Avoiding the Big Drawdown with Trend-Following Investment Strategies

/Avoiding the Big Drawdown with Trend-Following Investment Strategies

Avoiding the Big Drawdown with Trend-Following Investment Strategies

Market timing is akin to chasing the Investing Unicorn: Give me “High returns with limited risk.”

Now, we certainly love high returns with low risk. We also love winning with low effort and the ability to lose weight, but eat anything we see (especially the cookies!).

Unfortunately, there is a problem with the market timing investing unicorn:

Problem #1: Unicorns don’t exist, and neither do high returns with low risk. 

financial market unicorn

Bad attempt at humor by Wes

Sadly, high return assets with low risk profiles don’t exist. 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 problem in the search for high reward and low risk:

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 a variety of 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.

Trend-following systems, which represent a form of market timing, are no different. They don’t — and can’t — work all the time.

Unicorns Don’t Exist. Got it. What’s This Trend-Following Stuff All About?

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” investment strategies, better known as trend-following strategies.

Historically, two elements provide downside protection:

  1. Focus on Strong Absolute Performance
  2. Focus on Strong Trending Performance

Of course, past performance is certainly no guarantee of future performance; nonetheless, historically, these methodologies have avoided large drawdowns. They haven’t eliminated short-term volatility and one can be sure they will underperform a buy & hold index at some point; however, they have protected portfolios from the most extreme loss situations.

Let’s explore a simple trend-following 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.

For illustration purposes only.

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 long-term average. In general, avoid assets with poor trending performance.

For illustration purposes only.

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 discipline and being patient. In other words, can you stick with a process over a long period of time. Most people can’t.

Let’s simplify the analysis presented in formal academic research and focus on analyzing 2 simple rules. Let’s call our trend-following rules, the “Downside Protection Model:”

The Downside Protection Model (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).

These two rules are similar in nature and actually mathematically related.(1)

How can we combine these two principles in a simple way?

We find that complexity does not add value and simple models often beat experts. We extend this belief to our trend-following system by keeping it simple: 50 percent Absolute Performance (TMOM) and 50 percent Trending Performance (MA).

An Overview of the Downside Protection Model: 50% TMOM, 50% MA

Below is a figure that illustrates the basic trading rules we apply to provide downside protection on portfolios:

The system is simple: trigger one rule, go to 50% cash. Trigger both rules, go to 100% cash. No rules triggered implies 100% long risk.

How Has the Trend-Following System Performed?

We provide a series of empirical tests on the system, and apply the methodology to generic market indices. The goal is to identify if the system can achieve our goal of minimizing the chance of large drawdowns.(2)

Our core samples includes 5 asset classes, assessed over the 1976-2014 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 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.

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 & Sortino; Loss = Sharpe & Sortino worse; Tie = combination of some sort)
  • TMOM triggers around 20% less than MA does (number of triggers refers to 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:(3)

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.

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.

Comparison #2: Assess the Integrated Trend-Following Model: 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 & Sortino; Loss = Sharpe & Sortino worse; Tie = combination of some sort).

Bottom line: Combining the rules into a single Downside Protection Model (DPM) appears to work.

DPM Model vs Buy and Hold

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.

Note: We have a post on the, “World’s longest trend-following backtest,” and there are additional robustness tests are available in the appendix. We test every data set we can find!(4)

Are Trend-Following Models Sustainable?

The basic results above highlight that our simple trend-following system can potentially reduce the realized maximum drawdown for 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 market timing 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, we stress test this system across numerous time periods and different markets, all of which present similar conclusions. This helps alleviate fears of data-mining, but can never eliminate this potential.

However, we believe there is a behavioral story underlying the success of trend-following systems. 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.(5)

Stocks can—and have—gone down over 50 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 stocks at that point? If you’re like most humans, you 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). In other words, fear rules the day, not rationality. 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.” (One can review how market volatility affects our brains in more detail.)

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, trend-following 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.

Oh, we almost forgot the most important point, we should mention that following a trend system is incredibly challenging from a discipline standpoint. One can expect to underperform during bull markets, and the only recourse is that you have a shot at avoiding a large drawdown during a bear market. Many investors theoretically like that concept (give up some upside to avoid huge losses), but in practice it is extremely tough to lag on the buy and hold equivalent strategy for years on end. Many investors give up on the trend model, typically at the worst time. Human nature is tough to override.

Conclusion

Simple trend-following 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 a majority of the upside associated with a given asset class. Important to note, applying the trend system 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 trend-following construct.

Note: We implement our trend-following system in our new automated advisor offering, Alpha Architect Advisor, as well as in our Value Momentum Trend Index.


  • The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).
  • Join thousands of other readers and subscribe to our blog.
  • This site provides NO information on our value ETFs or our momentum ETFs. Please refer to this site.

Print Friendly, PDF & Email

References   [ + ]

1.

Mathematical Relationship Between TMOM and MA

time-series-and-ma

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.

2. Note, the goal is not to maximize return or minimize volatility, but minimize the chance of a large drawdown.
3.

Statistics Definitions

  • CAGR: Compound annual growth rate
  • Standard Deviation: Sample standard deviation
  • Downside Deviation: Sample standard deviation, but only monthly observations below 41.67bps (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)
4.

Robustness test of the integrated trend-following 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)
    • Bottom line: TMOM and MA provide downside protection.
Downside Protection sub-period

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.

Subperiod: 01/01/1996-12/31/2014

  • Bottom Line: DPM holds and provides better protection
Downside Protection sub-period II

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.

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 to 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.
    • Bottom line: TMOM and MA provide downside protection and have similar results to Downside Protection Model
Downside Protection out of sample

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.

Drawdown Comparison

  • Both TMOM and MA significantly lower downside risk when the top drawdowns of 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).
    • Bottom line: Downside Protection Model diversifies risk management by combining the rules.
Top 20 drawdowns

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.

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&MA): Equal weight on NKY_TMOM and NKY_MA; portfolio earns zero return when flat.
    • NKY_TMOM: Times series momentum applied on NKY with 12 month formation window and earns zero return when flat.
    • NKY_MA: 1 and 12 months MA rule applied on NKY and earns zero return when flat.
    • NKY_B&H: Buy and hold on Nikkei 225 price only series.

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.

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.
Top 17 Drawdowns

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.

DAX Summary Results (1961-2014)

  • Both TMOM and MA work well on drawdown protection. TMOM has higher CAGR and lower Drawdown.
  • Downside Protection Model is roughly equivalent to TMOM with lower Max Drawdown.
    • DAX_50,50 (TMOM&MA): Equal weight on DAX_TMOM and DAX_MA; portfolio earns zero return when flat.
    • DAX_TMOM: Times series momentum applied on DAX with 12 month formation window and earns zero return when flat.
    • DAX_MA: 1 and 12 months MA rule applied on DAX and earns zero return when flat.
    • DAX_B&H: Buy and hold on DAX 40 price only series.
DAX downside protection model results

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.

Drawdown Comparison (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.
Top 20 Drawdowns DAX

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.

5. see Bob Shiller lecture and papers on this topic. http://oyc.yale.edu/economics/econ-252-08/lecture-6

About the Author:

Wes Gray
After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes, ETF.com, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.
  • Doug

    Curious to know what the stats for the whole portfolio would be, with each asset class nominally equal-weighted (subject to the rules) vs. an equally-weighted, annually rebalanced portfolio with no rules.

  • Hi Doug,

    Great question.

    The stats for this sort of analysis are in another post (see section 3):
    https://alphaarchitect.com/2014/12/02/the-robust-asset-allocation-raa-solution/

    Summary: Gross returns are ~same, but the max drawdowns shoot up.

    Of course, B&H globally diversified is a lot less complex, has fewer transactions, and is easier to tax-manage (i.e., tax managing risk management events is very tricky if you have low basis). The decision to deploy a downside protection element is certainly not a slam-dunk for every situation.

  • Mark

    Thanks for the post! One thing we can draw from the post is that if the drawdown is less than 10%, the strategy is hard to add-value, but may in fact detract value after taking transaction cost into consideration. That means the strategy is likely to under perform for asset class which is modest volatile or the time period where the drawdown is modest.

    For SPX, I think the table miss the drawdown starting from August, 2000.

    By the way, can you talk about the logics behind the top 20 drawdown calculation ? Thanks again

  • JAK78

    Many academic studies show results after estimated transaction costs. Results can change significantly after doing this. Could you please show some results after transaction costs for TMOM, MA, and DPM?

  • Mark, on the drawdown table that is only up to 1975 to match the time period under analysis.

    re logic: As part of our standard analysis package, we include extreme drawdown tables to make sure we understand how things operate in the extreme tails. Sometimes ‘average’ statistics/tests hide things in the tails and the easiest way to understand the tails is to simply look at the tails…

  • To keep things simple, let’s say you average around 1 event a year (which is roughly correct). If roundtrip transaction costs are 50bps, you could take 50bps off the CAGR. Taxes can be a much bigger issue depending on the situation…could be ~0 if in a qualified account, or could be multiple % points in a taxable situation.

    For simplicity, I’d assume you drop 100bps a year, and if you really want to stress-test it, drop 200bps a year…

  • Mark

    Thanks again! Can you talk about the algorithm to calculate the top 20 drawdown? I was doing some similar analysis the other day, but had a hard time coding the drawdown in the recovery period ?

  • Non-trivial and most canned packages in python/R/bberg etc. are incorrect (they miss drawdowns within drawdowns).

    Basically, to get top drawdowns you need to find a drawdown, but then recursively go back through the drawdown. it is a coding/computer power pain in the a$$.

    Example for 2000-2014…

    Including 2 charts, one non-recursive search, one with recursive search. Non recursive misses the 4/2011-9/2011 drawdown and the 4/2010-6/2010 drawdown.

  • Jonathan

    Hi, I never see a discussion of market timing strategies and their associated returns and associated sharpe and sortino rations on an AFTER TAX basis. Can you provide any insight into how to think about how to think about the benefits that come with reducing volatility by using market timing vs. the negative impact market timing has on reducing after tax returns by introducing short term capital gains/losses and paying taxes sooner than one otherwise would?

    What is the value of these deferred taxes? To determine this we need simply ask how much any alternative investment would have to earn in order to match any given return that one could generate after selling its stake in a stock and, of course, paying those taxes to the Government. As it turns out, given a 35% corporate tax rate, the opportunity cost of switching is 48%. That is, if that stock can be expected to earn 10%, any competing investment must earn almost 15%.

    For most individuals subject to US capital gains taxes of 20%, once an investment has doubled over its original cost, any new investment must earn 11.1% (percent, not percentage points) more per annum, ad infinitum, in order to justify the switch.

  • Tax managing risk-management events is incredibly challenging. For example, if I own XYZ with $1 basis and it goes to $10, and THEN, a trigger hits and exposure needs to be ZERO–we have a tax problem…

    1) One can try and wrap the strategy in an ETF structure (expensive, high regulatory red tape, etc);
    2) one can tax-harvest and book tax insurance (not tough, but a hassle);
    3) and one can use futures to bring down exposure (not tough, but a hassle and complex for people with no experience in futures), without selling the core asset with low basis…
    4) one can wrap the strategy in insurance programs (annuity, life insurance, etc.)
    5) one can approach a bank and ask for a swap or structured product
    6) or one can combine elements of all of these.
    …and there are probably a few more, but they all involve costs/benefits.

    The value of deferred taxes is the compound growth you get on the dollars that stayed in the account and avoided Uncle Sam’s wrath…that can be worth A LOT over time.

  • Jonathan

    Can you explain what you mean by “tax harvest” and “book tax insurance?”

    How hard is it for an individual investor to implement the strategy you describe?

    One related question I have is as follows:

    Have you studied the optimal frequency of rebalancing portfolios constructed on value criteria (e.g. the lowest 10% EV/EBITDA stocks) or momentum criteria on an an AFTER-TAX rather than pre-tax basis?

    In other words, how frequently (or not) should I rebalance to hold the lowest decile value stocks or highest decile momentum stocks without lowering my AFTER TAX returns?

    Taxes have enormous consequences for individual investors and some institutions and as such I find it very surprising that quantitative finance academic research does NOT discuss these considerations. Am i mistaken?

    Any thoughts of yours are appreciated. Thanks again.

  • Hey Jonathan,

    You can do all these things, but it will take some time/thinking/planning.

    Here is a piece on tax-loss harvesting: https://www.kitces.com/blog/evaluating-the-tax-deferral-and-tax-bracket-arbitrage-benefits-of-tax-loss-harvesting/.

    example: You own SPY at $10 and it goes to $5. You would sell SPY, book a $5 loss, and turn around and buy IVV or something. You maintain your position in SP500, but you now have a $5 loss you can use to offset gains in your portfolio. And if you don’t have any gains to offset you get to “book tax insurance,” or keep a tax shield on hand for a rainy day.

    Yes, but we decided that it was too much brain damage and you can eliminate most of the rebalancing tax problems by focusing on exchange traded fund vehicles. Here is an explanation: https://alphaarchitect.com/2014/04/01/etfs-tax-efficient-mutual-funds/

    Our primary clients are ultra-HNW and family offices that hate taxes more than they like making money. Trust me when I make the claim that we think/know more about tax planning and tax engineering than your average bear…we just don’t discuss this sort of stuff in the public domain…happy to discuss offline at any time…

  • IlyaKipnis

    Drawdown is defined as your maximum equity up to the given date minus the value of your current equity. It is highly path-dependent. PerformanceAnalytics in R takes good care of you, though ^_^.

  • I don’t think the R function for drawdown table is correct. compare the results to the images I posted on non recursive and recursive…last i checked, the PA package wasn’t able to snag all the top drawdowns

  • Steve

    I think this is now my favourite piece on why there might be a real (behavioural) reason that “market timing” or trend following markets might be a good thing to do. I’m not easily convinced in this area. I’ve always ended up thinking, “yeah, it’s just another attempt to try and get the good returns of – say, value – without the pain.” Avoiding the pain probably avoids the returns. This is a good piece that forces me to consider an alternative.

    I really want to avoid an 80% drawdown! And halving the market drawdown is sooo appealing. Still, it seems to come at a price of a few percent, at least if you are using strategies like value (for example, risk-managed QV versus QV. I’ve seen similar with longer term studies of momentum). So, if you are going for totally maximum return, you might not want to use it (which is what makes me undecided), Could be another, “life stage” thing. Incorporate this kind of risk management if you want / need a smoother ride. A 30 year old might be happy going the max return approach…and moving over to risk-managed a bit later on.

    It’s nice to see that it unexpectedly ups the return a tiny bit…somewhat offsetting the cost of switching etc.

  • Adam Kearny

    The basic point on the fallibility / non-robustness of timing systems is well-taken. A good example would be the systems used by John Hussman at Hussman Funds. “Overbought, over-bullish, overvalued”–he had to modify this system by adding additional criteria, after it failed to work in 2013-14. Presumably, this was something that had worked in back-testing over the past 100 yrs (Hussman is a very sophisticated econometrician) but failed with the advent of quantitative easing. I think broad stock market timing is more art than science and involves subjectively incorporating as many inputs as possible–valuations, numerous sentiment indicators, macro backdrop, “technical” indicators, investor leverage, credit market fragility, market breadth, bull market duration, etc. Even then, it’s a probabilistic exercise. Perhaps part of successful timing is also the willingness to be a little “early”. Historically, you don’t miss anything durable by missing out on the last year or two of a bull market. I think timing should also be used very sparingly, i.e. don’t try to avoid corrections, just try to avoid the riskiest junctures (i.e. those sets of conditions that have historically led to huge draw-downs).
    Interestingly, people like Soros and Julian Robertson avoided / mitigated damage from the last two bear markets. How did they do it? They likely have an intuitive “sixth sense” that combines all of the factors / warning signs I’ve listed (and others).

  • Steve

    Also, to come up with the 50/50 “one rule triggered” you (I’m guessing) probably looked at results of using an, “only when both triggered” rule?

    i.e.
    When no rules triggered, 0% cash
    When both rules triggered, 100% cash.

    If you did look at that, did it deteriorate results much from the full model? Obviously the motivation behind my suggestion is to keep as much market exposure as possible (whilst still having some rule).

    Another, more extreme version would be…
    When no rules triggered, 0% cash
    When both rules triggered, 50% cash.

    Trying to get the, ‘best of both worlds’ with this one. i.e. when we’re getting a signal to go cash, we’ll only go 50% cash to hedge our bets, remembering that there are times when it’d be better to be in. This option has the motivation of wanting to have the cake, eat it, and not gain weight either 🙂

    Side note: I have in mind, when talking about this…the utilisation of a factor based strategy when ‘in’ the market. The reason I mention that is because this might deviate from the comparison with the market as a whole.

  • bitfool

    As a geologist by background, I find the specific analogy of using the San Andreas fault amusing, as it is one of the more naturally recurrent faults around. If I had to pick a time to build my house along the San Andreas, I would definitely choose sometime in the years right after a large quake, rather than 50 years later. With an average recurrence interval of about 100 years, this feels pretty safe for my use of the home. Because the standard deviation of that recurrence interval is measured in decades, 50 years later is too close for comfort. In addition, there are good geologic reasons (e.g., nearly constant tectonic plate motion rates on either side of the fault) for this recurrence interval to exist… unlike the so-called recurrence intervals between major market corrections that market timing hopes to discern. Market timing seems more analogous to seismologists trying to discern precursor earthquake swarms… in markets sometimes these are useful (2007-08), sometimes not so much (1987).

  • Hi Bitfool,

    Wow, thanks for the insight–that’s really cool.

    I don’t know the first thing about earthquakes and assumed that events were somewhat independent–sounds like they are actually highly cyclical/predictable.

  • Adam, thanks for the comments–thought-provoking as always.

    The evidence related to tactical valuation-based timing is sobering after some harsh robustness testing–it doesn’t work that well…and that was the empirical finding before Hussman even started. So I’m not sure why he ever included that in his models.

    Market timing might be more art than science, but I’m not very good at the “art” piece of the equation. Glad to know there are those out there who possibly have those skills. I personally don’t believe it is a robust capability, but we don’t have enough sampling opportunities to confirm/deny that hypothesis. The debate will always make for great cocktail discussions–woohoo!

  • Hey Steve,

    We are just trying to highlight a simple model that seems to work. One can tweak and twang these things a 100 ways, for sure. If you do any tweaking and twanging, feel free to post for the benefit of the crowd

  • bitfool

    No, not nearly what you would call “highly” predictable. Cyclical yes, for this case (San Andreas), but earthquake cyclicity all depends on the fault system where the earthquakes are coming from. Some few of them have reasonably recognizable recurrence intervals, but most seem not to. I say “seem” purposefully, because our seismology data is limited to a few decades of modern high-quality data. This is not unlike the difference between the available data for market backtesting over the past couple decades (intraday detail over a wide universe) compared to backtesting over the past couple of centuries. There is some merit to both types of studies (short and longer term), but limits to the conclusions we can draw and accuracy of the predictions we can make. There are unknowable unknowns lurking in the markets as well as the geology we live on.

  • Terran Melconian

    I wanted to say thanks for your very thoughtful blog; I always enjoy reading it and now you’ve gotten me interested in thinking about market timing again. I looked up my notes from the last time I worked on it and remembered something interesting. I initially did quite a bit of work with data that was made from monthly averages of closing prices. At first that fact didn’t seem important, but as I moved towards an executable strategy, I found that all the exploitable correlations in the data completely disappeared when I swapped in point monthly closing prices for the transactions. I know I’m not the only one who made that mistake, because some correlation graphs appearing in a paper from AQR were reproducible only using the monthly averages. 🙂

    Since these details turn out to be surprisingly important in any strategy looking at autocorrelation, would you be willing to share the specifics of how you calculated your MA and what prices you assumed for transacting?

  • Jack Vogel, PhD

    We use total returns (except for NKY and DAX), assess the rules at then end of the month, and assume end of month transaction (buy/sell on the close on last trading day of the month).

  • Jessie Yao

    Here’s a question from Justin: “i’m curious how equal weighting the 5 sectors using DPM would have worked historically.” See below tables (1976-2014):
    5 Sectors: SPX, EAFE, LTR, REIT and GSCI
    EW_5 Sectors: Equal Weight of 5 sectors
    DPM_5 Sectors: Apply Downside Protection Model of 5 sectors

  • Hannibal Smith

    No, it failed to work between 2010 and 2014 at cost of now a -40% drawdown or so in continuous hedging expenses. I don’t know what Hussman was doing sitting on his thumbs for five years, but it took him that long to figure out you don’t fully hedge/short a rising market until, when and only if investor sentiment actually changes to risk-avoidance from risk-seeking. Duh! He also hadn’t backtest the last 100 years. Before the subprime crisis he had only backtested up until WWII which is why the late 2008 Great Depression-like conditions were “out of sample” and forced him not to invest near the bottom. In my view, it is inexcusable for someone who likes to harp about his “fiduciary duty” to first launch a fund without having had a model stress tested under ALL possible economic conditions. Skipping the Great Depression is just a stupid exercise in wishful thinking. He learned on the job and at shareholder expense. For pulling off the same trick as every other idiot on Wall Street when claiming to be different is also inexcusable.

    Smooth a moving average long enough and you wind up avoiding all the bear market drawdowns, so a complex system like Hussman may not even be necessary, though he will argue that moving averages didn’t work in the past due to transaction costs. That is correct. What you’re paying for is psychological comfort at expense of long-term growth, assuming the whipsaws don’t get to you.

    If AA actually used historical transaction costs, you won’t see a significant CAGR outperformance — if at all — over buy and hold if you go back farther than the limited history they present, even when optimized. With today’s low transaction costs, it is arguable whether or not simple momentum timing rules are now profitable. My suspicion is that today’s low transaction costs also allows more to investors to get onboard a crowded trade as the last two month’s whipsaw from bullish to bearish and now back to bullish in the S&P 500 may demonstrate. In 1994 shortly after the bottom, there were four whipsaw in a row on a monthly basis! That’s tough on anyone.

    Frankly, if downside risk management is going to work after all, I rather let a roboadvisor or ETF deal with it. However, I am not convinced through extensive backtesting that after transaction costs and taxes that simple momentum approaches like AA is offering will consistently beat buy and hold, nor do I see the futility of worrying about volatility/MaxDD if you need at least a certain CAGR target to reach your goals. Shortfall risk should be far more important than drawdown risk.

  • Hannibal,

    Agreed. Transaction costs–and taxes–are serious issues to consider and one needs to ensure they have their head wrapped around those issues before contemplating tactical approaches.

    Also agree that downside protection is not a guarantee–at all–and buy and hold may end up being the best risk-adjusted approach out of sample. That said, the best shot at downside protection–for those who choose to pursue this approach–seems to lie with simple technical and momentum-based rules. Will they work out of sample? Who knows…but emerging data on lizard brain’s ability to dynamically shift risk preferences in the face of immense continuous stress may facilitate basic trend-rule’s ability to work out of sample. https://alphaarchitect.com/2015/09/02/how-market-volatility-affects-our-brains/

  • When it comes to market timing to avoid big drawdowns, the probability of optimization is so high because there are only a handful of events a system needs to “fit” to be correct. Even with a simple rule, the risk of optimization is high. With 2 rules–or layering on gut instinct–the probability of overoptimization approaches 100%!

    Bottomline: We’ve studied market timing so much my eyes are cross-eyed and I’ve come to the tentative conclusion that there is a very high probability that NONE of this stuff works any better than throwing darts at a wall. But, basic trend/momentum rules, seem to give an investor a fighting chance if they choose to believe in the evidence and the process…I also personally believe there is a behavioral aspect for why this works, so I’m a buyer over the long-haul…but I’ve also made plenty of bad calls in the past…

  • Adam Kearny

    Small sample sizes are a bitch, aren’t they? On the other hand, if things were too systematic and robust in the markets, there wouldn’t be any opportunity, because it would all be arbitraged away! That’s why the search for alpha will always be more art than science. Can’t just think like an engineer. There’s a time and a place for every strategy to outperform, and the real alpha comes from understanding the context and set-up (“initial conditions”) (i.e. what will work well over the next several years) rather than searching for some holy grail system that will work for 100 years.
    Wes, by the way, your QVAL is now neck-and-neck with GONIX. What happened? I thought GONIX was blowing up or something. Why was it up over the August/September period (and even up some in October during the rebound)?

  • Adam Kearny

    Hannibal,
    Great points. I also don’t have faith in the robustness of price momentum strategies over time–they seem too popular (informal approaches, as well as rules-based), and anything that gets popular will cease to work. I think value/quality will continue to work though–attention spans are shrinking due to the internet/digital world we now live in–this favors outperformance of contrarian value strategies.
    Your point on shortfall risk vs. drawdown risk is extremely well-taken though I would observe that drawdowns (or sub-optimal return periods, let’s say) can be multi-decade in duration. If you buy at a P/E of 22, then the market crashes to a P/E of 6, recovers some, but thereafter only bounces around between a P/E of 10 and 12 for a few decades, you have a problem if you’re a retiree living on your portfolio–multiple compression has crushed your long-term CAGR over the term of your withdrawals. This can happen because long-only equity portfolios are tethered to certain macroeconomic and/or monetary conditions. Historically, bonds in a 60/40 served the diversifying function, but from current initial conditions looking forward, I’m not so sure anymore. Certainly not if you’re German or Japanese!

  • Hannibal Smith

    Yes, you need to use the “all weather” concept these days and have assets that respond to all economic environments, such as the Permanent Portfolio which is jolly good at wealth preservation but absolutely terrible at growth. The irony here is widespread diversification has done poorly since QEternity commenced. Maybe we’ll all forced to become rampant savers to offset the lack of growth?

  • Hannibal Smith

    What do you think of Hedgeable’s downside protection approach? It uses Constant Proportion Portfolio Insurance. I remember reading the white paper on that a couple of years ago. They reacted to the increased risk of the past two months just as you would expect and are now almost fully invested again. It seems to be an interesting way to get the same effect without using absolute or relative momentum.

    https://www.hedgeable.com/hedgeable-investment-philosophy-white-paper#cppi

  • Adam Kearny

    I think the best approach at the current time (for probably the next few years at least) is diversified market neutral long/short–capture the dispersion without being hostage to broad macro/market risks. The current market environment features lots of overvalued low-quality stocks (particularly small-caps)–“hope” stocks, concept stocks, etc. that are only starting to be deflated. Similar to 1999 albeit less extreme. BPLSX has been around for 20 years. They made -12.8% in 1999 and followed it up with +60% in 2000 and +25% in 2001. They were down most of this year and turned positive recently. GONIX is another, more recent vehicle. They are still down -8% this year though have been coming back recently. This approach also preserves the optionality of cash, i.e. if the market collapses, you can pivot to greater long exposure without having suffered a drawdown. (Gotham also runs 120/60 fund and 170/70 fund). Such a pivot, even if timing is far from perfect, will massively add to your long-term CAGR.
    This is a unique environment where both stocks and bonds are badly overpriced and will not provide much in the way of long-term CAGR here over any reasonable timeframe.
    The theoretical risk, as with any short-selling strategy, is the extension of the craziness beyond (and broader than) 1999 levels to the point that the short book kills you.

  • Adam Kearny

    I think their fees are way too high considering how easy it is to replicate such a portfolio with ETFs these days. Also, I’m not optimistic about this portfolio providing much in the way of return going forward as I think all assets are overpriced (including gold and real estate). The world currently suffers from a lack of yield and carry. Sitting in cash forever is problematic as well. Need to do something tactical, pick your spots, etc. to have a chance at decent CAGR. Either do something diversified/systematic like GONIX or BPLSX, or take some idiosyncratic risks (concentrated portfolios, market timing, etc.). It’s very hard these days.

  • Hannibal Smith

    Point me the way where I can replicate a dynamic multi-asset portfolio using Constant Proportion Portfolio Insurance with ETF’s. I haven’t seen one. You rather pay over 2% for what is a simplistic long/short portfolio that anyone can do themselves by putting up 10 long and 10 short stocks?!! Aren’t there lower cost ETF’s for that? Taking this argument further, AA is overcharging at .50% for what is simplistic “market timing” that you can easily do yourself. Pacer’s TrendPilot is definitely overcharging .60% for a fully disclosed simplistic “market timing” strategy with extra filters that is superior to half of AA’s. Even PERM is overcharging at .49% for an ultra low-cost buy and hold portfolio that you’d only need to rebalance yourself once every 2-3 years on average! Time is money and wasting your time on these “market timing” strategies that are only going to return up to 10% CAGR at ideal best long-term before taxes is not very productive use of time. And did I neglect to mention the boatload of psychological behavioral issues that come along with doing it yourself? Outsource it and you’ll be much happier. So long as the fees are reasonable. 2% is not, especially when you have no guarantee the discretionary managers won’t screw up, leave the fund, etc. compared to quantitative mechanical strategies. Even Hussman may be cheap at 1.07% once (if) he (ever) gets his mojo back, although the longer he waits, the more it is likely some low-cost ETF will kick his ass.

  • Adam Kearny

    Individuals can definitely do long/short themselves–the only question is whether they can do it effectively. 10 long and 10 short introduces massive idiosyncratic stock-specific risk–you need a large number. Also, more fundamentally, there’s the question of whether individuals can analyze/value as effectively as an elite buy-side HF team led by someone like Greenblatt (EMH debate, of course). Most cannot. BPLSX also charges 2% and has clearly earned it over the last 20 years, judging by their results. Incidentally, GONIX is mechanical/rules-based.
    On the question of long-term outperformance, my personal view is that too much effort is put into finding an elusive “holy grail”, i.e. something that will outperform over 100 years. In reality, much of the alpha is generated by figuring out what will outperform over the next several years by determining what is popular/overvalued right now. For example, in 1999, the key, in thinking forward five years, was to avoid (or short) large-cap US growth stocks and tech stocks. If you nailed that one simple decision, you outperformed massively over the next decade. It’s not a random coincidence that BPLSX returned +60% in 2000 and +25% in 2001–it was baked in the cake by the initial conditions after the late ’90s.

  • Hannibal Smith

    That’s good to hear about GONIX! What was the CAGR for BPLSX over the past 20-years since I can’t get it out of Morningstar or Lipper?

  • Ray Sheedy

    I would like to know Dr. Gray’s view on constant proportion portfolio insurance as well??? Our firm runs a CPPI strategy with roughly $2 billion AUM.

  • disqus_WDjmvSqmLH

    Thanks for sharing this. Very interesting.
    Did the test check for the rules once a day? A month? Other frequency?
    Did you rebalance mom and ma? If so at what frequency?
    Do you think it will give similar results ( meaning reducing draw down while maintaining about the same returns) with individual stocks?
    What is the relation between this and a stop loss? Are those ideas equivalent to a stop loss?

  • We have done extensive analysis of just about everything you can ever imagine.

    To keep things simple we focus on a monthly check.

    We think long-term trend-following type rules work because of market-wide psychology shifts due to the effect extended durations of stress drive humans to eventually kick all risk to the curb: https://alphaarchitect.com/2015/09/02/how-market-volatility-affects-our-brains/. With individual stocks, you have so much “noise” related to actual fundamentals it is difficult to really get a signal when conducting this sort of analysis. You end up trading too much.

    I think they are somewhat related to a trailing stop with a reasonable loss attached (i.e., 10%). See Gary’s discussion on the topic here: http://www.dualmomentum.net/2015/06/momentum-and-stop-losses.html

  • Hannibal Smith

    I get the impression that the over and under valuedness determines how strong or weak the hedging is.

  • GM

    Hi Wes,

    This is one of my favourite blog posts – thank you!

    Rather than move to cash; as alternative do you think the signals provided by MA and TMOM could be used to short the relevant market (assuming one has cash available to do this) e.g. for the US perhaps by using the ETF SH (inverse S&P 500). I understand these are day trading instruments prone to tracking error but conceptually do you think this is valid or just rubbish thinking that is best discarded?

    The context of my thought is more in relation to managing a long portfolio of nano cap and illiquid nets nets from which moving into and out of is difficult, and likely to see one miss out on the return to the stock trading at its Net Current Asset Value given the highly volatile nature of net nets.

    Thank you,
    G

  • Hey G, I think it can work, but you would need to manage the volatility and keep the costs super low. In general, I’d say keep it simple, if possible.
    In your case, you may want to short an R2K future against the long only micro exposures

  • Omar Sheikh

    Hi Wes

    What’s your view of tail risk hedging using eg far out the money SP500 puts?

    The guys at Universa in Santa Monica do this.

    KR

    Omar

  • Puts are typically more efficiently priced forms of insurance. Trend-following, managed futures, etc. often serve the same purpose but are cheaper. But with puts you have a ‘guarantee,’ whereas TF and mgd fut provide insurance, in expectation. Pick your poison I guess.

  • Hello !

    I know this article dates back, but isn’t the drawdown from 11/29/2002 to 2/28/2003 missing even in the recursive search ? Around -9.72% from my computation…

    11/29/2002, SP500 TR: 2,899.14
    2/28/2003, SP500 TR: 2,617.46

    Cheers,

    Roman

  • looks to be the case. Not enough loops on the algo. Did in excel (and/or python) so efficiency limited. Would need matlab to really do it right and not blow up the cpu

  • Thanks for the answer, I will include the SP500 example as a non-regression test for a Javascript “top n drawdowns” algorithm I am designing.

    (Note: It took less than 0.5 second to compute the top 10 drawdowns on 2000-2014, so no specific cpu load here… If ever you are interested to copy/paste, I can PM the Github link when done)

  • cool. please post and share. we have some matlab code floating around as well–need to find and share

  • GM

    Hi Wes,

    What led to the preference of the 12 month Moving Average (MA) vs. the 10 month MA (which Meb Faber has written about extensively)?

    Is Time Series Momentum calculated as follows as an example?

    Market Index starting value = 50
    Market Index value at end of month 12 = 45
    Cumulative Return = (45 – 50) / 50 = -10%
    Risk Free Rate = 1%
    Result = go to cash/risk free asset?

    Thanks for this great post!
    G

  • Hi Omar,
    I think this is a great way to financially engineer the portfolio to minimize huge tail events, but it comes at an explicit costs: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2579232.
    Ideally you find a tail risk protection device that is cheaper. We think trend rules and/or mgd future type programs may be that answer.

  • Doesn’t matter what version you use — 10 month would essentially do the same thing — as would 14.36 months or 13.14. Out of sample 12 months will certainly not be the best answer, but it is an answer.

  • GM

    Thanks Wes – I guess that suggests “parameter stability”.

    Is my understanding of Time Series Momentum correct?

    Thanks,
    G

  • tsmom logic is correct

  • james

    If using MA within the past few years you’ve been whipsawed. Instead of waiting until the end of the month to asses and sell, have you looked at changing the time period to something shorter, say a week? This will obviously increase expenses, however you’re out of the market sooner and back in sooner. You may potentially get whipsawed more often, but each one could be smaller than doing it monthly, thus decreasing tracking error.

  • James,
    We’ve looked at so many angles on trend-following it would blow your mind–from the most complex to the simplest. Our basic conclusion is find a relatively simple rule and stick with it.

  • Ankur Choudhary

    Hey Wes,
    Great post as always. Was wondering what are your thoughts with respect to CPPI (as used by Hedgeable) instead of a momentum based protection. If you have already covered this somewhere please feel free to just point me to it. Thanks a ton.

  • We have not done an in-depth study on their particular approach, but after reading their cookbook I would venture to guess that their technique of pulling down risk roughly approximates what a generic trend-following approach will achieve.

  • Yogi Berra

    For a informed full time individual investors what would be the best strategy in your (even biased?) opinion after considering taxes and transaction costs etc? Long Term Mean reversal (E.g. 36 x 36 months) strategies Or momentum strategies like 12 x 6 or 6 x 6 or 12 x 12 etc? In the era of machine automated short term trading do you think patient investor should focus more on longer term strategies to gain an edge and sanity of mind?

    (Note- I also take this opportunity to appreciate your Quantitative Value book. I am using some of the ratios/formulas given in the book in my investment research)

    Cheers

  • awesome, thanks for sharing!!!

  • Jon Pildis

    Thank you for all of the work you post for the public to consume! One question: do you use adjusted closing price for SMA rules to properly account for dividends, splits and distributions?

  • Jon, these aspects are noted in the article, but hard to identify — aside from japan/dax, which are price-only, everything else is total return. One can run the analysis with price-only and come to similar conclusions.

  • We have not.