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School of Social Sciences

Profitable investments based on the mathematics of behaviour

Large Swiss and German investment funds have successfully used mathematical behavioural finance to deliver high returns with low volatility, even during the financial crisis.

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Since 2008 the MBF-inspired PTRI has created a total return of approximately 50%, with a volatility of about 9.2%, significantly outperforming the benchmark.

Our research in the burgeoning field of ‘Mathematical Behavioural Finance’ has supported growth for two corporate investors. AllMountain Capital and Deutsche Bank systematically used our models to manage two funds which have both reported average annual returns over 10%.

Our studies in the emerging research area known as ‘Mathematical Behavioural Finance’ (MBF) led to the development of new methods for modelling financial markets. Although these models are based on behavioural principles, they do not rely on the characterisation of individual agents – knowledge about investors’ individual beliefs and working practices, for example, are not required for the model to work.

Thorough evaluation studies have demonstrated the reliability and robustness of our MBF models; they are now at the heart of new investment strategies and are used to manage funds in a systematic fashion, according to model outputs and predictions.

The following examples illustrate the effectiveness of the MBF approach:

AllMountain Capital AG

This Swiss firm specialises in Managed Futures and systematic investment strategies. After using the mathematical results of our MBF research the company achieved an average annual return of +12%, with an annualized volatility of 15%. The funds coped well with both the global financial crisis and the post-crisis situation.

Deutsche Bank

This global banking giant used MBF research results to provide a theoretical framework for the development of the ‘Portfolio Total Return Index’ (PTRI), a rule-based value index built up of several different asset classes. In July 2012 Deutsche Bank held approximately EUR 84 million in assets within its PTRI Tracker funds.

Since its launch the MBF-inspired PTRI has achieved a total return of approximately 50%, with a volatility of around 9.2%, significantly outperforming the benchmark index (60% Stoxx 50 and 40% REX-P) that only generated a total return of approximately 17%, with a volatility of around 12.4%.

Key quote

“Since 2008 the MBF-inspired PTRI has created a total return of approximately 50%, with a volatility of about 9.2%, significantly outperforming the benchmark…”

Our research

MBF was developed through a multidisciplinary collaboration beginning in the early 2000s. A collaborative, international team of researchers, including Pro Igor Evstigneev from The University of Manchester, combined expertise in Mathematics, Economics and Finance to create a new line of mathematical financial analysis and market modelling.

The team was inspired to replace the conventional approach of General Equilibrium (GE) in Economic and Financial Theory with a viable alternative that would more adequately reflect the modern financial world.

In contrast with GE, MBF models go beyond Walrasian methodology, the current basis of Financial Economics teaching and research, to open new horizons in Theoretical Finance. MBF investment strategies are a synthesis of three general investment principles known in Financial Economics:

  • Kelly Rule
  • Capital Asset Pricing Model (CAPM)
  • Proportional allocation of wealth among assets according to their fundamental values

Key people