X-Sigma-Rho and Market Efficiency

Baigent, G. Glenn

doi:10.18533/jefs.v2i02.133

Cited by 1 publication

(5 citation statements)

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“…However, it is also important for a manager to quantify, how sensitive the portfolio volatility is with respect to a small change in ω. This can be achieved by differentiating the volatility with respect to weight, i.e., [11]. Note that the MCTR for source i is given by the following…”

Section: Posterior Distribution Of the Portfolio Covariance Matrixmentioning

confidence: 99%

“…We compare portfolios obtained under the two broad methodologies, that is Ledoit and Wolf (2004a) and the proposed methodolgy as in Section 3, using Σ 23 , as the regularization matrix. Another comparision We consider the period 2013 (Jul-Dec) in Table ( 11) to demonstrate the procedure of inference on a portfolio constructed solely on equity, considering this as the investment period. The same procedure of inference is carried out as in the case of 'Indices' dataset, the only difference is in terms of the size of the market portfolio is much larger, making the problem considerably "more" ill-posed.…”

Section: National Stock Exchange Of India Datamentioning

confidence: 99%

“…where ̺ = {̺ 1 , ̺ 2 , ..., ̺ p }, is known as the 'Marginal Contribution to Total Risk' (MCTR), see Menchero etal. (2011) [10] and Baigent (2014) [11]. Note that the MCTR for source i is given by the following expression…”

Section: If We Choose a = N0mentioning

confidence: 99%

“…We consider the period 2013 (Jul-Dec) in Table (11) to demonstrate the procedure of inference on a portfolio constructed solely on equity, considering this as the investment period. The same procedure of inference is carried out as in the case of 'Indices' dataset, the only difference is in terms of the size of the market portfolio is much larger, making the problem considerably "more" ill-posed.…”

Section: National Stock Exchange Of India Datamentioning

confidence: 99%

“…Note that from table (10), the size of the portfolio constructed under the proposed weights utilizes 10% of the market.We now proceed to examine the stocks common to both portfolios. For a stock with higher CCTR that is, P[ζ > 0] included in the portfolio constructed using the Ledoit and Wolf weights, presents an even higher P[ζ > 0] in the portfolio constructed using proposed weights as shown in Table (11) which provides a major point of difference between the two portfolios, apart from the significant difference in portfolio size. The posterior summary statistics for CCTR of 6 stocks over the two periods are presented in tables (8,9).…”

Section: National Stock Exchange Of India Datamentioning

confidence: 99%

See 4 more Smart Citations

Regularizing Portfolio Risk Analysis: A Bayesian Approach

Das¹,

Halder²,

Dey³

2016

Methodol Comput Appl Probab

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It is important for a portfolio manager to estimate and analyse 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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Section: Posterior Distribution Of the Portfolio Covariance Matrixmentioning

confidence: 99%

Section: National Stock Exchange Of India Datamentioning

confidence: 99%