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 buyandhold 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 buyandhold diversifyandrebalance 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 riskfree
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 buyandhold
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 buyandhold investments that are tanking solely for
appeasing the MPT diversification gods.
It is actually the
opposite of buyandhold 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 endtoend 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
doublespeak
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 EfficientMarket 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
selffulfilling 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
loglog 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 loglog 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 38year period is plotted
in blue in the figure
aboveright. 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 shortterm 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 23year 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 23year 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 DJ30
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 monthend versus only midmonth 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 monthend
bump in the Hurst exponent is quite notable and profound.
While there are no definitive studies showing the true cause of the
monthend 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 monthend 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 monthend 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 yearoveryear percentage returns
of S&P 500 market index over a 20year 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 longterm 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.
