Performance

The basic heuristics and algorithms I envisioned a year and a half ago have stood up well to testing, both internal testing and using external beta tester and client data.  Lessons learned have largely been associated with learning what is important to institutional investors.  Some of those lessons:

  1. To date, every client has avoided long-short portfolios.  All of my initial clients have asked for strictly long-only portfolio optimization. Based on their directions, I have temporarily incorporated a “zero-floor” for all securities, which modestly speeds up the optimization process.  (Note: this constraint can easily be reversed.)
  2. The initial portfolio-optimization code ran open-loop; that is to say that any asset could be assigned a weighting between 0 and 100%.  Generally, extreme asset-weightings were mathematically avoided for the majority of the “optimization surface.”   However, all Sigma1 clients have requested individual asset minimum and maximum asset-weighting constraints.  While these constraints somewhat reduce the enormous search space, in practice, they tend to slow down the heuristic algorithms.  Much of my optimization effort has been focused on efficiently enabling individual asset range constraints.
  3. The third major lesson was that some clients want layered asset-class constraints.  This capability has been incorporated into the base code.

The primary thesis behind HALO Portfolio Optimization is that compute technology and algorithms have sufficiently progressed to optimize portfolios beyond simple mean-variance optimization (MVO).  Moreover, creating a set of three(an efficient surface) of portfolios optimized for multiple objectives (three: risk1, risk2, and expected return) is performed, rather than a simpler 2-D optimization.

Much more run-time optimization is on the Sigma1 road map.  The primary speed up is via conversion of increasing conversion of key parts of the HALO Ruby code to C/C++.  In the meantime, upgrading to arguably the fastest processor on the planet, the Intel i7-4700K, has shown a 2.95X speed up over benchmarks running the i5-2647M CPU running Ruby code that is currently the HALO Portfolio Optimization run-time bottleneck.  The primary operations are (billions of) double-precision floating-point arithmetic computations.

The HALO portfolio-optimization algorithms/heuristics have already “fast enough” for every single institutional investor we have worked with to date.  That does not measurably dampen my personal desire to push optimization speed to its limit.  I intend to crush previous performance benchmarks, again and again.

Does a hard-working professional investment advisory team need optimization to faster than 30 minutes?  I’d argue “No.”  But do they want faster, of course “Yes!”  If the crunch time is reduced to 5 minutes — the same logic applies — they want faster.  I understand.

It could easily be argued that it would be better to apply my efforts to developing the web UI.  I am, in parallel, at my own pace.  Currently, however, my passion is speed.  Having achieved some speed, I crave more.  When I follow my passion, my productivity is dramatically improved.  Moreover, the skill set I am trying to master has intrinsic value beyond the field of portfolio optimization.  Fun and profit, in a start-up, is often more important than maximum profit (or maximum revenue).

The HAL0 algorithms and heuristics are intrinsically fast and scalable.  Since I am not planning on sharing their inner architecture (except for millions of dollars), the proof of their power is measured in raw performance.  If that effort results in temporary loss of revenue for enhanced future revenue, then so be it.

 

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Using HALO Portfolio Optimization Software

Setting up a basic HALO optimization requires a list of asset tickers, their min and max constraints, and expected returns.  Also at least one user specified category designation is required. Below is a short example:

SPY 7% 40% 9.11% Equities
PBP 0% 15% 8.53% Equities
USMV 5% 15% 9.05% Equities
VTI 5% 25% 9.35% Equities
IJH 5% 20% 9.55% Equities
VB 3% 15% 9.81% Equities
VEA 5% 12% 8.69% International
VEU 5% 20% 9.21% International
EEM 1% 11% 10.07% International
JNK 3% 15% 6.03% Bonds
BKLN 0% 8% 3.61% Bonds
AGG 1% 9% 2.32% Bonds

Generally, it is advisable to keep the sum of the individual asset minimums below 50%, and the sum of maximums above 200%. This provides the HALO optimizer the freedom to create a wide range of optimized portfolios with different risk/reward trade offs.

The above example is a very basic configuration. In order for asset managers to specify asset-class constraints, it is necessary to tell the optimizer that the “string” is a user-defined category.  Currently this is done with a leading gastritis (*):

*Equities       25% 85%
*International  10% 30%
*Bonds          15% 45%

The above config specifies that Equities must comprise a minimum of 25% of the investment portfolio and a maximum of 85%.  As with the individual asset constraints, it is advised to provide reasonably wide latitude to the optimization algorithms to produce a diverse set of optimized portfolios.

By default, the HALO Optimizer will produce a set of portfolios optimized to:

1) minimize:
a) semi-variance, σd (the default)
b) –OR– annualized standard deviation of total return, σ

2) maximize expected return, E(R)

The default time series used for computing σ and σis end-of-month total-return deltas for the previous 36 months.  (This requires 37 months of total-return data for each security.)  The time period can be customized to use, say 60 months worth of data in the analysis.  HALO also supports using weekly closing data or even daily closing data — however I generally recommend using monthly data for a variety of reasons.  First, it speeds the computation.  Second, monthly data captures multi-day and multi-week trends, correlations, and specifically low-correlation asset optimization.  Third, monthly data is closer to the sampling period of a “typical” high-net-worth retail investor.  [That said, a case could be made for using quarterly data — which is also supported.]

Frequently HALO clients want to model newer securities that do not have 37 months of historical data.  For example, min-volatility ETFs such as SPLV, USMV, and EEMV are popular ETFs that are less than 3 years old. The HALO software suite has utilities that can statistically back fill the missing data.  The configuration of the statistical back-fill process is beyond the scope of this blog post, however it is an important and popular HALO Optimization Suite capability that so far has been used by all of Sigma1’s clients and beta testers.

Occasionally, Sigma1 clients and beta testers have had in-house funds that do not externally report their price or total return data.  For in-house funds, HALO can read client-supplied total-return data.  Naturally, HALO can include stocks, bonds, commodities, futures, and other assets with historical data into the portfolio optimization mix.

 

 

Our Business: Portfolio Risk Mitigation

I bumped into a friend tonight at dinner, who introduced me to one of his friends who also happens to be a very successful software entrepreneur.  Naturally, I mentioned that I, too am an entrepreneur with a financial software product for portfolio optimization.

We spoke about the technical side of the HAL0 software and he provided me with some fresh perspectives about the technical side of my build-out plan.  Then the conversation transitioned over to the business side.  He challenged me to explain the value proposition of my product without using technical language.  I started with “software to build better portfolios.”  OK, better how?  “Optimized for lower risk, and higher return.”  And?  “Supporting risk models beyond standard deviation.”  Nope — too technical.

I appreciated the grilling.  I kept saying “Thank you, bring it on,” and “yes, that criticism stung a bit, but this is useful.”

Trying to pin down the essence of the business, I found myself oscillating back and forth from “too general” to “too technical.”  Finally we pieced together a tagline:  Portfolio Risk Mitigation.  It is succinct and non-technical.  It seems likely that these three words capture the essence of the company and its flagship product.

Now for the business plan.

The Market

As of 2010, there were $17.5 trillion dollars in retirement investments, including $4.7 trillion in IRAs, and just over $3 trillion in 401(K)s according to Investment Company Institute. Annual advice fees on these assets typically range from 0.4% to 0.75% according to this Multnomah Group White Paper. And according to Zero Hedge, total US household financial assets totaled $51.9 trillion in Q2 2012.  Applying a very conservative 0.4% value for advice fees on these assets, this translates to over $207 billion in annual revenue for investment portfolio advice.  This is the primary market Sigma1 Financial seeks to tap into.

The Market Segment

I believe the best way to gain a share of the $200+ billion financial and portfolio advice market is by providing best-in-class portfolio-optimization software to companies that provide wealth management and investment advice.  These companies pay in-house analysts to find financial assets with superior returns.  They also pay portfolio managers (AKA wealth managers) to transform their proprietary research into investment portfolios tailored to the needs of their individual investors.  Sigma1 Financial software provides powerful portfolio optimization and analytics that helps portfolio managers mitigate risk, while maintaining or even boosting investment returns for their clients.

We are presently working will select beta partners in this market segment to learn about their specific wants, needs, and requirements. Our goal is to continuously adapt and improve our products within this market segment. We have the core technology; our current challenge is presenting it in a way that easily integrates with the business practices of our beta partners.

The Competition

The number one competing product in the field is MCSI’s Barra Optimizer.  To the best of my knowledge MSCI does not publish pricing information for this product.  I have heard, however, that large users of the software pay through the nose — aka millions of dollars per year.

There is overlap between the HAL0 portfolio-optimizer and the Barra Optimizer.  There are also unique attributes that distinguish each software product.  I will concede, that Barra currently offers better integration with a suite of financial products.  Conversely, HAL0 offers unique three-objective optimization and an optimization engine tuned for PMPT optimization.  Futher, it is my plan to initially position HAL0 pricing models as extremely competitive compared to Barra pricing.  Further, the first one or two major HAL0 customers will be in an unique position of being able to request and receive solutions to their specific requirements.

The Value Proposition

To beta partners (and soon, paying clients) the proposition is simple and compelling.  Provide Sigma1 with a set of assets and, optionally any or all of : min allocations, max allocations, expected return, and a sample portfolio.  If a sample portfolio is provided, I seek to provide three alternative portfolios that 1) provide superior expected return for the same risk, 2) provide lower risk at the same return, 3) provide both higher return and lower risk than the sample portfolio.

For beta partners (or potential clients), I seek to provide a model that is low-effort on their part.  For no cost,    Sigma1 provides (to select organizations) a range of optimized portfolio options.  These potential clients can then choose how to proceed from there.  Naturally, Sigma1’s goal is to impress the potential clients/partners with portfolio solutions that offer superior risk/reward characteristics.

The Bottom Line

Sigma1 offers a world-class product with low sunk costs.  This enables Sigma1 to offer an extremely competitive offering while maintaining high profit margins.  Both the client and Sigma1 stand to benefit.

Show Me 3D

I was having a dinner conversation and showing some Sigma1 Financial images from this site on an Android phone to a UI developer.  I kept looking for a 3-D perspective plot, and soon realized that I hadn’t posted one yet!  How easily remedied:

 

This plot shows the objective space and the trade offs between return, variance, and semivariance. It contains the same information present in other example plots, but presented from a different perspective.

3-D Frontier of Optimizated Investment Portfolios
3-D Frontier of Optimized Investment Portfolios

Variance, Semivariance Convergence

In running various assets through portfolio-optimization software, I noticed that for an undiversified set of assets there can be wide differences between portfolios with the highest Sharpe ratios versus portfolios with the Sortino ratios.  Further, if the efficient frontier of ten portfolios is constructed (based on mean-variance optimization) and sorted according to both Sharpe and Sortino ratios the ordering is very different.

If, however, the same analysis is performed on a globally-diversified set of assets the portfolios tend to converge.  The broad ribbon of of the 3-D efficient surface seen with undiversfied assets narrows until it begins to resemble a string arching smoothly through space.  The Sharpe/Sortino ordering becomes very similar with ranks seldom differing by more than 1 or 2 positions.  Portfolios E and F may rank 2 and 3 in the Sharpe ranking but rank      2 and 1 in the Sortino ranking, for example.

Variance/Semivariance divergence is wider for optimized portfolios of individual stocks.  When sector-based stock ETFs are used instead of individual stocks, the divergence narrows.  When bond- and broad-based index ETFs are optimized, the divergence narrows to the point that it could be considered by many to be insignificant.

This simple convergence observation has interesting ramifications.  First, a first-pass of faster variance optimization can be applied, followed by a slower semivariance-based refinement to more efficiently achieve a semivariance-optimized portfolio.  Second, semivariance distinctions can be very significant for non-ETF (stock-picking) and less-diversified portfolios.  Third, for globally-diversified, stock/bond, index-EFT-based portfolios, the differences between variance-optimized and semivariance-optimized portfolios are extremely subtle and minute.

 

 

Engineering Profit versus Theoretical Profit

Either there is a veil of silence covering the world of finance, or the obvious parallels between electrical engineering (EE) have been overlooked.   I suspect the former.

Almost every EE worth their salt has been exposed to the concepts of signals and signal processing in undergrad.  From signal-to-noise ratios (SNR) to filters (dB/decade) to digital signal processors (DSPs), EE’s are trained to be experts at receiving the signal in spite of the noise.  More technobabble (but its not!) are the Fourier and Laplace transforms we routinely use to analyze the propagation of signals through circuits.  Not to mention wave-guides, complex-conjugate reflections, amplitude- and frequency- modulation, etc.   Then there are the concepts of signal error detection, error correction, and information content.

My point is that financial firms made a mistake in hiring more physicists than electrical engineers.  At the end of the day (or the project) the work of the EE has to stand up to more than just academic scrutiny; it has to stand up to the real world — real products, real testing, real use.

EE’s with years of experience have been there and done that.  Mind you, most are not interested in finance.  However, a handful of us are deeply interested in finance and investing.

These thoughts occurred to me as I was listening to speakers I built 15 years ago.  They still sound spectacular (unglaublich gut, for you Germans).  They are now my second-tier speakers relegated to computer audio.  Naturally, I have an amp fed by Toslink 48K/s 20-bit per channel audio data. My point is that these speakers have audio imaging that is achieved by a smooth first-order crossover with tweaters/speakers chosen to support phase-accurate performance over a the frequencies that the human ear can best make use of audio imaging.

My second point is that a lot of engineering went into these speakers.   This engineering goes beyond electrical.   Speakers are fundamentally in the grey region between mechanical and electrical engineering.  However the mechanical parameters can be “mapped” into the “domain” of electrical engineering concepts.  This positions EEs to pick the best designs and combine them in most advantageous designs  on a maximum value- per-dollar basis.

This post is targeting a different audience than most.  Apologies.  An EE with a CS (computer science) background is an even better choice..

The analysis of financial data as concurrent, superimposed discrete waveforms is natural to EEs as air is to mammals and water is is to fish.  Audio is, perhaps, the simplest application.   Just Google “Nyquist-Shannon” if you want to know of which I speak.

I’m not for hire — I only do contract work.  I’m just telling hiring managers to both broaden and restrict their search criteria.  A well-qualified EE with financial expertise and a passion for finance is likely to be a a better candidate than a Ph.D. in Physics.  Don’t hire Sheldon Cooper until you evaluate Howard Wolowitz (not an EE, but you get my point, I hope).

Optimizing Capital Gains and Losses

Wish #1: End the Long/Short-Term Gain Distinction

Ideally there would be no differentiation between short-term and long-term gains. Whether an asset is held for a microsecond or decade, the gain or loss should receive the same tax treatment.   A gain is a gain, a loss is a loss.  But as long as the tax code retains the current short-term/long-term bifurcation, it is important to account for the impact of short and long term gains.

Wish #2: Account for Inflation on Capital Gains

If you realize a capital gain of 10%, but inflation during that time is also 10% have you really earned anything?  According the the current tax code: Yes.  In real terms: No.  In fact, after taxes, you have lost real purchasing power.

I propose that the tax code be changed such that investors can optionally use the GDP deflator to adjust their cost basis when investments are sold.   The IRS could publish official monthly GDP deflator (inflation) data going back 1914.   Investors would have the option (on a sale-by-sale basis) of adjusting their cost basis upward by the ratio of the sale-month deflator to the purchase-month deflator.

In the 10% example, if you bought 100 shares of XYZ corp 4 years ago at $80 and sold those shares at $88 your traditional cost basis would be $8000 and your sales process would be $8800, resulting in a taxable $800 gain.  In my system your basis would be adjusted for inflation, making it $8800 — resulting in $0 of gain, and $0 of tax.   You wouldn’t pay for simply keeping up with inflation.

If, during the same time period you bought 100 shares of ACME corp at $100 each and sold them for $100 you would experience a long-term capital loss, because you lost real purchasing power.  Your revised basis would be $11,000 and proceeds $10,000 — resulting in a $1000 capital loss.

A Role for Optimization — Economic Reasoning and Tax Policy Seldom Coincide

The above wishes are likely to remain unrealized for years or decades to come.  Until then, it is important to factor in the implications of short-term, long-term, and unrealized gains and losses. This complexity can be more easily handled with a multi-objective optimization algorithm.

Exploring Risk Models

As I continue to explore patterns in beta-client data, I clearly see one common difference.  For globally-diversified, and asset-diversified ETF- and mutual-fund-based portfolios 36-month, monthly modified-semivariance and variance based portfolios tend to converge to produce similar results.   This is in sharp contrast to stock-based portfolios, where variance (MVO) and semivariance (PMPT) portfolios display a significant trade-off between Sharpe and Sortino ratios.

My preliminary conclusion, based on poring through individual optimized-portfolios, is that variance and semivariance are closely correlated for portfolios based on sufficiently-diversified ETFs.  On the other hand, the difference between variance-optimized, semivariance-optimized, and hybrid (blend of variance- and covariance-optimized) portfolio is significantly different if individual stocks and bonds are analyzed.  [Sufficiently-diversified in this context does not mean diversified per se.  It only means relative diversification within a given ETF or set or ETFs/ETNs/Mutual Funds.)

These preliminary findings suggest that semivariance and variance based optimizations are highly correlated for certain asset classes (and expected returns) while differing for other asset classes (and expected returns).  Stock-pickers are more likely to see benefits from semivariance-based optimization than are those who select from relatively-diverse ETFs.

These preliminary findings are causing a shift in the approach taken by Sigma1.  Since, so far, Sigma1 beta partners are primarily interested in constructing portfolios based primarily or exclusively around ETFs, ETNs, and mutual funds, our company is focusing more on Sharpe ratios (because they are quicker to optimize for than Sortino ratios).

Because Sigma1 HAL0 portfolio-optimization is tuned to optimize for 3 objectives this presents an interesting question:  “Your investment company wishes to optimize portfolios based on 1) expected return, 2) minimal variance, and 3)  <RISK MEASURE 3>?”

Sigma1 is posing questions:  What is your third criterion?  What is your other risk measure?   Answer these questions, and Sigma1 HAL0 software will optimize your portfolio accordingly; showing the trade-offs between Sharpe ratios and your other chosen risk metric.

Sigma1’s 3-objective-optimization is causing a few financial-industry players to ask the question of established optimization engines, “Can you do that?”  Sigma1 Software can.  Can your current portfolio-optimization software do the same?
 

Not your typical portfolio-optimization post

I am presently in Placencia Belize.  I love to learn about how the economy and culture of a country and how  regions within a country contribute to its place in the world.

My high-school education in history went deeper than most.  I studied AP history and my score exempted me from university history requirements.  The approach to history was, in part, a story of wars, victories, and defeats.  Differentials in leadership, technology, and manpower were used to explain, ex post, how wars were won and lost.

I  have learned that these are only part of the story.  The parallel, kindred theme is economic.  Superior economies provide great advantage.  This advantage is reflected in both income and the interest rate paid on bonds.  If a side loses the confidence of the bond market, the outcome of the conflict becomes largely predetermined.

I have a working theory about how people and governments respond to events.  At the core  of my working theory is positive feedback.  Despite the name “positive” feedback is not necessarily positive in the emotional sense.  “Positive” feedback simply means self-reinforcing.  Virtuous cycles and vicious cycles are both examples of self-reinforcing positive feedback.

Strangely, mindset is crucial.  There are two mindsets that favor positive outcomes: 1) economic self-confidence, 2)  patient self-development and willingness to defer economic self-gratification (spending).  The United States seems to be losing both of these factors.  The key word is “self”, as in individual.

US growth, anemic  as it is, is based largely on government leverage.  As long as this leverage can be financed at historically-low rates, this largely superficial growth can occur… until real, organic growth resumes, or the debt bubble bursts or begins deflating (signaled by erosion of the value of the USD).

Simply put, I have become bearish on the USD and am looking for safer harbors for my “non-risk” capital.  Alternatives include CAD, AUD, and NOK (kr) government bonds.  TIPs provide a degree of protection, if you believe CPI-U stats accurately reflect US inflation.  CASH in USD is suspect.

Back to Belize.  Belizean currency is pegged to the USD on 2:1 basis.  Belize’s unemployment rate is approximately 14.4%, and the trend is upward.  With the shear beauty and wonder of the country, reasonable English-proficiency, and a tiny 360,000 population, tourism should translate more effectively to income/capita, GDP/capita, and overall economic growth.

I am studying dissonant economic stagnation first hand.  Beauty surrounded by poverty.  Economic stagnation.  Hope concentrated outward on government, on divine intervention, on anything but self.

I study with objectivity laced with sadness.   These people could be much more, but they will likely not be any time soon.

This is a lesson for the US.  The US government’s fiscal situation is unsustainable.  The general outlook is looking outward for hope rather than inward (to oneself) for strength and betterment.   Until this attitude changes I see anemic US growth as the future.  This is likely to manifest in US inflation and USD devaluation.  Federal Reserve policy seems to concur.

My macro outlook can be reflected in the numbers I put into expected-return data for global market ETFs.  Sigma1 HAL0 software uses these projections and variance and semivariance optimization (or other metrics)  to help me revise my personal portfolio.

Feel free to disagree with my outlook.  Sigma1 HAL0 optimization will incorporate your projections, and build an optimized portfolio based upon them.  HAL0  portfolio optimization is algorithmic and objective.  Individual security expected-returns are typically based on user inputs.  HAL0 software optimizes within the provided framework.  User predictions matter, as does human discretion in using the HAL0 results.

Because my projections for expected-return may vary widely from yours, your company’s, and your analysts, the resulting portfolios will vary widely.

The bottom line is that Sigma1 portfolio-optimization software uses your hard-won security analysis and projections to build an accordingly-optimized investment portfolio. If you believe in your analysis, so will Sigma1.  Keep that in mind.  Your analysis matters.

 

Sharpe Ratio, Explained in Plain English

Sharpe Ratios Made Easy

In today’s near-zero interest rate economy, the reward versus risk of an investment portfolio can be measured using the Sharpe ratio.  Like a batting average, higher numbers are better, and 0.400 is very good.

If portfolio Z has a forward-looking Sharpe ratio of 0.400, and an expected return of 8%, there is a 68% chance its 1-year return will be between -12% and +28%.

The math is surprisingly easy.  Because the Sharpe ratio is a return/risk ratio it can be transformed into a risk/return ratio by finding its inverse (using the “1/x” button on a calculator).  The inverse of 0.400 is 2.5.  The return is 8%, so the “risk” is 2.5 times 8% which is 20%.

For the Sharpe ratio, the downside risk and the upside “risk” are the same.  So the downside is 8% -20%, or -12%.   The upside risk is 8%+20%, or 28%.  Easy!

Sharpe Ratios and Risk (more detail)

Where did the “68% chance” come from?  The answer is a bit more complicated, but still fairly easy to understand.

It comes from the 3-sigma1 rule of statistics.  The range of -12% to +28% comes from 1 standard deviations of the mean (or plus or minus one sigma).  The 3-sigma rule also says that 95% of outcomes will fall within two standard deviations.  Double the deviation means  two times the upside and downside risk, so the 95% confidence range becomes -32% to 48%.  Finally the 3-sigma rule means triple the upside and downside risk, meaning outcomes from -52% to +68% will occur 99.7 percent of the time.

Almost every investor will be be pleased with a positive sigma event, where the return is above 8%.   For example a +1 sigma (+1σ) occurrence has a +28% return — quite nice.

A downside event is potentially quite troublesome.  Even a -1σ event means a 12% loss.  A -2σ is a much worse 32% loss.

Ex Ante and Ex Post Sharpe Ratios

Forward-looking (ex ante) Sharpe ratios are predictions “prior to the event(s)”.  They are always positive, because no rational investor would invest in a negative expected return.  The assumptions baked into an ex ante Sharpe ratio predictions are 1) expected standard deviation of total return, σ,  2) expected future return.

Backward-looking, or after the fact, (ex post) Sharpe ratios can be negative or positive.  In fact, assuming “normal distributions of return”, there is a reasonable (but less than 50%) chance of a negative ex post Sharpe ratio.

Sigma1 HAL0 software optimizes for Sharpe ratios by optimizing for return and standard deviation.  It also optimizes for semivariance.  More “plain English” on that advantage later.