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Estimation Of Portfolio Return And Value At Risk Using A Class Of Gaussian Mixture Distributions

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  • Kangrong Tan
  • Meifen Chu

Abstract

This paper deals with the estimation of portfolio returns and Value at Risk (VaR), by using a class of Gaussian mixture distributions. Asset return distributions are frequently assumed to follow a normal or lognormal distribution. It also can follow Brownian motion or Geometric Brownian motion based upon the Gaussian process. However, many empirical studies have shown that return distributions are usually not normal. They often find evidence of non-normality, such as heavy tails, excess kurtosis, finite moments, etc. We propose a class of Gaussian mixture distributions to approximate the return distributions of assets. This class of Gaussian mixture distributions, having good statistical properties, can accurately capture the above-mentioned statistical characteristics of return distributions. The model is applied easily to estimate the return distribution of a portfolio, and to evaluate the VaR. We demonstrate the model theoretically and provide some applications.

Suggested Citation

  • Kangrong Tan & Meifen Chu, 2012. "Estimation Of Portfolio Return And Value At Risk Using A Class Of Gaussian Mixture Distributions," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 97-107.
    • Handle: RePEc:ibf:ijbfre:v:6:y:2012:i:1:p:97-107
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    References listed on IDEAS

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    Cited by:

    1. Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.

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    More about this item

    Keywords

    Gaussian mixture distribution; convolution density; portfolio; Value at Risk;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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