### 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:
http://lup.lub.lu.se/student-papers/record/1335470

- author
- Wohlfart, Peter and Nossman, Marcus
- supervisor
- organization
- year
- 2005
- 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}, }