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.
Methodology and Computing in Applied Probability – Springer Journals
Published: Oct 18, 2016
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