Regularizing Portfolio Risk Analysis: A Bayesian Approach

Regularizing Portfolio Risk Analysis: A Bayesian Approach 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Methodology and Computing in Applied Probability Springer Journals

Regularizing Portfolio Risk Analysis: A Bayesian Approach

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Statistics; Statistics, general; Life Sciences, general; Electrical Engineering; Economics, general; Business and Management, general
ISSN
1387-5841
eISSN
1573-7713
D.O.I.
10.1007/s11009-016-9524-5
Publisher site
See Article on Publisher Site

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.

Journal

Methodology and Computing in Applied ProbabilitySpringer Journals

Published: Oct 18, 2016

References

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