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Value at Risk in the Presence of the Power Laws
Company: Acta Physica Polonica B
Year Of Publication: 2005
Month Of Publication: July
Pages: 2575-2587
Download Count: 444
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Comment Num: 0
Language: EN
Source:
Who Can Read: Free
Date: 10-28-2006
Publisher: Administrator
Summary
The aim of this paper is to determine the Value at Risk (VaR) of theportfolio consisting of several long positions in risky assets. We considerthe case when the tail parts of distributions of logarithmic returns of theseassets follow the power law of the same degree and the lower tail of associatedcopula C follows the power law of degree 1. We provide the asymptoticformula for Value at Risk and determine the optimal portfolio. We showthat the part of the capital invested in the i-th asset should be equal to theconditional probability that the drop of the value of the i-th asset will besmaller than the others under the condition that the value of the all assetswill be smaller than c times their initial value (c ≪ 1).
Author(s)
Jaworski, Piotr Sign in to follow this author
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