Nikolay Nikolaev, Goldsmiths College, University of London

Portfolio Allocation and Value-at-Risk


Multivariate Dynamic Factor Models

The dynamics of multiple financial time series (for example of stock returns) is considered driven by a number of common factors as well as idiosynchratic components. This observation stimulates the development of Multivariate Dynamic Factor Models (MFDM) [Pitt, and Shephard, 1999], [Aguilar and West, 2000] to capture the correlation between the series. MFDM are designed especially for portfolio selection, with intention to learn economic latent factor levels as cross-covariances between the returns from the given idiosynchratic price series. This allows us to identify a small number of factors that explain common dependencies to all given stock prices. We consider a standard stochastic volatility model [Hull and White, 1987] to describe the time changing variances of the distributions of the stock returns. Problems arising from the unknown, typically fat-tailed and skewed distributions of financial data are handled using Bayesian inference.

Our research investigates Bayesian inference of factor models in two directions: using sampling methods, and using approximation techniques. We implement each of these techniques to find the latend factors as well as all parameters of the models, and design the following algorithms:

- Gibbs sampling algorithms for evaluation of MDFM;

- Variational approximation algorithms for estimation of MDFM.

Mulativariate Dynamic Factor Models using probabilistic filters that process the series online with the arrival of the prices in time are currently under active study [Nikolaev and Smirnov, 2012].


Dynamic Portfolio Selection

Portfolio management involves finding optimal allocation schemes for distribution of funds across various assets. This task requires an optimisation algorithm to identify the asset weights (market positions), guided by criteria provided by the classical mean-variance theory. According to these theories, the aim is to find such portfolios that yield attractive risk-adjusted returns, that is maximal returns with minimum variance. We apply these ideas and design algorithms that operate on forecasted returns of the individual stock prices, unlike the common research that simply uses past historical data. The stock returns and the correlations between them are predicted using stochastic volatility submodels embedded into mulativariate dynamic factor models. Such dynamic models capture the time-varying character of the return distribution and enable to adjust online the portfolios to the changing market conditions. The advantage of stochastic volatility models is that they allow random perturbations that are independent from the past, while classical GARCH describe the volatility entirely using historic information which can be problematic in dealing with financial data.

The current research combines the mean-variance theory with the capital asset pricing model. We implement software tools that compute efficient portfolios, leading to maximal return with minimal variance, using contemporary techniques for:

- improved forecasting of asset returns with Bayesian Multivariate Dynamic Factor Models;

- improved asset allocation according to Markowitz and Sharpe theories with optimisation algorithms;

- improved asset allocation using neural network connectionist models;

- sensible return adjustment through subjective views using the Black-Litterman framework.

Preliminary experimental results indicate that our probabilistic tools infer well balanced portfolios that can stimulate profitable investment behaviour which can exceed traditional performance. Along with finding the portfolio weights these tools calculate also exact analyical Value-at-Risk (VaR) estimates.


Nikolaev,N. and Smirnov,E. (2012). Analytical Factor Stochastic Volatility Modeling for Portfolio Allocation, In: R.Yager and R.Golan (Eds.) Proc. IEEE Conf. Computational Intelligence for Financial Engineering and Economics (CIFEr-2012), New York, pp.78-85.

Forni,M., Hallin,M., Lippi,M. and Reichlin,L. (2005). The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting, J. American Stat. Assoc., vol.100, pp.830-840.

Rachev,S.T., Fabozzi,F.J. and Menn,C. (2005). Fat-Tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio Selection, and Option Pricing, Wiley, New York.

Aguilar,O. and West,M. (2000). Bayesian Dynamic Factor Models and Portfolio Allocation, Journal of Business and Economic Statistics, vol.18, pp.338-357.

Markowitz,H.M., Todd,G.P. and Sharpe,W.F. (2000). Mean-Variance Analysis in Portfolio Choice and Capital Markets, Wiley, New York.

Pitt,M. and Shephard,N. (1999). Time Varying Covariances: A Factor Stochastic volatility Approach, In: Bayesian Statistics 6, Edited by J.M. Bernardo, J.O.Berger, A.P.Dawid and A.F.M.Smith, Oxford: Oxford University Press, pp.547-570.

Black,F. and Litterman,R. (1992). Global Portfolio Optimization, Financial Analysis Journal, vol.48, N:5, pp.28-43. World Scientific Publ. Co., Singapore.

Markowitz,H.M. (1991). Portfolio Selection: Efficient Diversification of Investments, Second Ed., Wiley, New York.

Hull,J. and White,A. (1987). The Pricing of Options on Assets with Stochastic Volatilities, The Journal of Finance, vol.42, N:2, pp. 281-300.

Sharpe,F. (1963). A Simplified Model for Portfolio Analysis, Management Science, vol.9, N:2, pp.277-93. <

Markowitz,H.M. (1952). Portfolio Selection, Journal of Finance, vol.7, pp.77-91.

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