William T. Shaw
Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution.
Tue, 03/01/2011 - 16:01 — SomNambulAuthors: William T. Shaw
Subjects: Portfolio Management
AbstractWe show how to reduce the problem of computing VaR and CVaR with Student T
return distributions to evaluation of analytical functions of the moments. This
allows an analysis of the risk properties of systems to be carefully attributed
between choices of risk function (e.g. VaR vs CVaR); choice of return
distribution (power law tail vs Gaussian) and choice of event frequency, for
risk assessment. We exploit this to provide a simple method for portfolio
optimization when the asset returns follow a standard multivariate T
distribution.Monte Carlo Portfolio Optimization for General Investor Risk-Return Objectives and Arbitrary Return Distributions: a Solution for Long-only Portfolios.
Tue, 08/24/2010 - 15:02 — SomNambulAuthors: William T. Shaw
Subjects: Portfolio Management
AbstractWe develop the idea of using Monte Carlo sampling of random portfolios to
solve portfolio investment problems. In this first paper we explore the need
for more general optimization tools, and consider the means by which
constrained random portfolios may be generated. A practical scheme for the
long-only fully-invested problem is developed and tested for the classic QP
application.A Model of Returns for the Post-Credit-Crunch environment.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: William T. Shaw
Subjects: Statistical Finance
AbstractThe market events of 2007-2009 have reinvigorated the search for realistic
return models that capture greater likelihoods of extreme movements. In this
paper we model the medium-term log-return dynamics in a market with both
fundamental {\it and technical} traders. This is based on a Poisson trade
arrival model with variable size orders. With simplifications we are led to an
SDE mixing {\it both arithmetic and geometric} Brownian motions, whose solution
is an given by a class of integrals of exponentials of Brownian motions, in
forms considered by Yor and collaborators.
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