True Sector Rotation Theory

Modern Portfolio Theory Teaches "Diversify and Rebalance" Which
 Inherently Produces Average Performance. Its Time to Change the Game.

Introduction

The bottom line objective of this page is to answer these common and excellent questions:
• How can AlphaDroid possibly know ahead of time which market sector will likely be best next month?
• AlphaDroid charts look spectacular now. What evidence is there that it will continue to work in the future?
• The Efficient Market Hypothesis seems to imply AlphaDroid cannot possibly work. How do you explain that?
• Most financial experts say to diversify and rebalance. How can you legitimately defend saying otherwise?

• Diversify and Rebalance?  The financial industry has hypnotized us into believing that buy-and-hold diversification and rebalancing is the only worthy investment strategy. Its principle derives from Modern Portfolio Theory (MPT) developed by Prof. Harry Markowitz in 1950, (perhaps not so modern anymore). Diversification inherently means owning a little bit of everything — which is the formula for achieving precisely average performance! Portfolio rebalancing further ensures little straying from average. No other industry proclaims average performance is the best you can expect to achieve. While the big Wall Street firms sell buy-and-hold diversify-and-rebalance to the masses through their financial advisors, it seems they prefer much better proprietary trading methods for their own money.

• You Must Trade Risk For Return?  Another important tenet of MPT is that markets are composed of rational investors who will trade risk for return. As depicted in the chart to the right, if the blue dots represent the risk/return profiles of all available portfolios, and the green dot represents a risk-free money market fund, then the red dots represent the set of best portfolios that can be created from various combinations of them - and these best portfolios lie on a line referred to as the efficient frontier. MPT further states that no portfolio can remain in the upper left region for more than a short time. To the true practitioners of MPT, AlphaDroid represents pure heresy because it claims it can create portfolios that remain in the upper left corner and you don't have to trade risk for return.

What MPT fails to consider is that a rational investor has choices other than buy-and-hold diversification. For example, while it is true that walking slower on an icy sidewalk is one method of reducing the risk of falling, you can also change the game by wearing spiked shoes, by salting the sidewalk, or using the dry sidewalk on the other side of the street. Similarly, rational investors don't need to buy-and-hold investments that are tanking solely for appeasing the MPT diversification gods.

It is actually the opposite of buy-and-hold diversification that enables one to create portfolios in the upper left corner of the risk/return chart. Only by owning the top momentum leaders and avoiding momentum laggards can one simultaneously improve returns and reduce risk of loss. When applied to market sectors, we call it True Sector Rotation!

• Time is Money! AlphaDroid's algorithms incorporate mathematics from the fields of electronic signal processing and information theory to reliably extract information from a noisy environment — in this case, extracting trend information from noisy market data to get clues about future market moves. In the end, trend analysis is the game!  By its very definition, "trend" means that information from the recent past tells you something about the near future. Better performance is all about getting those clues so you can improve your investment batting average. Digging trend signals out of noise is what AlphaDroid is designed to do — and in particular, it digs sector rotation trend signals out of noisy daily market data. Conversely, MPT is inherently clueless about what to own next month because all of its mathematical constructs are statistical in nature; it has entirely discarded the time domain data required for trend analysis. Better decisions are made with more information, not less! Better returns are the result. According to Gary Larson, even Einstein discovered that time is actually money.

Pertinent Market Wisdom

Below are a few worthy words of market wisdom, each with somewhat obscure but quite important meanings that are fundamentally relevant in forming a basis for understanding why AlphaDroid works.

• If the nation's economists were laid end-to-end they would point in all directions (A. H. Motley). This fairly humorous quote is actually quite profound. In fact, in freely traded markets it is intrinsically always true. Take, for example, the question of the current value of your favorite blue chip stock ... should you be a buyer or a seller? If there becomes an imbalance between buyers and sellers, the price quickly adjusts until again there is an equal number of buyers and sellers — and thus all of the investors, talking heads, and newsletters will again point equally in all directions — each with all the good reasons why they are right. If that is the case, then there is no actionable information available from them that is worth more than a crap shoot in Las Vegas — true investment information will have to come from somewhere else.

• Past performance is no guarantee of future results. But yet, all professional investors use either fundamental analysis or technical analysis to guide their investment decisions — one of which relies on past performance reported in financial statements, and the other which relies on past performance of its stock price. Why then is this warning found on virtually every investment document, advertisement, and Web site?  While seemingly a double-speak C.Y.A. phrase, note that saying past performance is no guarantee of future results does not say it provides no valid indication of future results, just that the indication comes with a lot of variability, including possible loss. Widespread use of fundamental and technical analysis implies that in fact past performance IS an indicator of future performance. This will be demonstrated to be an absolute fact later in this document. AlphaDroid's performance depends on it and stands as confirmation of its truth.

• The trend is your friend. This simple statement follows from the more complex statement above, and has fundamentally important implications. Without trends, your portfolio only has the random "luck of the draw" working for you. A 50/50 chance of beating (or not beating) the market averages should tell us quite clearly that spending more time and effort is neither a wise investment of time nor of money. To do better than random luck we must get a sneak peek into the future. A trend is in fact a sneak peek into the future. We instinctively know that a current high performance friend, company, vineyard, or dairy cow is more likely to be in the high performance category next month than one that is currently in the low performance category. Extracting useful trend information from market data laden with noise is what AlphaDroid's algorithms are all about.

• Diversification reduces the risk of loss in a portfolio. (industry dogma)
• Wide diversification is only required when investors do not understand what they are doing. (Warren Buffet)
• Don't put all your eggs in one basket. (idiomatic phrase)
• Put all your eggs in one basket and — WATCH THAT BASKET. (Mark Twain)

Both Warren Buffet and Mark Twain seem to think that you can do better than ordinary diversification if you are willing to pay attention to and manage what's in your portfolio. Mindless diversification is the easy way to achieve average performance: just own a bit of everything. For risks that are not foreseeable, diversification abates risk as well as one could reasonably expect. However, when risks and returns are foreseeable — such as would be the case if the trend is your friend — then you can do better than diversification. In the sections below, you will see how the statistical analysis methods of MPT employed by the financial industry destroys valuable temporal market data required for achieving anything better than  average performance. AlphaDroid chooses instead to embrace the wisdom of Warren Buffet and Mark Twain.

Is the Efficient Market Hypothesis True?

At the very heart of fundamental, technical, and quantitative analysis (including AlphaDroid) is the requirement for trends to exist. If there are no trends, there is no value in looking at an annual report, no value in the Wall Street Journal, and no value in paying attention to the S&P 500 or other equity price charts. In fact, this is exactly what the Efficient-Market Hypothesis (EMH) implies if it is actually true.

The EMH is an influential economic theory first expressed by Louis Bachelier, a French mathematician, in 1900 and was largely ignored until the 1950s. EMH asserts that it is impossible to consistently "beat the market" because competition from millions of investors actively digesting all publicly available information quickly drives prices to their fair values. EMH concludes that searching for undervalued stocks, predicting market trends, and market timing strategies are pointless. As evidenced by many publications on the Web, EMH continues to enjoy a strong following, particularly among those also embracing MPT.

Clearly we have a great divide between the beliefs of EMH academics, and the beliefs of investors, traders, and the news media making a living down in the trenches. Fortunately there is no shortage of market data to analyze to help resolve this difference in beliefs. We will examine the data shortly — and no, it will not favor the academics. The glaring error in EMH is found in the phrase "publicly available information." This phrase has two parts: "publicly available," and "information."  Let's take a look at each.

Regarding the meaning of "publicly available," consider this teaching by Sun Tzu, a 6th century BC Chinese General, military strategist, and author of The Art of War where he says, "All men can see these tactics whereby I conquer, but what none can see is the strategy out of which victory is evolved." The strategies of corporations are typically only superficially described in annual reports for competitive reasons, and thus are only partially publicly available at best. Furthermore, most of us are focused on chasing kids and careers and have little or no time to read or consider the strategies of the corporations in which they are invested. The intrinsic inability of most investors to instantly know about a corporate strategy, a lawsuit, or a new product  release inherently creates trend characteristics. It takes time for everyone to hear the news, more time to understand it and form an opinion, and even more time to act on it. When this process feeds on itself excessively with irrational exuberance, a self-fulfilling prophesy will emerge that overshoots the reality of the situation and creates a market bubble. By its very definition, a market bubble has an excessive price trend, which is not an EMH random walk.  
 

Regarding the meaning of "information" consider this bit of wise verse by Witatschimolsin:

    What you know I need to hear
    Words you use may be clear
    We talk the same, but we don't
    I want to know, but I won't.

What's information to you may be no more than gobbledygook to me. I may not have the proper educational, cultural, or life experience background to fathom your words. It may take me a while to figure out what the true meaning and implication is of your words, and I may be emotionally predisposed to a particular meaning following some seemingly relevant personal experience. There are others who will get it right sooner, and still others who will figure it out later. That constitutes a trend, not an instant adjustment. Information transmitted is not information received until it is understood. EMH erroneously focuses on transmitted information versus received information.

While the EMH conclusions may in fact hold for a strictly narrow meaning of "publicly available information," in the real world searching for undervalued stocks, predicting market trends, and market timing strategies is apparently not pointless because "publicly available" and "information" are not instant and final, but rather have shades of grey that take root over time. Thus, in the real world, the Efficient Market Hypothesis is inherently false.

Here are four documents from the media, industry, and academia confirming trends are real and EMH is false.
• The Economist: Momentum in Financial Markets. A survey of strategy results and expert commentary.
• Columbine Capital: Price Momentum - a Twenty Year Research Effort. Industry momentum white paper.
• Jegadeesh & Titman: Profitability of Momentum Strategies. A fundamental academic momentum paper.
• Robert Shiller, Nobel laureate: Irrational Exuberance. An examination of market bubbles and their cause.

 

The Hurst Exponent Reveals Trends

While such debate about intangible human behavior is interesting, if trends do exist, evidence should be found easily directly in the market data. The following discussion includes excerpts from Chaos and Order in the Capital Markets by Edgar Peters, published in 1996 by John Wiley & Sons, Inc. (Peters).  Greater depth of treatment on this topic can be found there.

In 1906 Harold Hurst, a hydrologist working on the Nile River Dam project, was examining historical data regarding inflow of river water to determine important parameters for the dam's capacity. In the process he masterfully developed an important dimensionless ratio for a time series of data that is calculated by taking the data range (max - min) and dividing it by its standard deviation. This analysis is called rescaled range analysis (R/S).  

In a normal random process, when the time frame is increased, this ratio will increase by the square root of the increase. For example, if the time period is 2 times as long, then the ratio will increase by 1.414, and plotted on a log-log scale it will have a slope of 0.5. If the time series data is absolutely flat like a line, the ratio will increase linearly with the time scale and will have a log-log plot slope of 1.0. The slope of the plotted data has become known as the Hurst exponent. For example, the Hurst Range/Scale Analysis chart to the right shows a sloped line identified as a Random Walk with H = 0.50, and another sloped line identified as a Linear Trend with H = 1.0. We will come back to this chart in a moment.

Interestingly, it has been shown that the Hurst exponent is the inverse of the fractional or fractal dimension of the data. A straight line has dimensionality of 1.0 — it has only the single dimension of length. But, a wiggly line takes up more than one dimension, and some lines are much more wiggly than others. Earlier we noted that the process of a Random Walk had a Hurst exponent of 0.5, and thus a fractional dimension of 2.0. What this means, for example, is if we put an insect on a piece of paper and draw a line on the paper tracking the random path of the insect, eventually the entire paper will be covered by the line and thus the line fully has 2.0 dimensions; that of length and width.

While it is clear that the S&P 500 is not a smooth straight line with Hurst exponent H = 1.0 (and fractal dimension of 1.0), the fundamentally important question is whether it is similar to a Random Walk, a straight line, or something between a straight line and a Random Walk.

If the S&P 500 price movements were like a Random Walk, the frequency distribution charted in the figure to the right (Peters) would appear normally distributed — like the bell curve it is plotted with. It is quite noticeable that its standard deviation (peak to width ratio) is quite different and that its significant tails indicate a much higher probability of significant market moves up and down.

The Hurst rescaled range analysis (R/S) method for the S&P 500 over a 38-year period is plotted in blue in the figure above-right. As previously noted, a straight line representing Random Walk data with a Hurst exponent H = 0.5, and a straight line representing Linear Trend data with a Hurst exponent H = 1.0 are also plotted for reference. On the right half of the chart, the Hurst exponent for the S&P 500 is about 0.50, indicating a Random Walk. However, on the left half of the chart, the Hurst exponent is about 0.78, indicating something about half way between a perfect Linear Trend and a perfect Random Walk. The slope gradually changes from one to the other at approximately 40 months (where LOG(Months) = 1.6). 

A Hurst exponent of 0.78 means it has Statistical Trending characteristics that are quite significant in the short-term  and dissipate slowly over numerous months. The data shows that the full meaning and impact of an event that occurs today does indeed take a while to play out in the market.

One additional thing we need to know about this Hurst exponent is whether it has changed over time. This has also been addressed by Peters and is summarized in the chart to the right. The chart contains the Hurst Range/Scale Analysis for the decades of the 1930s, 1940s, 1950s, 1960s, 1970s, and 1980s. Quite interestingly, their plots are all nearly identical and overlay one another — in spite of recession, depression, boom, bust, war, politics, technology, and affluence. This characteristic is called statistical stationarity, and is something worthy of serious contemplation, and will be further discus.

If the S&P 500's Hurst exponent is not affected by any of those things listed above, then what is responsible for giving it these characteristics, including such stability? Perhaps the best answer is the following conjecture. The market is nothing more than interactive people. People make the observations, make the evaluations, draw the conclusions, and click the buy and sell buttons. Over millions of years people have evolved a set of generally successful characteristics for observing, evaluating, and taking action. The amount of information required to successfully draw the right conclusion and the speed with which conclusions should be drawn to enhance our survival has been optimized in our evolving genetic over millions of years ... but remains stable in character over millennia, including through recession, depression, boom, bust, war, politics, technology, and affluence.

Regardless of the true reason for such character, a stationary 0.78 Hurst exponent for decades is quite profound! An expectation that future decades will behave similarly looks like a pretty good bet. The trending character of the markets revealed by its Hurst exponent is the backbone of AlphaDroid's success, and it is the profound stability of its character over numerous decades that provides the credibility AlphaDroid will continue to perform as well in the future as it has in the past.

Trend Signal Stationarity

In this Fidelity sector fund Strategy shown on the black chart, one can clearly see that the 1st half and 2nd half of the 23-year time interval show dramatically different price performances for each of the 12 constituent funds.

If the character of the trend data that AlphaDroid uses to make its decisions actually does have stationarity, then we should find that the optimum parameters for measuring the trend should be the same in both half periods. Trend duration and intensity are characteristics different from price patterns. The trend characteristics we need should be agnostic to whether the market is going up, down, or sideways.

Plotted on the white chart is the annualized return for the Strategy versus the averaging time constant used by AlphaDroid's algorithm for measuring trends to determine which of them has momentum leadership. The three lines plotted are for the first half period (red), the second half period (blue), and the overall 23-year period (green).  This chart makes it pretty clear that one can neither arbitrarily choose a time constant nor a trend measuring algorithm and expect optimum results. Character evaluation matters. It should further be noted that the location of the performance peak varies with the makeup and mix of ticker symbols. (i.e. stocks, sectors, market indices, bonds, and commodities all have different characteristics)

While it is to be expected that the achievable returns during the first half and second half would be different, the important take away from this chart is that the location of the peak in each period is roughly at 17 days. Thus, independent of how the market is really doing in these periods, the trend character used by AlphaDroid remains stationary. 

This is very much just like tuning a radio receiver today, and finding that next week the music is still playing. The radio station frequency modulation and the background radio noise occupying the same frequency spectrum may both have many random properties, but their characters exhibit stationarity that enable a radio receiver to be tuned today and still work tomorrow.

AlphaDroid's Trend Fingerprint 

One might reasonably ask how one can be sure that it really is the trend signal embedded in market data that is responsible for AlphaDroid's superior performance.

The first chart on the right shows the Hurst exponent for the DJ-30 Industrials when the Hurst exponent is calculated only on a specific day of the month. As can be seen, the Hurst exponent is measurably higher right around the end of the month. Thus, one would expect that the performance of a AlphaDroid Strategy would be higher were trading done only month-end versus only mid-month if AlphaDroid indeed derives its performance from these trend signals.

The second chart on the right correspondingly shows the performance of the Fidelity KickAss Sectors Strategy when its trading day is limited to a particular day of the month. Its match to the month-end bump in the Hurst exponent is quite notable and profound.

While there are no definitive studies showing the true cause of the month-end trading effect, what is known is that (a) all movements in market data are caused by human trading activity, and (b) we live in a society that demands month-end reporting. Thus, it should not be surprising that fund managers take action to improve investment returns synchronously with the monthly reporting cycle. This effect is the reason you will find the default selection for newly created AlphaDroid Strategies to be month-end trading.

Why MPT Is Blind to Market Trends

Modern Portfolio Theory is the basis behind the financial industry's strategy for broad diversification within and between asset classes (such as stocks, bonds, money market, and commodities) as well as for the industry's strategy of periodically rebalancing asset allocations back to the original target percentages of the portfolio's total investment.

Here is a test of your observational skills — read the following Wikipedia definition of MPT and see if you notice what useful information MPT has discarded: "More technically, MPT models an asset's return as a normally distributed random variable, defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not correlated, MPT seeks to reduce the total variance of the portfolio. MPT also assumes that investors are rational and markets are efficient." So, what's missing?

The answer is that all of the mathematical functions listed above include only statistical functions — which means that there can be no time domain analysis results, and thus no trend analysis results. This is why an MPT practitioner can tell you which five things to buy and hold based on statistical performance in the past, but cannot tell you anything about which of them would be best to own next month. In fact, because MPT incorrectly models an asset's return as a normally distributed random variable and incorrectly assumes that markets are efficient, it inherently dismisses the existence of trend information, and follows by applying a suite of mathematical analysis tools that destroys the time domain information and thus can't possibly answer the question, "Which funds would be best to own next month?"

As an analogy, consider an Iowa farmer wanting to know if now is the time to plant his corn. He contacts the Modern Portfolio Farm Agent and is told (a) the average world temperature today was 62°F, (b) the average temperature in his town for the last decade was 58°F, (c) the temperature in his town is most well correlated with that of Hamburg, Germany, and  most uncorrelated with that of Sydney, Australia and La Paz, Bolivia, and (d) the standard deviation of temperature from average is 3.5°F within his state. After pondering all of this great information, the farmer still has no idea whether to plant corn or wait another week. There is no temperature trend information whatsoever from which the farmer might be able to improve his chance of having a great crop this season.

What should a farmer do with the Modern Portfolio Farm Agent's advice? It's obvious — run out and buy a few other farms scattered around the world to abate the risk of any one of them doing poorly — and certainly not waste time trying to improve results by observing trends in the weather, pests, or environmental regulation.  Hmmm...

•  By discarding time domain information MPT is inherently unable to suggest what to buy or sell next month.
•  MPT may be ideal for "buy and hold" investors, but "buy and sell" decisions require time domain data analysis. 

What Really Is Risk?

The definition of risk depends on whom you ask. The financial industry's MPT definition is "Risk is the unexpected variability of returns measured as the coefficient of variation, which is calculated as the standard deviation divided by its mean return." Stated simply, risk is the deviation from average performance.

The chart to the right shows the year-over-year percentage returns of S&P 500 market index over a 20-year period from 1990 to 2010. For example, you can see that during the years forming the dot com bubble, the average market return was 20% to 30%, and, during the 2008 global financial meltdown the average return dipped to about -40% per year.

Under MPT, risk is measured as the deviation from the long term average return — shown by the black line. To better illustrate risk, small deviations are plotted in green, moderate deviations are plotted in amber, and large deviations are plotted in red. You might note the upper areas in red and ask, aren't higher than average returns supposed be a good thing?  Why would higher than average returns be considered risky? That's a good question! This is a problematic consequence of choosing the standard deviation as a measure of risk. Punishing all deviation from average, including positive deviation, inherently drives investment results to achieve exactly, precisely, and only average performance. Average may feel great if you are otherwise hopelessly floundering, but its not what's expected from a proficient practitioner.

The dictionary, on the other hand, says: "Risk is the probability of portfolio value loss due to market factors." That's pretty simple. Risk is the probability of losing money. When we're making big money we feel euphoric confidence, but when we're losing big money we feel scared senseless. While there may be disappointment in earning less than average in a particular year, people don't worry much until there is actual persistent loss.

We believe there are two kinds of investment risk:
  • Journey Risk
  • Destination Risk

Journey Risk is the probability of losing money in the market on your way to retirement. Basically, it's the same as the dictionary definition. AlphaDroid's measure of risk is the probability of loss of real money over a one year period. This is a measure that matters to real people (as opposed to academic modelers), and thus is a measure that correctly drives investment decisions to reduce risk without punishing returns. A detailed description of how it is calculated can be found in the About AlphaDroid Charts portion of the User Guide page.  

Destination Risk is the probability that at age 65 your retirement savings are insufficient. This is about the really big picture of your life, not what happened last month or last year.  While we all like to imagine retirement in a nice house with plenty of spending cash, failing to achieve sufficient long-term returns creates big risk for retirement plans. They might be CANCELED and replaced with a new reality leaving you with two choices (1) you could either live in a small shack with only beans to eat, or (2) skip retirement altogether and work until you drop! While hopefully an exaggeration, the point is that good returns are required to reduce retirement risk. MPT focuses only on relatively shorter term investment risk and doesn't consider the longer term retirement risk problem at all — which may result in winning the battle but losing the war. AlphaDroid addresses this risk by providing the industry's most comprehensive retirement calculator (if you don't have an account, log in as user=demo, password=demo) that allows you to plan your retirement with all of your assets and test different investment styles to help ensure that your rendezvous with retirement takes place as planned.
 

How to Minimize Risk:  Two Schools

The MPT school says that diversification abates risk, therefore own a little bit of everything so that if any one of the investments goes sour its losses will be mitigated by the performance of the other investments. This fits quite well with the old adage, "Don't put all of your eggs in one basket." 

The AlphaDroid school says that avoiding losers altogether reduces risk without punishing returns. Therefore, monitor the trends of each candidate fund and sell the poorly trending ones in favor of owning only the nicely trending ones. This fits better with Mark Twain's suggestion, which here is more completely quoted from his 1894 Pudd'nhead Wilson novel: Behold, the fool saith, "Put not all thine eggs in the one basket" - which is but a manner of saying, "Scatter your money and your attention"; but the wise man saith, "Put all your eggs in the one basket and - WATCH THAT BASKET." Note that there is an important distinction between having one basket forever (buy and hold) versus having one basket at a time (AlphaDroid and serial monogamy).

To help resolve whether MPT or AlphaDroid better understands and addresses risk, a mathematical model of market data processed by both MPT and AlphaDroid has been constructed so that the properties of each can be tested and compared. The interesting charts below were produced from the model. The underlying spreadsheet model may be downloaded by clicking anywhere on the charts. You may freely examine the methods employed and manipulate control parameters to your heart's content. Should you have any questions or comments, please send them to us via the Contact Us page.  If you are able to further improve or extend this model in a meaningful way, we would be glad to post your results, a spreadsheet hyperlink, and provide you due credit for your improvement of the model. 

Both of the charts to the right were generated from the same 10 sets of simulated monthly market data with both statistical and trend properties similar to that of the S&P 500. These properties include:

  • Data points per set: 1,000
  • Average Return: 0.8% per month
  • Standard Deviation: 2.5% of nominal value per month
  • Hurst Exponent: 0.75

In the first chart, entitled "MPT: Averaging Simulated Data," the standard deviation decreases by the square root of the number of data sets as expected for uncorrelated data sets. At 9 data sets, the value is about 0.8 which is about 1/3 of the value for a single data set. The average return also behaves as expected — staying constant at 0.8% independent of the number of data sets averaged. The probability of loss charted is scaled as the probability that the portfolio will loose 2.5% (the standard deviation of a single data set) during any month. As the standard deviation (in red) decreases toward the average return (in green), the probability of loss then approaches zero as expected (because at this point, the variation in return is seldom larger than the average return).

In the second chart, entitled "AlphaDroid: True Sector Rotation," a very different set of characteristics is observed. First, it is noted that the standard deviation does not decrease nearly as much as for MPT averaging. Since AlphaDroid holds only a single data set, it would be expected that its standard deviation should be fairly similar to that of a single data set, but slightly better if indeed some of the negative extremes were avoided by avoiding them in favor of better performance.

While the standard deviation is interesting, recall from the prior section that this measure of risk erroneously includes positive deviations in its measure. Up spikes are a good thing, not a bad thing. So, looking then to the probability of loss curve, it is clear that AlphaDroid reduces the probability of loss much more quickly than does MPT. This is a characteristic one would expect if funds with performance potholes were being avoided rather than being averaged in with strong performing funds.

Finally, the most notable difference in the two charts is how AlphaDroid's average return improves by adding additional uncorrelated data sets. While MPT averaging dooms the return to exactly the .8%/mo. average of the data sets, AlphaDroid utilizes temporal differences in the data sets to direct the investment to only the data set with the best trend.

To simultaneously reduce risk and improve returns is generally considered impossible according to the tenets of MPT. Arguably this is certainly true within the constraints of the analysis tools it embraces. However, when considering that MPT entirely dismisses and discards temporal data (the important trend data evidenced by the Hurst exponent), it is not surprising that AlphaDroid's performance comes entirely from embracing this data to which MPT is blind.