  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.
