# LUP Student Papers

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### Comparing Mean-Variance and CVaR optimal portfolios, assuming bivariate skew-t distributed returns

(2005)
Department of Economics
Abstract
In this paper we are building portfolios consisting of the
S&P 500 index and a T-bond index. The portfolio weights are
chosen in such a way that the risk for the portfolio is minimized.
To be able to minimize the risk for a portfolio, we first have to
specify how to measure the portfolios risk. There are several ways
of measuring the risk for a portfolio. In this paper we are
investigating how the portfolio weights differ whether we measure
the portfolios risk by the variance or by the Conditional
Value-at-Risk (CVaR). To measure the risk for the portfolios we
first estimated a two-dimensional density function for the returns
of the assets, using a skew student-t distribution. The time horizon
for each portfolio was one week. The result... (More)
In this paper we are building portfolios consisting of the
S&P 500 index and a T-bond index. The portfolio weights are
chosen in such a way that the risk for the portfolio is minimized.
To be able to minimize the risk for a portfolio, we first have to
specify how to measure the portfolios risk. There are several ways
of measuring the risk for a portfolio. In this paper we are
investigating how the portfolio weights differ whether we measure
the portfolios risk by the variance or by the Conditional
Value-at-Risk (CVaR). To measure the risk for the portfolios we
first estimated a two-dimensional density function for the returns
of the assets, using a skew student-t distribution. The time horizon
for each portfolio was one week. The result shows that the weights
in the S&P 500 index always were lower for the portfolios
constructed by minimizing CVaR. The reason for this is that the
distribution for the returns of the S&P 500 index exhibits a
negative skewness and has fatter tails than the returns of the
T-bond index. This fact isn't taken care of when choosing weights
according to the variance criteria, which leads to an
underestimation of the risk associated with the S&P 500 index.
The underestimation of the risk leads to an overestimation of the
optimal weights in the S&P 500 index. (Less)
Please use this url to cite or link to this publication:
author
supervisor
organization
year
type
H1 - Master's Degree (One Year)
subject
keywords
mean-variance, CVaR, portfolios, skew-t, Economics, econometrics, economic theory, economic systems, economic policy, Nationalekonomi, ekonometri, ekonomisk teori, ekonomiska system, ekonomisk politik
language
English
id
1335470
date added to LUP
2005-09-21
date last changed
2010-08-03 10:53:12
```@misc{1335470,
abstract     = {In this paper we are building portfolios consisting of the
S&P 500 index and a T-bond index. The portfolio weights are
chosen in such a way that the risk for the portfolio is minimized.
To be able to minimize the risk for a portfolio, we first have to
specify how to measure the portfolios risk. There are several ways
of measuring the risk for a portfolio. In this paper we are
investigating how the portfolio weights differ whether we measure
the portfolios risk by the variance or by the Conditional
Value-at-Risk (CVaR). To measure the risk for the portfolios we
first estimated a two-dimensional density function for the returns
of the assets, using a skew student-t distribution. The time horizon
for each portfolio was one week. The result shows that the weights
in the S&P 500 index always were lower for the portfolios
constructed by minimizing CVaR. The reason for this is that the
distribution for the returns of the S&P 500 index exhibits a
negative skewness and has fatter tails than the returns of the
T-bond index. This fact isn't taken care of when choosing weights
according to the variance criteria, which leads to an
underestimation of the risk associated with the S&P 500 index.
The underestimation of the risk leads to an overestimation of the
optimal weights in the S&P 500 index.},
author       = {Wohlfart, Peter and Nossman, Marcus},
keyword      = {mean-variance,CVaR,portfolios,skew-t,Economics, econometrics, economic theory, economic systems, economic policy,Nationalekonomi, ekonometri, ekonomisk teori, ekonomiska system, ekonomisk politik},
language     = {eng},
note         = {Student Paper},
title        = {Comparing Mean-Variance and CVaR optimal portfolios, assuming bivariate skew-t distributed returns},
year         = {2005},
}

```