Cornish-Fisher Expansion and Value-at-Risk method in application to risk management of large portfolios
Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
One of the major problem faced by banks is how to manage the risk
exposure in large portfolios. According to Basel II regulation banks
has to measure the risk using Value-at-Risk with confidence level 99%.
However, this regulation does not specify the way to calculate Valueat-
Risk. The easiest way to calculate Value-at-Risk is to assume that
portfolio returns are normally distributed. Altough, this is the most
common way to calculate Value-at-Risk, there exists also other methods.
The previous crisis shows that the regular methods are unfortunately
not always enough to prevent bankruptcy. This paper is devoted to
compare the classical methods of estimating risk with other methods
such as Cornish-Fisher Expansion (CFVaR) and assuming generalized
hyperbolic distribution. To be able to do this study, we estimate the risk
in a large portfolio consisting of ten stocks. These stocks are chosen from
the NASDAQ 100-list in order to have highly liquid stocks (bluechips).
The stocks are chosen from different sectors to make the portfolio welldiversified.
To investigate the impact of dependence between the stocks
in the portfolio we remove the two most correlated stocks and consider
the resulting eight stock portfolio as well. In both portfolios we put equal
weight to the included stocks.
The results show that for a well-diversified large portfolio none of the
risk measures are violated. However, for a portfolio consisting of only
one highly volatile stock we prove that we have a violation in the classical
methods but not when we use the modern methods mentioned above.
Place, publisher, year, edition, pages
2011. , 94 p.
Financial Mathematics, Value-at-Risk, Expected Shortfall, Cornish-Fisher Expansion, Gaussian distribution, Generalized Hyperbolic distribution
Probability Theory and Statistics Other Mathematics
IdentifiersURN: urn:nbn:se:hh:diva-16274Local ID: IDE1112OAI: oai:DiVA.org:hh-16274DiVA: diva2:442078
Subject / course
2011-05-30, Wigforssallen, Halmstad University, Halmstad, 12:27 (English)
UppsokPhysics, Chemistry, Mathematics
Bordag, Ljudmila A., Professor Dr.
Bordag, Ljudmila, Professor Dr.