In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen stochastically based on the random projection method. Randomness of factors has the consequence that correlation and covariance matrices are well preserved in a linear factor representation. It also enables derivation of probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances. As an application, we analyze reproduction of time-series and their cross-correlation coefficients in the well-diversified Russell 3,000 equity index.

No abstract

Sufficient solvency of a pension insurance company responsible for definedbenefit pensions guarantees that the pensions are paid regardless of turbulence in the financial market. In the Finnish occupational pension system TyEL, the required level of solvency capital (solvency limit) and its computation are specified in the statutes. Before the solvency limit can be determined, financial instruments must be classified into the five statutory asset classes based on risk. The solvency limit is computed on the basis of this classification and the average return, volatility and correlation parameters defined in the statutes. The solvency limit framework is formulated in the spirit of Markowitz portfolio theory and implicitly assumes that returns follow Gaussian distributions. This, however, is not actually the case with many-if not most-financial instruments. Similarly, it is not obvious how to handle illiquid assets, those with short time series, and which collection of financial instruments can be combined into a single asset (portfoliocation) for the purpose of classification. In this study, we propose two methods of handling these issues: (1) a decision tree-based method; and (2) a Bayesian method. We show how fat tails of return distributions are taken into account in the classification process, and how qualitative assessment of risks is combined with quantitative classification of financial assets. Coupled with suitable data transformations, both proposed methods provide efficient and suitable bases for asset classification in the TyEL pension scheme.

No abstract

No abstract