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Regularizing Portfolio Risk Analysis: A Bayesian Approach

Author

Listed:
  • Sourish Das

    (Chennai Mathematical Institute)

  • Aritra Halder

    (Chennai Mathematical Institute)

  • Dipak K. Dey

    (University of Connecticut)

Abstract

It is important for a portfolio manager to estimate and analyze portfolio volatility, to keep the portfolio’s risk within limit. Though the number of financial instruments in the portfolio can be very large, sometimes more than thousands, daily returns considered for analysis are only for a month or even less. In this case rank of portfolio covariance matrix is less than full, hence solution is not unique. It is typically known as the “ill-posed” problem. In this paper we discuss a Bayesian approach to regularize the problem. One of the additional advantages of this approach is to analyze the source of risk by estimating the probability of positive ‘conditional contribution to total risk’ (CCTR). Each source’s CCTR would sum up to the portfolio’s total volatility risk. Existing methods only estimate CCTR of a source, and does not estimate the probability of CCTR to be significantly greater (or less) than zero. This paper presents Bayesian methodology to do so. We propose a simple Monte Carlo (MC) approach to achieve our objective, which can be paralleled. Estimation of various risk measures, such as Value at Risk and Expected Shortfall, becomes a by-product of this Monte-Carlo approach.

Suggested Citation

  • Sourish Das & Aritra Halder & Dipak K. Dey, 2017. "Regularizing Portfolio Risk Analysis: A Bayesian Approach," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 865-889, September.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9524-5
    DOI: 10.1007/s11009-016-9524-5
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    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    2. Vasyl Golosnoy & Yarema Okhrin, 2007. "Multivariate Shrinkage for Optimal Portfolio Weights," The European Journal of Finance, Taylor & Francis Journals, vol. 13(5), pages 441-458.
    3. G. Glenn Baigent, 2014. "X-Sigma-Rho and Market Efficiency," Journal of Economic and Financial Studies (JEFS), LAR Center Press, vol. 2(2), pages 41-44, April.
    4. repec:mir:mirfin:v:1:y:2014:i:1:p:39-43 is not listed on IDEAS
    5. Das, Sourish & Dey, Dipak K., 2010. "On Bayesian inference for generalized multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1492-1499, October.
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    Cited by:

    1. Sourish Das & Rituparna Sen, 2021. "Sparse Portfolio Selection via Bayesian Multiple Testing," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 585-617, November.
    2. Raghu Nandan Sengupta & Rachit Seth & Peter Winker, 2023. "Reliability in Portfolio Optimization using Uncertain Estimates," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 199-233, May.

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