# Methodology

## Methodology

| General Analytic Framework | Rational vs Ingenuity | An information-centric modelling approach | Information Processing and Models Building | Software design pattern | Further readings | References |

### General Analytic Framework

We take a generic viewpoint and information-centric approach in our investment methodology. An investment is represented as an optimization problem, with objective function to be maximized as:

$$\Psi^T = \int_{t_0}^{t_f} {\Psi(t | …) + \lambda(\Psi, t, …)} dt$$

where Ψ is a performance benchmark (such as Alpha or Sharpe ratio), and ƛ represents a regularizer function subject to individual investors. The regularizer is typically a loss-aversion preference or a smoothening restraint (steady income preferred over jumpy returns).

Next, we recognize that investment performance is the consequence of adopting a certain set of strategies. We can write

$$\Psi = \Omega(\{e_t\}, t)$$

where
{et} is the information set available at time t
A trading strategy is also called a model in our framework, a natural naming extension from our mathematical treatment on the subject.

Reader might inquire the need to use rigorous mathematical framework in expressing the common sense logics. To answer, such framework will be instrumental when it is recognized that investment is a complex problem. It is not uncommon when numerous lines of thoughts, which are conflicting or duplicative with one another simultaneously occur. Under such circumstances, the use of a scientific framework and the expression of idea using mathematical language would enable the investor to be rational, quantitative and maintains logical clarity with his/her mind. Additionally, other benefits for such framework include

(1) Incorporative and flexible
The framework does not fall into the dualism classification of investor vs. speculating approaches (others include value- vs. growth- stocks, trend-following vs reversal approaches etc). We believe that such pre-built cognitions are restrictive to the investor’s strategies and options. Our framework treats the approaches from different schools as plain information, and it is up to the investor to build a model to capture usefulness of these informations.

(2) Mapping for high-order thinking
A framework facilitates the organization of high-order thinking. For example, it could provide hints to the direction to development strategies, such as possible combination/extension of different models. Ideas, models and information can be built into the framework naturally as structural elements.

(3) Prevention of human cognition biases
Human mind is prone to cognition errors for complex problem under stress conditions – a scenario all too common in the field of financial investment. Emotional behaviours, which are predominantly destructive in investment decisions, can be minimized with a logical framework and more abstract thinking.

### Rational vs Ingenuity

For to be possessed of a vigorous mind is not enough; the prime requisite is rightly to apply it. The greatest minds, as they are capable of the highest excellences, are open likewise to the greatest aberrations; and those who travel very slowly may yet make far greater progress, provided they keep always to the straight road, than those who, while they run, forsake it.” ~ René Descartes, ‘Discourse on the Method

##### Drawback of human reasoning

Individual’s ingenuity is often overrated in the field of financial investment. We believe that over-reliance on human judgement is a slippery act that introduces unnecessary risk to the system. Crucial to financial management, the art of logical reasoning and quantitative assessment is an acquired skill, and is not innate to human mind. It takes a well-trained and disciplined mind to comply and act rationally. It is well documented that human mind suffer from cognitive and other biases that make them bad judges of probabilities [1, 2]. As an example, most people prefers a mechanistic viewpoint on the world despite its obvious probabilistic nature, for example the using of limited personal experience (aka subjective probability), tendency to believe they can predict and/or exert control on a purely probabilistic event (e.g. throw a dice harder when a bigger number is preferred), tendency of correlating positive serial autocorrelations in independent sequential events (e.g. a ‘hot-hand’ of a basketball player) etc. These cognitive biases are probably biologically [3] in-built for humans, and hence difficult to steer clear from. Knowing such drawback of human reasoning, it is imperative for an investor to set rules in advance as to prevent his/her potentially irrational actions during critical periods.

##### Computer-assisted decision making

The rapid development of computing in past few decades has opened the possibility of high-level computer-assisted thinking. This is further boosted by the development of statistical learning architectures (aka machine learning). Human experts could derive rules from their knowledge/experiences and encode them in a testable mathematical model. Interestingly, these models usually yield better (and almost never worse) results than do individual human experts [4-9] in complex situations, as substantiated by evidences from multiple domains.

We believe that, computer-assisted decision-making will emerge as the mainstream approach in the recent future. In addition to financial knowledge, it would be essential for future investors to have a good understanding of technical skills in computer sciences to succeed. Several prominent examples of this approach include Renaissance Technologies and D.E. Shaw & Co., both are highly successful investment management firms that adopts a model-driven and/or quantitative trading system. And such is the direction our methodology development will follow.

### An information-centric modelling approach

“Truth … is much too complicated to allow anything but approximations.” – John von Neumann

Ideally, a system is completely predictable given all the governing laws and information about it. However in business world (and the real world), with high inherent variability and missing information, the best equivalence of governing laws can only estimated with statistical models. Under our framework, an investment endeavour is about devising an actionable model, which when provided essential information, capable of accurately predicting the evolution of system (typically the pricing of an financial instrument).

We define our information-centric approach as follows:

A piece of information e is said to be relevant, if with respect to some strategy e, there is an improvement on the performance measure Ψ, as compared to the best next strategy Ω<sub>0</sub> which does not incorporating this information. Mathematically, we can write

$E(\Psi(\Omega_e | e)) > E(\Psi(\Omega_0))$

$$\Psi$$: measurement of performance
$$\Omega$$: strategy / model
$$e$$: new piece of information

A direct inference from the formulation is that, model and information must go hand-in-hand. Information without appropriate model to incorporate with is deemed irrelevant, as it will have no effect on the actionable strategies. While it seems trivial, in practice this provides a simple guideline to filter out noises and irrelevant information, which are too common in our information age.

### Information Processing and Models Building

##### Boosting and Heuristic

It is reminded that Scube system is designed for practical purpose rather than an academic exercise. The system is benchmarked for its profitability rather than its theoretical foundation. Therefore, instead of meticulously modelling the financial world from first principles, our strategy is to collect and assimilate known models (aka ‘boosting meta-algorithm’ in computer science language). Broadly speaking, these models can be categorized into three groups by their conventional analysis:

• Aggregated Supply and Demand (aka Macro-economics)
• Market Psychology (Technical Analysis)

Further documentations of some of the models can be found at “Presentations” page.

In correspondence, a survey and critical review of the currently available models are performed. Several criteria of the review include (i) the preconditions of the model, (ii) the validity of the model (iii) redundancy / synergy with current framework. Selected models were then suitably consolidated into our framework.
While it is desirable to have a mathematically accurate combined model, this is likely to be an intractable problem. Instead, model combination/consolidation is performed in a heuristic approach, with the aim of providing target candidates in a timely and robust manner. In practice, methods such as divide-and-conquer, dual-decomposition etc, can often be applied for a good approximation. In fact, currently an even simplistic rule is used:

$$\bigcap_i^n {\left \{ x \mid Pr(M_i(x) > \theta_i) > \alpha_i \right \}}$$

(i.e. the final target candidates are the intersection set among candidates from all models)

### Software design pattern

For the software platform, we chose to adopt a rapid application development paradigm. This is in contrast to the traditional development method (e.g. waterfall model), as we are facing with an environment which is highly variable, fast adaptive, with high error cost, and complex information structure. Additionally, some other important design patterns include

2. Robustness
3. Hierarchical / Modularity

Many core concepts building the system stem from the field of machine learning (aka computational intelligence, artificial intelligence etc). Serious reader is advised to familiarize with the subject. One good book to start with is user guide for WEKA

For general problem-solving technique and the methodology of heuristics,

### References

1. D. Kahneman, and A. Tversky, “On the psychology of prediction,” Psychological review,vol. 80, no. 4, pp. 237-51, 1973.
1. S. Lichtenstein, F. Baruch, and L. D. Phillips, “Calibration of probabilities: The state of the art to 1980,” Judgment under uncertainty: Heuristics and biases, D. Kahneman, P. Slovic and A. Tversky, eds.: Cambridge University Press, 1982
1. Hot-hand bias in rhesus monkeys. Blanchard, Tommy C.; Wilke, Andreas; Hayden, Benjamin Y. Journal of Experimental Psychology: Animal Learning and Cognition, Vol 40(3), Jul 2014, 280-286.
1. Yiftach Nagar and Thomas W. Malone. Combining Human and Machine Intelligence for Making Predictions. MIT Center for Collective Intelligence. 2011.
1. R. M. Dawes, D. Faust, and P. E. Meehl, “Clinical versus actuarial judgment,” Science,vol. 243, no. 4899, pp. 1668-1674, 1989
1. W. M. Grove, D. H. Zald, B. S. Lebowet al., “Clinical versus mechanical prediction: A meta-analysis,” Psychological Assessment,vol. 12, no. 1, pp. 19-30, 200
1. L. R. Goldberg, “Man versus model of man: A rationale, plus some evidence, for a method of improving on clinical inferences,” Psychological Bulletin,vol. 73, no. 6, pp. 422-432, 1970.
1. J. S. Armstrong, “JUDGMENTAL BOOTSTRAPPING: INFERRING EXPERTS’ RULES FOR FORECASTING,” Principles of forecasting: A handbook for researchers and practitioners, J. S. Armstrong, ed., Norwell, MA: Kluwer Academic Publishers, 2001.
1. T. R. Stewart, “Improving reliability of judgmental forecasts,” Principles of forecasting: A handbook forresearchers and practitioners, J. S. Armstrong, ed., pp. 81-106: Kluwer Academic Publishers, 2001