Quant Cross-Training

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:

JPEG 20X Compressed

IC_DXB1.1 20X Compressed

SVD 20X Compressed

 

 

 

 

 

 

 

 

 

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:

1. Accelerating downward pressure on advisory fees
2. Taking of market share and AUM
3. 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.

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Beta Software, First Month

This marks the first month (30 days) of engagement with beta financial partners.  The goal is to test Sigma1 HAL0 portfolio-optimization software on real investment portfolios and get feedback from financial professionals.  The beta period is free.  Beta users provide tickers and expected-returns estimates via email, and Sigma1 provides portfolio results back with the best Sharpe, Sortino, or Sharpe/Sortino hybrid ratio results.

HAL0 portfolio-optimization software provides a set of optimized portfolios, often 40 to 100 “optimal” portfolios, optimized for expected return, return-variance and return-semivariance.   “Generic” portfolios containing a sufficiently-diverse set of ETFs produce similar-looking graphs.  A portfolio set containing SPY, VTI, BND, EFA, and BWX is sufficient to produce a prototypical graph.  The contour lines on the graph clearly show a tradeoff between semi-variance and variance.

 

Portfolio Optimization Graph

 

Once the set of optimized portfolios has been generated the user can select the “best” portfolio based on their selection criteria.

So far I have learned that many financial advisers and fund managers are aware of post-modern portfolio theory (PMPT) measures such as semivariance, but also a bit wary of them.  At the same time, some I have spoken with acknowledge that semivariance and parts of PMPT are the likely future of investing.  Portfolio managers want to be equipped for the day when one of their big investors asks, “What is the Sortino ratio of my portfolio? Can you reduce the semi-variance of my portfolio?”

I was surprised to hear that all of Sigma1 beta partners are interested exclusively in a web-based interface. This preliminary finding is encouraging because it aligns with a business model that protects Sigma1 IP from unsanctioned copying and reverse-engineering.

Another surprise has been the sizes of the asset sets supplied, ranging from 30 to 50 assets. Prior to software beta, I put significant effort into ensuring that HAL0 optimization could handle 500+ asset portfolios. My goal, which I achieved, was high-quality optimization of 500 assets in one hour and overnight deep-dive optimization (adding 8-10 basis points of additional expected-return for a given variance/semi-variance). On the portfolio assets provided to-date, deep-dive runtimes have all been under 5 minutes.

The best-testing phase has provided me with a prioritized list of software improvements. #1 is per-asset weighting limits. #2 is an easy-to-use web interface. #3 is focused optimization, such as the ability to set max variance.  There have also been company-specific requests that I will strive to implement as time permits.

Financial professionals (financial advisers, wealth managers, fund managers, proprietary trade managers, risk managers, etc.) seem inclined to want to optimize and analyze risk in both old ways (mean-return variance) and new (historic worst-year loss, VAR measures, tail risk, portfolio stress tests, semivariance, etc.).

Some Sigma1 beta partners have been hesitant to provide proprietary risk measure algorithms.  These partners prefer to use built-in Sigma1 optimizations, receive the resulting portfolios, and perform their own in-house analysis of risk.  The downside of this is that I cannot optimize directly to proprietary risk measures.  The upside is that I can further refine the HAL0 algos to solve more universal portfolio-optimization problems.  Even indirect feedback is helpful.

Portfolio and fund managers are generally happy with mean-return variance optimization, but are concerned that semivariance-return measures are reasonably likely to change the financial industry in the coming years.   Luckily the Sharpe ratio and Sortino ratio differ by only the denominator (σ_p versus σ_d) .  By normalizing the definitions of volatility (currently called modified-return variance and modified-return semivariance) HAL0 software optimizes simultaneously for both (modified) Sharpe and Sortino ratios, or any Sharpe/Sortino hybrid ratios in-between.  A variance-focused investor can use a 100% variance-optimized portfolio.  An investor wanting to dabble with semi-variance can explore portfolios with, say, a 70%/30% Sharpe/Sortino ratio.   And an investor, fairly bullish on semivariance minimization, could use a 20%/80% Sharpe/Sortino hybrid ratio.

I am very thankful to investment managers and other financial pros who are taking the time to explore the capabilities of HAL0 portfolio-optimization software.  I am hopeful that, over time, I can persuade some beta partners to become clients as HAL0 software evolves and improves.  In other cases I hope to provide Sigma1 partners with new ideas and perspectives on portfolio optimization and risk analysis.  Even in one short month, every partner has helped HAL0 software become better in a variety of ways.

Sigma1 is interested in taking on 1 or 2 additional investment professionals as beta partners.  If interested please submit a brief request for info on our contact page.

 

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.