The more we learned about the current crop of robo advisory firms, the more we realized we could do better. This brief blog post hits the high points of that thinking.

Not Just the Same Robo Advisory Technology

It appears that all major robo advisory companies use 50+ year-old MPT (modern portfolio theory). At Sigma1 we use so-called post-modern portfolio theory (PMPT) that is much more current. At the heart of PMPT is optimizing return versus semivariance. The details are not important to most people, but the takeaway is the PMPT, in theory, allows greater downside risk mitigation and does not penalize portfolios that have sharp upward jumps.

Robo advisors, we infer, must use some sort of Monte Carlo analysis to estimate “poor market condition” returns. We believe we have superior technology in this area too.

Finally, while most robo advisory firms offer tax loss harvesting, we believe we can 1) set up portfolios that do it better, 2) go beyond just tax loss harvesting to achieve greater portfolio tax efficiency.

Think Ahead About Your Role in a Robo Advisory World

Financial innovation is here and it is here to stay. Financial advisors, broker/dealers, hybrids, and even financial planners should be thinking about how to adapt to inevitable changes launched by disruptive investing technologies.

Robo Design — Chip designers have been using it for decades

I have an unique perspective on technological disruption. For over ten years, my job was to develop software to make microchip designers more productive. Another way of describing my work was to replace microchip design tasks done by humans with software. In essence, my job was to put some chip designers out of work. My role was called (digital circuit) design automation, or DA.

In reality my work and the work of software design automation engineers like myself resulted in making designers faster and more productive — able to develop larger chips with roughly the same number of design engineers.

Robo Advisors: Infancy now, but growing very fast!

“The robos are coming, the robos are coming!” It’s true. Data though the end of 2014 shows that robo advisors managed $19 billion in assets with a 65% growth rate in just eight short months. This is essentially triple-digit growth, annual doubling. $19 billion (likely $30 billion now), is just a drop in the bucket now… but with firms like Vanguard and Schwab already developing and rolling out robo advising option of their own these crazy growth rates are sustainable for a while.

With total US assets under management (AUM) exceeding $34 trillion, an estimated $30 billion for robo advisors represents less than 0.1% of managed assets. If, however, robo advisors grow double their managed assets annually for the next five years that amounts to about 3% of total AUM management by robo advisors. If in the second five years the robo advisory annual grow rate slows to 50% that still mean that robo advisors will control in the neighborhood of 20% of managed assets by 2025.

“Robo-Shields” and Robo Friends

Deborah Fox was clever enough to coin and trademark the term “robo-shield.” The basic idea is for traditional (human) investment advisors to protect their business by offering robo-like services ranging from client access to their online data to tax harvesting. I call this the half-robo defense

Another route to explore is the “robo friends”, or “full robo-hybrid” approach. This is partnering with an internal or external robo advisor. As an investment advisor, the robo advisor is subservient to you, and provides portfolio allocation and tax-loss harvesting, while you focus on the client relationship. I believe that the “robo friends” model will win over the pure robo advising model — most people prefer to have someone to call when they have investment questions or concerns, and they like to have relationships with their human advisors. We shall see.

What matters most is staying abreast of the robo advisor revolution and having a plan for finding a place in the brave new world of robo advising.

A very astute professor of finance told our graduate finance class that the best way to become a bona fide quant is NOT to get a Ph.D. in Finance! It is better, he said, to get a Ph.D. in statistics, applied mathematics, or even physics. Why? Because a Ph.D in Finance is generally not sufficiently quantitative. A quant needs a strong background in Stochastic Calculus.

“Quants for Hire?”

Our company has been described as a “quants for hire” firm. That is flattering. While we currently have 4 folks with master’s of science degrees (and one close to finishing a master’s) what we do is probably more accurately described as “quant-like” or “quant-lite” software and services. However “Quants for Hire” definitely has a nice succinct ring to it.

Quant-like Tangents to Financial Learning

Most of our quant-like work has been fairly vanilla — back testing trading strategies in Excel, Monte Carlo simulations (also in Excel), factor analysis, options strategy analysis. So far our clients like Excel and are not very interested in R. The main application of R has been to double-check our Excel back tests!

We have attracted fairly sophisticated clients. They seem reasonably comfortable about talking about viewing portfolios as unit vectors that can be linearly combined. They tend to understand correlation matrices, Sortino ratios, and in some cases even relate to partial derivatives and gradients. But they tend to push back on explanations involving geometric Brownian motion, Ito’s lemma, and the finer points of Black-Scholes-Merton. They do, however, appear to appreciate that we “know our stuff.”

I’ve got a decent set of R skills, but I’m looking to take them to the next level. I’m taking a page from my professor in tackling non-financial quantitative problems. My current problem du jour image compression. I came up with an R script that achieves very high compression levels for lossy compression. It is shorter than 200 lines commented and shorter than 100 lines when stripped of comments and blank (formatting) lines.

It can easily achieve 20X or greater compression, albeit with a loss in quality. In my initial tests my R algorithm (IC_DXB1.1) was somewhat comparable to JPEG (GIMP 2.8) at 20X compression, though I the JPEG clearly looks better in general. I also found an elegant R compressor that is extremely compact R code… the kernel is about 5 lines! Let’s call this SVD (singular value decomposition) for reference. So here’s the bake off results (all ~20X compressed to ~1.5KB):

JPEG: IC_DXB1.1:

What’s interesting to me is that each algorithm uses radically different approaches. JPEG uses DCT (discrete cosine transform) plus a frequency “mask” or filter that reduces more and more high-frequency components to achieve compression. My ic_dxb1.1 algorithm uses a variant of B-splines. The SVD approach uses singular value decomposition from linear algebra.

Obviously tens of thousands of hours have been invested in JPEG encoding. And, unfortunately, 99%+ of JPEG images are not as compact as they could be due to a series of patent disputes around arithmetic coding. Even thought the patents have all (to the best of my knowledge) expired, there is simply too much inertia behind the alternative Huffman coding at the present. It is worth noting that my analysis of all 3 algorithms is based on Huffman coding for consistency. All three approaches could ultimately use either Huffman or arithmetic coding.

So this Image Stuff Relates to Finance How?

Another of my professors explained that, fundamentally, finance is about information. One set of financial interview questions start with the premise that you have immediate (light-speed, real-time) access to all public information. Generally how would you make use of this information to make money trading? Alternatively you are to assume (correctly) that information costs money… how would your prioritize your firm’s information access? How important is frequency and latency?

Having boat loads of real-time data and knowing what to do with it are two different things. I use R to back test strategies, because it easy to write readable R code with a low bug rate. If I had to implement those strategies in a high-frequency trading environment, I would not use R, I would likely use C or C++. R is fast compared to Excel (maybe 5X faster), but is slow compared to good C/C++ implementations (often 100X slower).

My thinking is that while knowledge is important, so is creativity. By dabbling in areas outside of my “realm of expertise”, I improve my knowledge while simultaneously exercising my creativity.

Both signal processing and quant finance can reasonably be viewed as signal processing problems. Signal processing and information theory are closely related. So I would argue that developing skills in one area is cross-training skills in the other… and with greater opportunity for developing creativity. Finance is inextricably linked to information.

The Future of Finance Requires Disruptive (Software) Technology

It aint gonna be pretty for traditional financial advisors, hybrid advisors, broker/dealers, etc. Not with the rapid market acceptance of robo advisors.

Robo advising will have at least three important disruptive impacts:

Accelerating downward pressure on advisory fees

Taking of market share and AUM

Increasing market demand for investment tax management services such as tax-loss harvesting

Are you ready for the rise of the bots? We at Sigma1 are, and we are looking forward to it. That is because we believe we have the software and skills to make robo advisors work better. And we are not resting on our laurels — we are focusing our professional development on software, computer science, advanced mathematics, information theory, and the like.

In this post I explain how less is more when it comes to using “big data.” The best data is concise, meaningful, and actionable. It is both an art and a science to turn large, complex data sets into meaningful, useful information. Just like the later paintings of Monet capture the impression of beauty more effectively than a mere photograph, “small data” can help make sense of “big data.”

There is beauty in simplicity, but capturing simplicity is not simple. A young child’s drawings are simple too, but they very unlikely to capture light and mood like Monet did.

Worry not. There will be finance and math, but I will save the math for last, in an attempt to retain the interest of non “mathy” readers.

The point of discussing impressionist painting is show that reduction — taking things away — can be a powerful tool. In fact, filtering out “noise” is both useful and difficult. A great artist can filter out the noise without losing the fidelity of the signal. In this case, the “signal” is emotion and color and light as as perceived by a master painter’s mind.

Applying Impressionism to Finance

Massive amounts of data are available to the financial professional. Two questions I have been asking at Sigma1 since the beginning are 1) How to use “Big Compute” to crunch that data into better portfolios? 2) How to represent that data to humans — both investment pros and lay folk whose money is being invested? After considerable thought, brainstorming, listening, and learning, I think we are beginning to construct a preliminary picture of how to do that — literally.

While not a beautiful as a Monet painting, the picture above is worth a thousand words (and likely many thousands of dollars over time) to me. The assets above constitute all of the current non-CASH building blocks of my personal retirement portfolio. While simple, the above image took considerable software development effort and literally millions of computations to generate [millions is very do-able with computers].

This simple-looking image conveys complex information in an easy-to-understand form. The four colors — red, green, blue, and purple — convey four asset types: fixed income, US stocks, international stocks, and convertible securities. The angle between any two asset lines conveys the relative correlation between the pair. In portfolio construction larger angles are better. Finally the length of the line represents the “effectiveness” with which each asset represents its “angular position” within the portfolio (in addition to other information).

With Powerful Data, First Comes Humility, Next Comes Insight

I have applied the same visualizations to other portfolios, and I see that, according to my software, many of the assets in professionally-managed portfolios exhibit superior “robustness” to my own. As someone who prides myself in having a kick-ass portfolio, this information is humbling, and took some time to absorb from an ego standpoint. But, having gotten over it, I now see potential.

I have seen portfolios that have a significantly wider angle than my current portfolio. What does this mean to me? It means I will begin looking for assets to augment my personal portfolio. Before I do that let me share some other insights. The plot combines covariance matrix data for the 16 assets in the portfolio, as well as semi-variance data for each asset. Without getting to “mathy” yet, the data visualization software reduces 136 pieces of data down to 32 (excluding color). The covariance matrix and semi-variance calculation itself are also a reducers in that they combines 5 years monthly total-return data — 976 data points down to 120 unique covariance numbers and 16 semi-deviation numbers. Taking 976 down to 32 results in a compression ratio of 30.5:1.

Finally, as it currently stands, the visualization software and resulting plot say nothing about expected return. The plot focuses solely on risk mitigation at the moment. Naturally, I intend to change that.

Time for the Math and Finance — Consider Yourself Warned

I mentioned a 30.5:2 (71:2) compression ratio. Just as music and other data, other information, including financial information can be compressed. However, only so much compression can be achieved in lossless manner. In audio compression researchers have learned which portions of music and other audio can be “lost” without the listener telling the difference. There is a field of psychoacoustics around doing just that — modeling what the human ear (and brain) can hear, and what gets “masked” by various physiological factors.

Even more important that preserving fidelity is extracting meaning. One way of achieving that is by removing “noise.” The visualization software performs significant computation to maintain as much angular fidelity as possible. As it optimizes angles, it keeps track of total error vis-a-vis the covariance matrix. It also keeps track of individual assets error (the reciprocal of fitness — fit versus lack of fit).

The real alchemy comes from the line-length computation. It combines semi-variance data with various fitness factors to determine each asset line length.

Just like Mercator projections for maps incur unavoidable error when converting from a 3-D globe to a 2-D map, the portfolio asset visualizations introduce error as well. If one thinks of just the correlation matrix and semi-variance data, each asset has a dimensionality of 8.5 (in the case of 16 assets). Reducing from 8.5-D to 2-D is a complex process, and there are an infinite number of ways to perform such an operation! The art and [data] science is to enhance the “signal” while stripping away the “noise.”

The ultimate goals of portfolio data visualization technology are:

1) Transform raw data into actionable insight

2) Preserve sufficient fidelity of relevant data such that the “map” can be used to reliably get to the desired “destination”

I believe that the first goal has been achieved. I know what actions to take… trying various other securities to find those that can build a “higher-angle”, and arguably more robust, more resilient investment portfolio.

However, the jury is still out on the degree [no pun intended] to which goal #2 has or has not been achieved. Does this simple 2-D map help portfolio builders reliably and consistently navigate the 8+ dimensional portfolio space?

What about 3-D Modelling and Visualization?

I started working with 2-D for one key reason — I can easily share 2-D images with readers and clients alike. I want feedback on what people like and dislike about the visuals. What is easy to understand, what is not? What is useful to them, and what isn’t? Ironing out those details in 2-D is step 1.

Of course I am excited by 3-D. Most of the building blocks are in my head, and I can heavily leverage the 2-D algorithms. I am, however, holding off for now. I am waiting for feedback from readers and clients alike. I spend a lot of time immersed in the language of math, statistics, and finance. This can create a communication gap that is best mitigated through discussion with other people with other perspectives. I wish to focus on 2-D for a while to learn more about market needs.

That being said, it is hard to resist creating a 3-D portfolio asset visualizer. The geek in me is extremely curious about how much the error terms will reduce when given a third degree of freedom to work with.

The bottom line is: Please give me any feedback: positive, negative, technical, aesthetic, etc. This is just the start. I am extremely enthusiastic about where this journey will take me and my company.

Disclosure and Disclaimer

Securities mentioned in this post are holdings in my personal retirement accounts (e.g. 401K, IRA, Roth IRA) as of the day of initial publication of this post. The purpose of this post is to illustrate features of Sigma1 Financial software. This is NOT investment advice, and NOT a recommendation to buy, sell, or hold any securities. Please refer to the “Disclaimer” Tab of the main page of this site for further information.

I am happy to announce that the latest version of the HALO Portfolio-Optimization Suite is now available. Key features include:

Nativeasset constraint support

Nativeasset-category constraint support

Dramatic run-time improvements of 2X to over 100X

Still supported are user-specified risk models, including semi-variance and max-drawdown. What has been temporarilyremoved (based on minimal client interest) is 3-D 2-risk modelling and optimization. This capability may be re-introduced as a premium feature, pending client demand.

Here is a quick screenshot of a 20-asset, fixed-income portfolio optimization. The “risk-free” rate used for the tangent capital allocation line (CAL) is 1.2% (y-intercept not shown), reflecting a mix of T-Bills and stable value funds. Previously this optimization took 18 minutes on an $800 laptop computer. Now, with the new HALO software release, it runs in only 11 seconds on the same laptop.

A significant and growing portion of today’s individual investors have never placed a trade using a human stock broker.

Developing an Automation Mindset for Investing

In 2010, I bought the domain name Sigma1.com with the idea of creating an hedge fund that I would manage. In order to measure and manage my investment strategies objectively, I began thinking about benchmarks and financial analysis software. And as I ran scenarios through Excel and some light-weight analysis software I created, I began to realize that analysis, by itself was very limited. I could only back-test one portfolio at a time, and I had to construct each portfolio’s asset weights manually. It soon became obvious that I needed portfolio optimization software.

I learned that portfolio optimization software with the capabilities I wanted was extremely expensive. Further, I realized that even if, say, I negotiated a deal with MSCI where they provided Sigma1 Financial with their Barra Portfolio Manager for free, it would not differentiate a Sigma1 hedge fund from other hedge funds using the same software.

I was beginning to interact with several technology entrepreneurs and angel investors. I quickly learned that legal costs and barriers to entry for a new hedge were intractable. If Sigma1 attracted $10M in assets from accredited investors in 12 months, and charged 2 and 20, it would be a money loosing enterprise. Cursory research revealed that critical mass for a profitable (for the hedge fund managers) hedge fund could be as high as $500M. Luckily, I had learned about the concept of the “entrepreneurial pivot“.

The specific pivots Sigma1 used were a market segment pivot followed by a technology pivot. I realized that while the high cost of good portfolio optimization software is bad for a hedge fund startup, it was great for a financial software startup. Suddenly, the Sigma1 Financial target market switched from accredited investors to financial professionals (investment managers, fund managers, proprietary traders, etc). This was a key market segment pivot.

Just creating a cheaper portfolio optimizer seemed unlikely to provide sufficient incentive to displace entrenched portfolio optimizers. Sigma1 needed a technology pivot — finding a solution using a completely different technology. Most prior portfolio optimizers use some variant of linear programming (LP) [or QP or NLP] to help find optimal portfolios. Moreover they also create an asset covariance matrix as a starting point for the optimization.

One stormy day, I realized that some algorithms I created to solve statistical electrical engineering problems in grad school could be adapted to optimize investment portfolios. The method I devised not only avoided LP, QP, or NLP methods; it also dispensed with the need for a covariance matrix. Over then next several days I realized that by eliminating dependence on a covariance matrix, the algorithm I later named HALO, could use both traditional and alternate risk measures ranging from variance-based (eg. standard-deviation of return) to covariance-based ones (e.g. beta) to semivariance to max draw down. By developing a vastly different technology, HALO could optimize for risks such as semivariance and Sortino ratios, or max drawdown, or even custom risk measures devised by the client.

Algorithms Everywhere

Long before Sigma1 began developing HALO, the financial industry has been increasingly reliant on digital systems and various financial algorithms. As digital communication networks and electronic stock exchanges gained trading volume, various forms of program trading began to flourish. This includes the often maligned high-frequency trading variant of automated trading.

Concurrently, more and more trading volume has gone online. A significant portion of today’s individual investors have never placed a trade using a human stock broker.

Automated Investment Advice, Analysis, and Trading

There are now numerous automated investment analysis tools, many of which come free with a brokerage account, while others are free or low-cost stand-alone online tools. Examples of the former include the Fidelity’s nascent GPS (Guided Portfolio Summary) to more seasoned offerings such as Financial Engines. Online portfolio analysis offering range from Morningstar’s Instant X-Ray, to sites like ETFreplay.

However these software offerings are just the beginning. A company call FutureAdvisor has partnered with Fidelity and TD Ameritrade to allow its automate portfolio software to make trades on its users behalf. Companies like Future Advisor have the potential to help small investors benefit from custom-tailored investment advice utilizing proven academic research (e.g. Fama French) at a very low cost — costs so low that they would not be profitable for human investment advisers to provide.

If successful (and I believe some automated investment companies will be), why should they stop at small-time investors, with less than $500,000 in investable assets? Why not $1,000,000 or more? Nothing should stop them!

I could easily imagine Mark Zuckerberg, Sergey Brin, or Larry Page utilizing an automated investment company’s software to manage a large part of their portfolios. If we, as a society, are considering allowing automated systems to drive our cars for us, surely they can also manage our investment portfolios.

The Future Roll of the Human Financial Adviser

There will always be some percentage of investors who want a personal relationship with a financial adviser. Human investment advisers can excel at explaining investment concepts and putting investors at ease during market corrections. In some ways human investment advisers even function as personal financial counselors, listening to their clients emotional financial stories. And, of course, there are some people who want to be able to pick up the phone and yell at a real person for letting them suffer market losses. Finally, there are people with Luddite tenancies who want as little to do with technology as possible. For all these reasons human investment advisers will have a place in the future world of finance.

Investment Automation will Accelerate

There are some clear trends in the investing world. Index investing will continue to grow, as will total ETF assets under management (AUM). Alternative investments from rental property to master limited partnerships (MLPs) to private equity are also likely to become part of the portfolios of more sophisticated and affluent investors.

With the exception of high-frequency trading, which has probably saturated arbitrage and front-running opportunities, I expect algorithmic (algo) management to increase as an overall percentage of US and global AUM. Some algorithmic trading and investing will be of the “hardwired” variety where the algo directly connects to the exchanges and makes trades, while the rest of the algo umbrella will comprise trading and investing decisions made by financial software and entered manually by humans with minimal revision. There will also be hybrid methods where investment decisions are a synthesis of “automated” and “manual” processes. I expect the scope of these “flavors” of automated investing to not only increase, but to accelerate in the near term.

It is important to note, however, that for the foreseeable future, the ultimate arbiters of algorithmic investing and portfolio optimization will be human. The software architects and developers will exercise significant influence on the methodology behind the fund and portfolio optimization software. Furthermore, the users of the software will have supreme control over what parameters go into the optimization process such as including or excluding or bounding certain assets and asset classes (amongst many other factors under their direct control).

That being said, the future of investing will be increasingly the domain of financial engineers, software developers and testers, and people with skills in financial mathematics, statistics, algorithms, data structures, GUIs, web interfaces and usability. Additionally, the financial software automation revolution will have profound impacts on legal professionals and marketers in the financial domain, as well as more modest impacts on accountants and IT professionals.

Some financial professionals will take the initiative and find a place on the leading edge of the financial automation revolution. It is likely to be a wild but lucrative ride. Others will seek the short-term comfort of tradition. They may be able to retain many of their current clients through sheer charisma and inertia, but may find it increasingly difficult the appeal to younger affluent clients steeped in a culture of technology.

Explaining technical investment concepts in a non-technical way is critical to having a meaningful dialog with individual investors. Most individual investors (also called “retail investors”, or “small investors”) do not have the time nor the desire to learn the jargon and concepts behind building a solid investment portfolio. This is generally true for most individual investors regardless of the size of their investment portfolios. Individual investors expect investment professionals (also called “institutional investors”) to help manage their portfolios and explain the major investment decisions behind the management of their individual portfolios.

In the same way that a good doctor helps her patient make informed medical decisions, a good investment adviser helps her clients make informed investment decisions.

I get routinely asked how the HALO Portfolio Optimizer works. Every time I answer that question, I face two risks: 1) that I don’t provide enough information to convince the investment profession or their clients that HALO optimization provides significant value and risk-mitigation capability and 2) I risk sharing key intellectual property (IP) unique to the Sigma1 Financial HALO optimizer.

This post is my best effort to provide both investment advisers and their clients with enough information to evaluate and understand HALO optimization, while avoiding sharing key Sigma1 trade secrets and intelectual property. I would very much appreciate feedback, both positive and negative, as to whether I have achieved these goals.

First Principle of Portfolio Optimization Software

Once when J.P. Morgan was asked what the market would do, he answered “It will fluctuate.” While some might find this answer rather flippant, I find it extremely insightful. It turns out that so-called modern portfolio theory (MPT) is based understanding (or quantifying) market fluctuations. MPT labels these fluctuations as “risk” and identifies “return” as the reward that a rational investor is willing to accept for a given amount of risk. MPT assumes that a rational investor, or his/her investment adviser will diversify away most or all “diversifiable risk” by creating a suitable investment portfolio tailored to the investor’s current “risk tolerance.”

In other words, the primary job of the investment adviser (in a “fiduciary” role), is to maximize investment portfolio return for a client’s acceptable risk. Said yet another way, the job is to maximize the risk/reward ratio for the client, without incurring excess risk.

Now for the first principle: past asset “risk” tends to indicate future asset “risk”. In general an asset that has been previously more volatile will tend to remain more volatile, and and asset that has been less volatile will tend to remain less volatile. Commonly, both academia and professional investors have equated volatility with risk.

Second Principle of Portfolio Optimization Software

The Second Principle is closely related to the first. The idea is that the past portfolio volatility tends to indicate future portfolio volatility. This thesis is so prevalent that it is almost inherently assumed. This is evidenced by search results that reaches beyond volatility and looks at the hysteresis of return-versus-volatility ratios, papers such at this.

Past Performance is Not Necessarily Indicative of Future Results.

Third Principle of Portfolio Optimization Software

The benefits of diversification are manifest in risk mitigation. If two assets are imperfectly correlated, then their combined volatility (risk) will beless than the weighted averages of their individual volatilities. An in-depth mathematical description two-asset portfolio volatilities can be found on William Sharpe’s web page. Two-asset mean-variance optimization is relatively simple, and can be performed with relatively few floating-point operations on a computer. This process creates the two-asset efficient frontier*. As more assets are added to the mix, the computational demand to find the optimal efficient frontier grows geometrically, if you don’t immediately see why look at page 8 of this paper.

A much simpler explanation of the the third principle is as follows. If asset A has annual standard deviation of 10%, and asset B an annual standard deviation of 20%, and A and B are not perfectly correlated, then the portfolio of one half invested in A and the other half invested in B will have a annual standard deviation of less than 15%. (Non-perfectly correlated means a correlation of less than 1.0). Some example correlations of assets can be found here.

In so-called plain English, the Third Principle of Portfolio Optimization can be stated: “For a given level of expected return, portfolio optimization software can reduce portfolio risk by utilizing the fact that different assets move somewhat independently from each other.”

Forth Principle of Portfolio Optimization Software

The Forth Principle of Portfolio Optimization establishes a relationship between risk and return. The classic assumption of modern portfolio theory (MPT) is that so-called systematic risk is rewarded (over a long-enough time horizon) with increased returns. Portfolio-optimization software seeks to reduce or eliminate unsystematic risk when creating an optimized set of portfolios. The portfolio manager can thus select one of these optimized portfolios from the “best-in-breed” list created by the optimization software that is best suited to his/her client’s needs.

Fifth Principle of Portfolio Optimization Software

The 5th Principle is that the portfolio manager and his team adds value to the portfolio composition process by 1) selecting a robust mix of assets, 2) applying constraints to the weights of said assets and asset-groups, and 3) assigning expected returns to each asset. The 5th Principle focuses on the assignment of expected returns. This process can be grouped under the category of investment analysis or investment research. Investment firms pay good money for either in-house or contracted investment analysis of selected securities.

Applying the Portfolio Optimization Principles Together

Sigma1 Financial HALO Software applies these five principles together to help portfolio managers improve or fine-tune their proprietary-trading and/or client investment portfolios. HALO Portfolio Optimization software utilizes the assets, constraints, and expected returns from the 5th Principal as a starting point. It then uses the 4th Principal by optimizing away systematic risk from a set of portfolios by taking maximum advantage of varying degrees of non-correlation of the portfolio assets. The 3rd Principle alludes to the computational difficulty of solving the multi-asset optimization problem. Principles 1 and 2 form the bedrock of the concepts behind the use of historical correlation data to predict and estimate future correlations.

The Fine Print

Past asset volatility of most assets and most portfolios is historically well correlated with future volatility. However, not only are assets increasingly correlated, there is some evidence that asset correlations tend to increase during times of financial crisis. Even if assets are more correlated, there remains significant value in exploiting partial-discorrelation.
(*) The two-asset model can be represented as two parametric functions of a single variable, “t”, ER(t), and var(t). t simply represents the investment proportion invested in asset 0 (aka asset A). For three variables, expected return becomes ER(t0,t1) as does var(t0,t1). And so on for increasing numbers of assets. The computational effort required to compute ER(t0…tn) scales linearly with number of assets, but var(t0…tn) scales geometrically.
Optimizing efficiently within this complex space benefits from creative algorithms and heuristics.

When evaluating investment portfolios, a higher Sharpe ratio is typically better than a lower Sharpe ratio. Similarly, a higher Sortino ratio is better than a lower one. Finally, for portfolios with identical expected returns, the one with a lower standard deviation (sigma, σ) is better.

My best estimate is that less than 2% of portfolio assets are currently optimized for semivariance of any kind (mean-return semivariance, return semivariance, semivariance with respect to minimum acceptable return, etc.). Meanwhile at least 60% of portfolio assets take variance into account. According to the laws of supply and demand, the variance contribution (often related to beta) of an asset is strongly priced into its market value. Conversely, the asset’s semivariance is essentially not priced in.

If, as I believe, semivariance-based models continue to play an increasing roll in portfolio optimization strategies then asset-semivariance contributions will increasingly price in. If this prediction holds true, then early adopters of semivariance optimization will front-run asset pricing changes by buying assets with superior price-to-semivariance properties and shunning assets that detract from, say, Sortino ratios.

Sharpe and Sortino ratios differ only in the denominator (σ_{p} versus σ_{d}) . For portfolio-optimization, I prefer to modify σ_{p} and σ_{d} such that they would be identical for a normal distribution. In such a scenario, each sigma is the square root of its corresponding (return) variance. Because downside variance (σ_{d} ), in a normal distribution, is half of total variance I multiply downside variance by 2. For the same reason, I tend to avoid anything mathematically arbitrary such as minimum acceptable return (MAR), and use zero or mean-return instead. Empirically, I have found that zero works quite well.

My preliminary data shows is that for virtually any portfolio σ_{p} ≠ σ_{d}. While σ_{p} and σ_{d} are positively correlated, their ex-post correlation is as low as 0.5. In some cases, for optimized portfolios of the same return, increasing σ_{p} by one unit (say 0.01) reduces σ_{d} by a similar amount and vice versa. This is an astounding trade off — it means variance and semivariance compete head to head.

I don’t believe that the investment industry will switch from variance to semivariance models overnight. Similarly individual investment houses desire to shift gradually (each on their own timescale). Thus I propose the use of hybrid variance/semivariance ratios. With hybrid ratios, financial professionals can choose just how much they want semivariance to factor into their optimization… from zero to 100%, and everything in between.

The shifting portfolio-optimization market is large enough large enough for several players to make healthy profits. For those players that can and do make a shift to semivariance, I recommend a contiguous hybrid model.

In order to create software that is appealing to the enterprise market today, Sigma1 must create software for five years from now. In this post I will answer the questions of why and how Sigma1 software intends to achieve this goal.

The goal of Sigma1 HAL0 software is to solve financial asset allocation problems quickly and efficiently. HALo is portfolio-optimization software that makes use of a variety of proprietary algorithms. HALo’s algorithms solve difficult portfolio problems quickly on a single-core computer, and much more rapidly with multi-core systems.

Savvy enterprise software buyers want to buy software that runs well on today’s hardware, but will also run on future generations of compute hardware. I cannot predict all the trends for future hardware advanced, but I can predict one: more cores. Cores per “socket” are increasing on a variety of architectures: Intel x86, AMD x86, ARM, Itanium, and IBM Power7 to name a few. Even if this trend slows, as some predict, the “many cores” concept is here to stay and progress.

Simply put — Big Iron applications like portfolio-optimization and portfolio-risk management and modelling are archaic and virtually DOA if they cannot benefit from multi-core compute solutions. This is why HAL0 is designed from day 1 to utilize multi-core (as well as multi-socket) computing hardware. Multiprocessing is not a bolt-on retrofit, but an intrinsic part of HAL0 portfolio-optimization software.

That’s the why, now the how. Google likes to use the phrase “map reduce” while others like the phase embarrassingly parallel. I like both terms because it can be embarrassing when a programmer discovers that the problems his software was slogging through in series were being solved in parallel by another programmer who mapped them to parallel sub-problems.

The “how” for HAL0’s core algorithm is multi-layered. Some of these layers are trade secrets, I can disclose one. Portfolio optimization involves creating an “efficient frontier” comprised of various portfolios along the frontier. Each of these portfolios can be farmed out in parallel to evaluate its risk and reward values. Depending on the parameters of a particular portfolio-optimization problem this first-order parallelism can provide roughly a 2-10x speedup — parallel, but not massively parallel.

HALo was developed under a paradigm I call CAP (congruent and parallel). Congruent in this context means that given the same starting configuration, HAL0 will always produce the same result. This is generally easy for single-threaded programs to accomplish, but often more difficult for programs running multiple threads on multiple cores. Maintaining congruence is extremely helpful in debugging parallel software, and is thus very important to Sigma1 software. [Coherent or Deterministic could be used in lieu of Congruent.]

As HAL0 development continued, I expanded the CAP acronym to CHIRP (Congruent, Heterogeneous, Intrinsically Recursively Parallel). Not only does CHIRP have a more open, happier connotation that CAP, it adds two additional tenets: heterogeneity and recursion.

Heterogeneity, in the context of CHIRP, means being able to run, in parallel, on a variety of machines will different computing capabilities. On on end of the spectrum, rather than requiring all machines in the cloud or compute queue having the exact same specs (CPU frequency, amount of RAM, etc), the machines can be different. On the other end of the spectrum, heterogeneity means running in parallel on multiple machines with different architectures (say x86 and ARM, or x86 and GPGPUs). This is not to say that HAL0 has complete heterogeneous support; it does not. HALo is, however, architected with modest support for heterogeneous solutions and extensibility for future enhancements.

The recursive part of CHIRP is very important. Recursively parallel means that the same code can be run (forked) to solve sub-problems in parallel, and those sub-problems can be divided into sub-sub problems, etc. This means that the same tuned, tight, and tested code can leveraged in a massively parallel fashion.

By far the most performance-enhancing piece of HAL0 portfolio-optimization CHIRP is RP. The RP optimizations are projected to produce speedups of 50 to 100X over single-threaded performance (in a compute environment with, for example, 20 servers with 10 cores each). Moreover, the RP parts of HAL0 only require moderate bandwidth and are tolerant of relatively high latency (say, 100 ms).

Bottom line: HAL0 portfolio-optimization software is designed to be scalable and massively parallel.

Saturday, I had a fascinating morning starting a 10-week entrepreneurship program. I sat face-to-face with a couple of people who could likely write 7-figure checks that would clear the bank.

Tuesday was day 2 of the entrepreneurship class. I can sum up the general mood of the class with two words: energy and optimism. Speakers, coaches, and students were increasingly energized as the 3.5 hour class progressed. There are some talented students in my class who have already have revenue, employees, and venture capital. Others have a Ph.D. thesis and novel ideas from their post-doc work. I am presently somewhere in between: I am beyond the idea phase and well into the software product development phase. I have demo-able software and am self-funded to the tune of approx. $50,000.

Apparently my ideas and software are starting to get traction within the group. It is possible that some college students will write the Sigma1 Financial business plan as a for-credit exercise. If this pans out, I get a free first-draft business plan, and they get college credit. That spells “win-win” to me.

I have also learned that my “elevator pitch” needs work. My off-the-cuff pitch on Day 1 was my best. Successive effort have been worse. Feedback examples include: I felt buried; too much financial jargon; too long. This is great feedback! Better ideas from the group include gems such as:

Financial Risk: If you can see it, you can avoid it. Understand risk, visualize risk, and using proprietary software decrease risk by X%.

Nobody likes risk, but almost nobody truly understands it. Sigma1 software does.

Helping financial advisers model and explain risk to their clients.

Visualizing risk… Really!

Here’s the revised elevator pitch based off of their feedback. “Hi, I founded Sigma1 Software. If you own an investment portfolio there is one think you should know: it was probably constructed with using flawed risk models. Sigma1 Software can analyze your existing portfolio using better risk models. It will also build alternative portfolios and display the results visually. Our software not only reduces risk; it helps you visualize risk.

Few people like financial risk, and fewer still truly understand risk. Sigma1 Software does, and it uses advanced risk models and proprietary algorithms to help you build a better portfolio.

That’s the pitch: Smarter risk models, risk reduction, and powerful visualization tools. It’s what we do at Sigma1 Software.”

Building a Solid Team

To take Sigma1 Software to the next level, I need a great team. At a minimum I need a salesperson. This person needs both sales experience and experience in the financial industry. Having a wide network of connections to financial professionals is a plus. I’m looking for someone will no only close deals, but work with me and our attorneys to construct standard contracts and pricing models. A person who will build and maintain long-term relationships with our customers while finding new customers. Finally a salesperson who listens to customer needs in order to help us improve our software and software support.

Next on my hiring list is a second software developer specializing in user interface development for Windows, Linux, and Web applications. I’m looking for a developer who also has the interpersonal skills to 1) contribute to a highly collaborative environment, 2) conduct customer training, 3) join sales visits to demo Sigma1 software and answer technical questions. Pluses would be Windows and/or Linux sysadmin and IT skills. The software developer position would also require occasional work performing unit, regression, and beta testing of the portfolio-optimization suite.

It is crucial that any employees, partners, or employee/partners believe in Sigma1’s mission: To build and sell revolutionary portfolio-optimization technologies which will revitalize and reinvent the financial industry. To that end, equity in the form of voting, non-voting, dilutable, and possibly non-dilutable stock are likely to be an important part of any hiring agreement.