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Regularizing Portfolio Risk Analysis: A Bayesian Approach

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  • Sourish Das
  • Aritra Halder
  • Dipak K. Dey

Abstract

It is important for a portfolio manager to estimate and analyze recent 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 use a parallelizable and easy to use Monte Carlo (MC) approach to achieve our objective. Estimation of various risk measures, such as Value at Risk and Expected Shortfall, becomes a by-product of this Monte-Carlo approach.

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  • Sourish Das & Aritra Halder & Dipak K. Dey, 2014. "Regularizing Portfolio Risk Analysis: A Bayesian Approach," Papers 1404.3258, arXiv.org, revised Oct 2015.
    • Handle: RePEc:arx:papers:1404.3258
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    References listed on IDEAS

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    1. Susanne Still & Imre Kondor, 2009. "Regularizing Portfolio Optimization," Papers 0911.1694, arXiv.org.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. 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.
    4. 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.
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