**CSS Analytics's Personal Page**- Toronto - Our research approach utilizes conventional statistical methods in conjunction with a unique focus on adaptive algorithms. This highly proprietary technology combines the power of artificial intelligence together with the principles of robust statistics to generate strategies that can learn from the ever-changing market environment.

In the last post on Probabilistic Momentum we introduced a simple method to transform a standard momentum strategy to a probability distribution to create confidence thresholds for trading. The spreadsheet used to replicate this method can be found here. This framework is intellectually superior to a binary comparison between two assets because the tracking error […]

In the last post, I introduced the concept of viewing momentum as a probability of one asset outperforming the other versus a binary decision driven by whichever return is greater between a pair of assets. This method incorporates the joint distribution between two assets that factors in their variance and covariance. The difference in the […]

Momentum remains the most cherished and frequently used strategy for tactical investors and quantitative systems. Empirical support for momentum as a ubiqutous anomaly across global financial markets is virtually iron-clad– supported by even the most skeptical high priests of academic finance. Simple momentum strategies seek to buy the best performers by comparing the average or […]

The strength of FTCA is both speed and simplicity. One of the weaknesses that FTCA has however, is that cluster membership is determined by a threshold to one asset only at each step (either MC or LC). Asset relationships can be complex, and there is no assurance that all members of a cluster have a […]

In a previous post I introduced Random Subspace Optimization as a method to reduce dimensionality and improve performance versus standard optimization methods. The concept is theoretically sound and is traditionally applied in machine learning to improve classification accuracy. It makes sense that it would be useful for portfolio optimization. To test this method, I used […]

Mean-variance optimization (MVO) was introduced by Markowitz as a means of compressing forecasts into an expression of portfolio weights for asset allocation. The theory and mathematical concepts have become central to modern finance. Views on MVO are highly polarized- some feel that it is worthless while others think it is the holy grail. Somewhere in […]

The picture above is not a Sharknado. It is a school of fish that are travelling together in a swarm demonstrating the properties of intelligent social behavior. This observation along with other examples in nature helped to inspire the creation of Particle Swarm Optimization (PSO). PSO is a robust stochastic optimization method based upon the […]

A Gentle Introduction to Optimization The field of optimization has evolved significantly over the past few decades. Several new theoretical, algorithmic, and computational methods for optimization have been proposed to solve complex problems in diverse fields such as finance, engineering and molecular biology. In finance, optimization is required to solve portfolio problems, model/predict time series […]

Most asset return processes can be characterized as containing a primary trend, along with mean-reversion around that trend, as well as a certain amount of random noise. Econometricians classify these elements using a Hurst Exponent as either : 1)black noise (trending/positive autocorrelations- Hurst>.5) 2) pink noise (mean-reverting/negative autocorrelations- Hurst<.5) or 3) white noise ( no trend/mean-reversion, low/insignificant autocorrelations- Hurst=.5). [...]

The Minimum Variance Algorithm was compared to several standard optimization methods and algorithms in a recent set of tests done by Michael Kapler of Systematic Investor. Michael created a webpage for MVA to review some details of these tests and also to summarize some of the background information. We plan to release a whitepaper on [...]

The Minimum Variance Algorithm (MVA) follows much of the same logic as the Minimum Correlation Algorithm (MCA) and differs primarily in the objective function which is to minimize portfolio variance versus correlations. Both are “heuristic” algorithms that seek to approximate the results of more complex methods that require employing quadratic optimization. In a recent whitepaper, [...]

Often readers ask about methods for approximating minimum variance portfolios. In practice the minimum variance portfolio can be calculated in closed form only for long-short portfolios, and requires a quadratic optimizer to solve for long-only portfolios. Source code and examples for long-only minimum variance can be found at Systematic Investor - a very good blog that [...]

The recent popularity of “tactical” investment strategies has given rise to a dizzying array of new terminology and strategy descriptions. Most investors and investment professionals lack a deeper understanding of the core nature of such strategies. They can hardly be faulted for all of the marketing material floating around that often obfuscates the difference between [...]

In the last post, we introduced the “All-Weather” Sector Portfolio which was developed using data from Fidelity Asset Allocation Research. I created a heuristic approach to integrate a variety of factors (length of stage, sector performance ranking by stage) in order to create the final portfolio allocation. It is obviously very interesting to examine the [...]

The central concept of the “All-Weather” portfolio is balance: having an allocation that will perform equally well across different economic regimes. The original portfolio balances portfolio risk and performance with broad asset classes to be neutral to changes in economic growth and inflation.This basic concept can be extended to create an “All-Weather” equity sector portfolio. [...]

The All-Weather Portfolio was designed by Ray Dalio (and clearly influenced by Harry Browne of the Permanent Portfolio) as a robust static allocation that can be used by investors to deliver consistent performance over time. The logic of the portfolio construction is to be neutral to risk/uncertainty with respect to inflation or economic growth–the two primary [...]

In the last post we looked at the performance of static versus dynamic clusters on Dow 30 stocks. It is also logical to look at the same comparison on multiple asset classes. Michael Kapler of Systematic Investor ran the same set of tests on major market asset class ETFs for comparison. To avoid distortion in [...]

A natural comparison for an allocation method that makes use of dynamic clustering is to use a static clustering method. An example of the use of static clustering are the sector classifications made by large index firms. Typically clusters are formed based on the type of business or industry associated with a company (ie utilities, energy [...]