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.

 

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Capital Allocation

Let’s start with the idea that CAPM (Capital Asset Pricing Model) is incomplete.   Let me prove it in a  few sentences.  Everyone knows that, for investors, “risk-free” rates are always less than borrowing (margin) rates.  Thus the concept of CAL (the capital asset line) is incomplete.  If I had a sketch-pad I’d supply a drawing showing that there are really three parts of the “CAL” curve…

1. The traditional CAL that extends from Rf to the tangent intercept with the efficient-frontier curve.
2. CAC (capital-asset curve)
3. CAML (capital-asset margin line, pronounced “camel”)

Why?  Because the CAML has it’s own tangent point based on the borrower’s marginal rate.  Because the efficient frontier is monotonically-increasing the CAL and CAML points will be separated by a section of the EF curve I call the CAC.

All of this is so obvious, it almost goes without saying.  It is strange, then, that I haven’t seen it pointed out in graduate finance textbooks, or online.  [If you know of a reference, please comment on this post!]  In reality, the CAL only works for an unleveraged portfolio.

CAPM is Incomplete; Warren Buffett Shows How

Higher risk, higher return, right?  Maybe not… at least on a risk-adjusted basis.  Empirical data suggests that high-beta stock and portfolios do not receive commensurate return.  Quite to the contrary, low-beta stocks and portfolios have received greater returns than CAPM predicts.   In other words, low-beta portfolios (value portfolios in many cases) have had higher historical alphas.  Add leverage, and folks like Warren Buffett have produced high long-term returns.

Black Swans and Grey Swans

On the fringe of modern-portfolio theory (MPT) and post-modern portfolio theory (PMPT), live black swans.   Black swans are essentially the most potent of unknown unknowns, also known as “fat tails”.

At the heart of PMPT is what I call “grey swans.”  This is also called “breakdown of covariance estimates” or, in some contexts, financial contagion.  Grey-swan events are much more common, and somewhat more predictable… That is if one is NOT fixated on variance.

Variance is close, semivariance is closer.  I put forth the idea that PMPT overstates its own potential.  Black swans exists, are underestimated, and essentially impossible to predict.  “Grey swans” are, however, within the realm of PMPT.   They can be measured in retrospect and anticipated in part.

Assets are Incorrectly Priced

CAPM showed a better way to price assets and allocate capital.  The principles of semivariance, commingled with CAPM form a better model for asset valuation.  Simply replacing variance with semivariance changes fifty years of stagnant theory.

Mean-return variance is positively correlated with semivariance (mean semi-variance of asset return), but the correlation is far less than 1.   Further, mean variance is most correlated when it matters most; when asset prices drop.  The primary function of diversification and of hedging is to efficiently reduce variance.  Investors and pragmatists note that this principle matters more when assets crash together — when declines are correlated.

The first step in breaking this mold of contagion is examining what matter more: semivariance.   Simply put, investors care much less about compressed upward variance than they do about compressed downward variance.   They care more about semivariance.  And, eventually, they vote with their remaining assets.

A factor in retaining and growing an AUM base is content clients.  The old rules say that the correct answer the a key Wall Street interview question is win big or lose all (of the client’s money).  The new rules say that clients demand a value-add from their adviser/broker/hybrid.  This value add can be supplied, in part, via using the best parts of PMPT.  Namely semivariance.

That is the the end result of the of the success of semivariance.  The invisible hand of Sigma1, and other forward-looking investment companies, is to guide investors to invest money in the way that best meets their needs.  The eventual result is more efficient allocation of capital.  In the beginning these investors win.  In the end, both investors and the economy wins.  This win/win situation is the end goal of Sigma1.

 

 

Benchmarking Financial Algorithms

In my last post I showed that there are far more that a googol permutations of portfolio of 100 assets with (positive, non-zero) weights in increments of 10 basis points, or 0.1%.    That number can be expressed as C(999,99), or C(999,900) or 999!/(99!*900!), or ~6.385*10¹³⁸.  Out of sheer audacity, I will call this number Balhiser’s first constant (K_β1).  [Wouldn’t it be ironic and embarrassing if my math was incorrect?]

In the spirit of Alan Turing’s 100th birthday today and David Hilbert’s 23 unsolved problems of 1900, I propose the creation of an initial set of financial problems to rate the general effectiveness of various portfolio-optimization algorithms.  These problems would be of a similar form:  each having a search space of K_β1. There would be 23 initial problems P₁…P₂₃.  Each would have a series of 37 monthly absolute returns.  Each security will have an expected annualized 3-year return (some based on the historic 37-month returns, others independent).  The challenge for any algorithm A to score the best average score on these problems.

I propose the following scoring measures:  1) S”(A) (S double prime) which simply computes the least average semi-variance portfolio independent of expected return.  2) S'(A) which computes the best average semi-variance and expected return efficient frontier versus a baseline frontier.  3) S(A) which computes the best average semi-variance, variance, and expected return efficient frontier surface versus a baseline surface.  Any algorithm would be disqualified if any single test took longer than 10 minutes.  Similarly any algorithm would be disqualified if it failed to produce a “sufficient solution density and breadth” for S’ and S” on any test.  Obviously, a standard benchmark computer would be required.  Any OS, supporting software, etc could be used for purposes of benchmarking.

The benchmark computer would likely be a well-equipped multi-core system such as a 32 GB Intel  i7-3770 system.  There could be separate benchmarks for parallel computing, where the algorithm + hardware was tested as holistic system.

I propose these initial portfolio benchmarks for a variety of reasons.  1)  Similar standardized benchmarks have been very helpful in evaluating and improving algorithms in other fields such as electrical engineering.  2)  Providing a standard that helps separate statistically significant from anecdotal inference. 3)  Illustrate both the challenge and the opportunity for financial algorithms to solve important investing problems. 4)  Lowering barriers to entry for financial algorithm developers (and thus lowering the cost of high-quality algorithms to financial businesses).  5)  I believe HAL0 can provide superior results.

Seeking a Well-Matched Angel Investor (Part I)

Most of the reading I have done regarding angel investing suggests that finding the right “match” is a critical part of the process.  This process is not just about a business plan and a product, it is also about people and personalities.

Let me attempt to give some insight into my entrepreneurial personality.  I have been working (and continue to work) in a corporate environment for 15 years. Over that time I have received a lot of feedback.  Two common themes emerge from that feedback.  1)  I tend to be a bit too “technical”.  2)  I tend to invest more effort on work that I like.

Long Story about my Tech Career

Since I work in the tech industry, being too technical at first didn’t sound like something I should work on.  I eventually came to understand that this wasn’t feedback from my peers, but from managers.   Tech moves so fast that many managers simply do not keep up with these changes except in the most superficial ways.  (Please note I say many, not most).  While being technical is my natural tendency, I have learned to adjust the technical content to suite the  composition of the meeting room.

The second theme has been a harder personal challenge.  Two general areas I love are technical challenges and collaboration.  I love when there is no “smartest person in the room” because everybody is the best at at least one thing, if not many.  When a team like that faces a new critical issue — never before seen — magic often occurs.  To me this is not work; it is much closer to play.

I have seen my industry, VLSI and microprocessor design, evolve and mature.  While everyone is still the “smartest person in the room”, the arrival of novel challenges is increasingly rare.   We are increasingly challenged to become masters of execution rather than masters of innovation.

Backing up a bit, when I started at Hewlett-Packard, straight out of college, I had the best job in the world, or darn near.  For 3-4 months I “drank from a fire hose” of knowledge from my mentor.  After just 6 months I was given what, even in retrospect, was tremendous responsibilities (and a nice raise).  I was put in charge of integrating “logic synthesis” software into the lab’s compute infrastructure.  When I started, about 10% of the lab’s silicon area was created via synthesis; when I left 8 years later about 90% of the lab’s silicon was created via logic synthesis.  I was part of that transformation, but I wasn’t the cause — logic synthesis was simply the next disruptive technology in the industry.

So why did change companies?  I was developing software to build advanced “ASICs”.  First the company moved ASIC manufacturing overseas, then increasingly ASIC hardware design.  The writing was on the wall… ASIC software development would eventually move.  So I made a very difficult choice and moved into microprocessor software development.  Looking back now, this was the likely the best career choice I have ever made.

Practically overnight I was again “drinking from a fire hose.”   Rather than working with software, my former teammates and I had built from scratch, I was knee-deep in poorly-commented code that been abandoned by all but one of the original developers.  In about 9 months my co-developer and I had transformed this code into something that resembled properly-architected software.

Again, I saw the winds of change transforming my career environment: this time, microprocessor design.  Software development was moving from locally-integrated hardware/software design labs to a centralized software-design organization.  Seeing this shift, I moved within the company, to microprocessor hardware design.  Three and a half years later I see the pros and cons of this choice.  The largest pro is having about 5 times more opportunities in the industry — both within the company, and without.  The largest con, for me, is dramatically less software development work.  Hardware design still requires some software work, perhaps, 20-25%.  Much of this software design, however, is very task-specific.  When the task is complete — perhaps after a week or a month — it is obsolete.

A Passion for Software and Finance

While I was working, I spent some time in grad school. I took all the EE classes that related to VLSI and microprocessor design. The most interesting class was an open-ended research project. The project I chose, while related directly to microprocessor design, had a 50/50 mix of software design and circuit/device-physics research. I took over the software design work, and my partner took on most of the other work. The resulting paper was shortened and revised (with the help of our professor and third grad student) and accepted for presentation at the 2005 Society of Industrial and Applied Mathematics (SIAM) Conference in Stockholm, Sweden.  Unfortunately, none of us where able to attend due to conflicting professional commitments.

Having exhausted all “interesting” EE/ECE courses, I started taking grad school courses in finance.  CSU did not yet have a full-fledged MSBA in Financial Risk Management program, but it did offer a Graduate Certificate in Finance, which I earned.  Some research papers of note include “Above Board Methods of Hedging Company Stock Option Grants” and “Building an ‘Optimal’ Bond Portfolio including TIPS.”

Software development has been an interest of mine since I took a LOGO summer class in 5th grade.  It has been a passion of mine since I taught myself “C” in high school.  During my undergrad in EE, I took enough CS electives to earn a Minor in Computer Science along with my BSEE.   Almost all of my elective CS courses centered around algorithms and AI.   Unlike EE, which at times I found very challenging, I found CS courses easy and fun.  That said, I earned straight A’s in college, grad and undergrad, with one exception: I got a B- in International Marketing.  Go figure.

My interest in finance started early as well.  I had a paper route at the age of 12, and a bank account.  I learned about compound interest and was hooked.  With help from my Dad, and still 12 years old, I soon had a money market account and long-maturity zero-coupon bond.  My full-fledged passion for finance developed when I was issued my first big grant of company stock options.  I realized I knew quite a bit about stocks, bonds, CD’s and money market funds, but I knew practically nothing about options.  Learning about options was the primary reason I started studying Finance in grad school.  I was, however, soon to learn about CAPM and MPT, and portfolio construction and optimization.  Since then, trying to build the “perfect” portfolio has been a lingering fascination.

Gradually, I began to see flaws in MPT and the efficient-markets hypothesis (EMH).  Flaws that Markowitz acknowledged from the beginning!  [Amazing what you can learn from going beyond textbooks, and back to original sources.]   I read in some depth about the rise and demise of Long-Term Capital Management.  I read about high-frequency trading methods and algorithms.  I looked into how options can be integrated into long-term portfolio-building strategies.  And finally, I started researching the ever-evolving field of Post-Modern Portfolio Theory (PMPT.)

When I finally realized how I could integrate my software development skills, my computer science (AI) background, my graduate EE/ECE work and my financial background into a revolutionary software product, I was thunderstruck. I can and did build the alpha version of this product, HAL0, and it works even better than I expected.  If I can turn this product into a robust business, I can work on what I like, even what I love.  And that passion will be a strength rather than a “flaw”.   Send me an angel!

 

Sigma1 Financial Software: Development Begins

I started Sigma1 with $35,000 in seed capital, a Linux workstation and a domain name I acquired in auction for $760.  The original plan was to create a revolutionary hedge fund with accredited investors as clients.  I started studying for the Series 65 exam and all went well until I started reading about securities laws and various legal case studies.  I gradually realized two things:

1. U.S. Securities Law is very restrictive, even for “lightly regulated” hedge funds
2. The legal start-up costs for a hedge fund were much higher than I anticipated

The first realization was the most devastating to my plans.  The innovative fee structure I wished to use was likely to face serious legal challenges to implement. Without a revolutionary fee structure, more favorable to clients, the Sigma1 Fund would be hard to differentiate from the hundreds of other funds already available.

The second objective of Sigma1 has been to develop proprietary financial software.  Until now the Sigma1 Proprietary Trading Fund has been constructed based on research, pencil-and-paper securities analysis and some rudimentary Excel simulations.  Some quantitative analysis has been applied, but without the mathematical rigor I prefer.   That is about to change.

I recently devised a way to apply techniques developed while studying Electrical Engineering and Finance in grad school.  In a nutshell, I will apply evolutionary algorithms to optimize portfolio construction.  The same fundamental techniques my electrical engineering colleagues and I used to explore and optimize around the random perturbations inherent in fabricated silicon circuits can be used to optimize portfolios by efficiently exploiting conventional (linear) and unconventional (non-linear) correlations between diverse assets.

I have sequestered myself in a beautiful, tranquil location while on a well-earned sabbatical from work.  While evolutionary algorithms will be a significant part of the software suite I will develop, I also intend to incorporate heuristics and machine-learning techniques as well.  Similarly I intend to use techniques from CAPM such as efficient-frontiers, but only as a first-order guide.  Many of the limitations of CAPM (and Fama-French enhancements thereof) consist on their intrinsic reliance on Gaussian or “normal-distribution” statistical models.  Such models do not properly model long-tail events, nor asymmetrical distributions, nor even log-normal distributions.  Classic CAPM models even struggle with geometric-mean of expected or passed returns and generally use arithmetic means to preserve the use of linear systems analysis.  Heuristic algorithms and other AI techniques need not use such assumptions as a mathematical crutch.   The software I intend to develop should be able to find near-optimal solutions to financial problems that classic statistical methods “solve” only by making grossly inaccurate assumptions about probability distributions.

My intention is to develop one or more software products for fund managers that will aid in portfolio analysis, construction and refinement.