Really Bad Months

Last month saw most asset classes decline, with the exception of US equities.  I thought I would put the declines in perspective – the below is since 1972 for the following main asset classes.

Most equity like assets have had worst months of over -20%.  Bonds, 7-15%.  Can you fathom that?

An old post on what to do after really bad months here.


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QTAA Paper Update: Weightings 10/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  


No two investors are alike.  Some investors value wealth preservation with low volatility above all else, while others can handle a 50% loss in an attempt at generating higher gains.

Below we look at a few different allocations that we will call GTAA Conservative, Moderate, and Aggressive.

GTAA Conservative   

This allocation broadly follows the allocation of GTAA Moderate, but with more in bonds (40% vs. 20%).  Cash is invested in 10 Year US Government Bonds.



GTAA Moderate 

This allocation is the same as mentioned in the prior Extension.




GTAA Aggressive 

This portfolio begins with the asset classes listed in the GTAA Moderate allocation.  It then selects the top six out of the thirteen assets as ranked by an average of 1, 3, 6, and 12-month total returns (momentum).  This method was detailed in our white paper “Relative Strength Strategies for Investing.  The assets are only included if they are above their long-term moving average, otherwise that portion of the portfolio is moved to cash.  We also include the effects of only investing in the top three out of thirteen assets.

Another extension we covered is to apply leverage to generate excess returns. An investor would simply invest twice as much in each asset class, and the maximum portfolio exposure would be 200% if all of the asset classes were on buy signals simultaneously. 

Note:  Implementing the leveraged model at many retail brokerages is not ideal due to prohibitive borrowing costs.  Leveraged ETFs likewise are not ideal due to large tracking error relative to the benchmark index.  An investor must be careful when pursuing leveraged returns.


Figure 20: Buy & Hold vs. Various GTAA Allocations, 1973-2012


Economic Fundamentals Suggest Higher Yield

I really look forward to Minerd’s purple charts of the week in their Macro View.  Today’s:

“Historically, the real yield on 10-year Treasuries has closely tracked the University of Michigan Consumer Sentiment Index. The correlation broke down, however, in 4Q2011, as a result of the Federal Reserve’s asset purchase program. The yield on 10-year Treasuries would be roughly 150 basis points higher than it is today if the market was not being distorted by Ponzi (uneconomic) buying.”


QTAA Paper Update: Alt Cash Strategies 9/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  



On average the tactical portfolio is invested in 30% cash.  This is a drag on the portfolio, and many investors employ other means to increase the yield on the cash portion of the portfolio using any number of funds or concepts.  Below we look at a simple method of taking on more duration risk by investing the portfolio in 10 year government bonds instead of Treasury Bills. 


Figure 19: Buy and Hold and GTAA Portfolios, 1973-2012



An investor would have realized an additional 1.37% per annum in returns for marginally more volatility and drawdown – but how much of this is simply due to the major bull market in bonds?  We decided to examine a period of sharply rising interest rates from 1973-1981, and found that the benefit of taking on additional duration risk actually helped!


Figure 19: Buy and Hold and GTAA Portfolios, 1973-2012




QTAA Paper Update: Extensions 8/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  


Other than simplicity, there is no reason to only focus on five asset classes.  (Technically, we believe there are only four real asset classes:  stocks, bonds, commodities, and currencies. Everything else (like REITs) is a combination of the prior four.)  

At the same time, expanding a portfolio with allocations less than 5% of the total does not do enough to move the needle on the entire portfolio’s risk and reward characteristics. (This ignores derivatives and holdings with highly asymmetric payoffs). 

We also have the challenge that many asset classes and indexes simply have not existed for a very long time.  For example, we do not include TIPs, junk or high yield bonds, emerging bonds, foreign REITs, fundamental indexes, managed futures, currencies, or other asset classes we might otherwise consider.  However, thirteen asset class subgroups will likely cover the majority of the world that we would like to allocate to.

Below we expand the original portfolio from:




…to include the following:



We then take a look at the historical returns compared to the simple strategy of five asset classes.  As you can see, it improves returns about 150 basis points, likely enough to warrant increasing the assets in the portfolio.

Figure 18: Buy and Hold and GTAA Portfolios, 1973-2012



A lot of people are moving into cash “substitutes” to increase their yield, likely with unintended consequences.  Below is a nice piece from Vanguard on floating rate bonds:



QTAA Paper Update: Vol Clusters 7/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  


One of the benefits of a quantitative system is that it protects the investor from innate behavioral biases.  A discussion of some of the more insidious biases can be found in the Appendix.  Of course, this information is not only valuable for figuring out our own biases – other people’s mistakes leave the door open for us to soak up some of that elusive alpha.  As far as excess returns are concerned, for someone to gain, someone else has to lose.  People consistently make the same mistakes that are hard-wired into their brains, and they do so over and over again.

Humans use a different part of their brain when they are losing money than when they are making money.  We put together a 17-page white paper to address the topic called “Where the Black Swans Hide and the Ten Best Days Myth”.

Figure 18 shows the annualized returns and volatility for the five markets we studied in this paper.  On average, the returns are 60% lower and the volatility 30% higher when the market is below its 10-month simple moving average.  Commodities are the one exception where volatility is not higher when below the moving average, which makes intuitive sense.  Commodities are often driven by supply shocks that can result in price spikes.

2008 is a prime example with volatility levels in stock markets around the globe exploding to record levels.  However, this volatility has occurred after the markets already began declining. 

Figure 18: Volatility Clustering Across Various Asset Classes



QTAA Update: In Practice 6/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  


There are a few practical considerations an investor must analyze before implementing these models for real-world applicability – namely, management fees, taxes, commissions, and slippage.

Management fees should be identical for both the buy and hold and timing models, and will vary depending on the instrument used for investing.  0.10% to 0.70% is a fair estimate range for these fees using ETFs and no-load mutual funds (obviously the lower the better).  Many all-ETF portfolios can be formed for approximately 0.1% to 0.3%.

Commissions should be a minimal factor due to the low turnover of the models.  On average, the investor would be making three to four round-trip trades per year for the portfolio and less than one round-trip trade per asset class per year.  Likewise, slippage should be nearly negligible, as there are numerous mutual funds (end-of-day pricing means zero slippage) as well as liquid ETFs an investor can choose from.

Taxes, on the other hand, are a very real consideration.  Many institutional investors such as endowments and pension funds enjoy tax-exempt status.  The obvious solution for individuals is to trade the system in a tax-deferred account such as an IRA or 401(k).  Due to the various capital gains rates for different investors (as well as varying tax rates across time, as well as the impact of dividends) it is difficult to estimate the hit an investor would suffer from trading this system in a taxable account.  Most investors rebalance their holdings periodically and introduce some turnover into the portfolio even for a buy and hold allocation – and it is reasonable to assume a normal turnover of approximately 20%.  The system has a turnover of almost 70%. 

Gannon and Blum (2006) presented after-tax returns for individuals invested in the S&P 500 since 1961 in the highest tax bracket.  After-tax returns to investors with 20% turnover would have fallen to 6.72% from a pre-tax return of 10.62%.  They estimate that an increase in turnover from 20%-70% would have resulted in an additional haircut of less than 50 basis points to 6.27%. 

There is some good news for those who have to trade this model in a taxable account.  The system results in a high number of short-term capital losses, and a large percentage of long-term capital gains.  Figure 17 depicts the distribution for all the trades for the five asset classes since 1973.  This should help reduce an investor’s tax burden.


Figure 17: Length of Trades for Timing Model, 1973-2012






QTAA Update: Global Tactical 5/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  



Given the ability of this very simplistic market-timing rule to add value to various asset classes, it is instructive to examine how the returns would look in the context of an investor’s portfolio.   Here we introduce a version of the timing model we refer to as “Global Tactical Asset Allocation” or “GTAA”.   GTAA consists of five global asset classes:  US stocks, foreign stocks, bonds, real estate and commodities.  The returns for a buy and hold allocation are referenced as “Buy & Hold” or “B&H” and are equally weighted across the five asset classes.  The timing model also uses equal weightings and treats each asset class independently – it is either long the asset class or in cash with its 20% allocation of the funds.  Figure 12 illustrates the percentage of months in which various numbers of asset classes were held.  It is evident that the system keeps the investor 60%-100% invested the vast majority of the time (approximately ~80% of the time the portfolio is at least 60% invested).  On average, the investor is 70% invested.

Figure 12: Percent of the Time Invested, 1973-2012




Figures 13 and 13b below present the results for the buying and holding of the five asset classes equal-weighted versus the timing portfolio.  The buy and hold returns are quite respectable on a stand-alone basis and present evidence of the benefits of diversification. 


Figure 13: Buy & Hold vs. Timing Model, 1973-2012, log scale





Figure 13b: Buy & Hold vs. Timing Model, 1973-2012, non-log scale





However, the additional advantages conferred by timing are striking.  Timing results in a reduction of volatility to single-digit levels, as well as a single-digit maximum drawdown.  Drawdown is reduced from 46% to less than 10%, and the investor would have only experienced one down year of less than -1% since inception in 1973.  Figure 19 details the yearly returns, and post-2005 is highlighted as the out-of-sample period. 


Figure 14: Yearly Returns for Buy & Hold vs. Timing Model, 1973-2012


It is possible that Siegel (or others) have optimized the moving average by looking back over the period tested.  As a check against optimization, and to show that using the 10-month SMA is not a unique solution, Figure 15 presents the stability of using various moving averages lengths ranging from 3 to 12 months.  Calculation periods will perform differently in the future as cyclical and secular forces drive the return series, but all of the parameters below seem to work similarly for a long-term trend-following application. 

Figure 15: Parameter Stability of Various Moving Average Lengths, Timing Model 1973-2012



While it is instructive to examine the model in various asset classes, the true test of a model is how it performs out of sample in real time.  Since the paper was originally published in 2006 with results up to 2005, returns after 2005 should be seen as out of sample.  Figure 16 illustrates the returns for B&H and timing portfolios. 



Figure 16: Summary Annualized Returns for B&H vs. Timing Model, 2006-2012




The model performed exactly as one would expect it to from historical data.  Namely, even though it only outperformed in three out of seven years, it beat buy and hold by over two percentage points per year, with much less volatility and most importantly to many investors, lower drawdowns.

QTAA Paper Update: Manage Your Risk 4/10

Below we have updated our 2006 white paper.  While you can download the full 70+ page paper here, I’ve also chopped it up into a series of more digestible posts for the blog.  



There are a few criteria that are necessary for a model to be simple enough for investors to follow, and mechanical enough to remove emotion and subjective decision-making. 


They are:

1.  Simple, purely mechanical logic.

2.  The same model and parameters for every asset class.

3.  Price-based only.


Moving-average-based trading systems are the simplest and most popular trend-following systems (see for example Taylor and Allen (1992) or Lui and Mole (1998)).  For those unfamiliar with moving averages, they are a way to reduce noise.  The example below shows the S&P 500 with a 10-month simple moving average (SMA).

Figure 6 – S&P 500 vs. 10-Month Simple Moving Average, 1990-2012



The most often cited long-term measure of trend in the technical analysis community is the 200-day simple moving average.  In his 2008 book Stocks for the Long Run 5/E: The Definitive Guide to Financial Market Returns & Long-Term Investment Strategies, Jeremy Siegel investigates the use of the 200-day SMA in timing the Dow Jones Industrial Average (DJIA) from 1886 to 2006.  His test bought the DJIA when it closed at least 1 percent above the 200-day moving average, and sold the DJIA and invested in Treasury bills when it closed at least 1 percent below the 200-day moving average. 

 He concludes that market timing improves the absolute and risk-adjusted returns over buying and holding the DJIA. Likewise, when all transaction costs are included (taxes, bid-ask spreads, commissions), the risk-adjusted returns are still higher when employing market timing, though timing falls short on an absolute return measure.

When applied to the NASDAQ Composite Index since 1972, the market timing system thoroughly outperforms buy-and hold, both on an absolute and risk-adjusted basis. Siegel finds that the timing model outperforms buy and hold by over 4% per year from 1972-2006 even when accounting for all costs, and with 25% less volatility.  Unfortunately, Siegel does not report drawdown figures, which would have further demonstrated the superiority of the timing model.  (Note: Siegel’s system is twice as active as the system presented in this paper, thus increasing the transaction costs).  Sigel is updating the book with a 2013 edition, and we look forward to see the results including the 2006-2012 period.

It is possible that Siegel already optimized the moving average by looking back over the period in which it is then tested.  To alleviate fears of data mining, the approach will be examined across various parameters and other markets to test for validity.

The system is as follows:


Buy when monthly price > 10-month SMA.


Sell and move to cash when monthly price < 10-month SMA.


1.  All entry and exit prices are on the day of the signal at the close.  The model is only updated once a month on the last day of the month.  Price fluctuations during the rest of the month are ignored.

2.  All data series are total return series including dividends, updated monthly.

3.  Cash returns are estimated with 90-day Treasury bills, and margin rates (for leveraged models to be discussed later) are estimated with the broker call rate.

4.  Taxes, commissions, and slippage are excluded (see the Practical Considerations section later in the paper).


S&P 500 FROM 1901 – 2012


To demonstrate the logic and characteristics of the timing system, we test the S&P 500 back to 1901.  Total return series is provided by Global Financial Data and results pre-1971 are constructed by GFD.  Data from 1901-1971 uses the Standard and Poor’s Composite Price Index and dividend yields supplied by the Cowles Commission and from S&P.

Figure 7 presents the annualized returns for the S&P 500 and the timing method for the past 100+ years.  A cursory glance at the results reveals that the timing solution improved compounded returns while reducing risk, all while being invested in the market approximately 70% of the time and making less than one round-trip trade per year.  (Volatility is measured as the annualized standard deviation of monthly returns.)

Figure 7: S&P 500 Total Returns vs. Timing Total Returns (1901-2012)



The timing system achieves these superior results while underperforming the index in roughly half of all years since 1901.  One of the reasons for the overall outperformance is the lower volatility of the timing system.  It is an established fact that high volatility diminishes compound returns.  This principle can be illustrated by comparing average returns with compounded returns (the returns an investor would actually realize.)  The average return for the S&P 500 since 1901 was 11.26%, while timing the S&P 500 returned 11.22%.  However, the compounded returns for the two are 9.32% and 10.18%, respectively.  Notice that the buy and hold crowd takes a hit of nearly 200 basis points from the effects of volatility, while timing suffers a smaller decline of around 100 basis points.  Ed Easterling has a good discussion of these “volatility gremlins” in John Mauldin’s 2006 book, Just One Thing: Twelve of the World’s Best Investors Reveal the One Strategy You Can’t Overlook.

Figure 8 shows the superiority of the timing model over the past century, largely avoiding the significant bear markets of the 1930s and 2000s.  Figure 8b shows that timing would not have left the investor completely unscathed from the late 1920s early 1930s bear market, but it would have reduced the drawdown from a catastrophic 83.66% to a more manageable 42.24%. 

Figure 8: S&P 500 Total Returns vs. Timing Total Returns (1901-2012)


Figure 8b: S&P 500 Drawdowns vs. Timing Drawdowns (1901-2012)



Figure 9 is charted on a non-log scale to detail the differences in the two equity curves. Examining the most recent 22 years, a few features of the timing model stand out. First, a trend-following model can underperform buy and hold during a roaring bull market similar to the U.S. equity markets in the 1990s.  On the flip side, the timing model can avoid lengthy and protracted bear markets.  Consequently, the value added by timing is evident only over the course of entire business cycles. 

For example, the timing model exits a long position in October of 2000, thus avoiding two of the three consecutive years of losses, and its 16.52% drawdown is much shallower than the 44.73% setback suffered by buy-and-hold investors.  The timing model again exited the S&P 500 on December 31, 2007 and avoided the entire bear market of 2008-2009 and the 50.95% drawdown.


Figure 9: S&P 500 Total Returns vs. Timing Total Returns (1990-2012)




A glance at Figure 10 presents the ten worst years for the S&P 500 for the past century, and the corresponding returns for the timing system.  It is immediately obvious that the two do not move in lockstep.  In fact, the correlation between negative years for the S&P 500 and the timing model is approximately -0.38, while the correlation for positive years is approximately 0.83.  This reflects the ability of the timing model to stay long in up markets while exiting the long position during down markets.

Figure 10: S&P 500 Ten Worst Years vs. Timing, 1900-2012




Figure 11 gives a good pictorial description of the results of the trend-following system applied to the S&P 500.  The timing system has fewer occurrences of both large gains and large losses, with correspondingly higher occurrences of small gains and losses.  Essentially, the system is a model that signals when an investor should be long a riskier asset class with potential upside, and when to be out and sitting in cash.  It is this move to a lower-volatility asset class (T-bills) that drops the overall risk and drawdown of the portfolio.  Most importantly, it avoids the far left tail of big negative losses.

Figure 11: Yearly Return Distribution, S&P 500 and Timing 1900-2012




Appendix B breaks down the returns down by decade for the S&P 500 and the timing model.  While the timing model outperforms in about half of all decades on an absolute basis, it improves risk-adjusted returns in about two-thirds of all decades and improves drawdown in all but two decades.  Another interesting observation is the wide variance in Sharpe ratios per decade for buy and hold, ranging from -0.23 to 1.44.  The past decade has seen compound returns of -0.94% per year for buy and hold while the 1950s saw returns of 19% per year. 

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