results are hypothetical, 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. Original Post