dorsal/arxiv
View SchemaLeptokurtic Portfolio Theory
| Authors | Robert Kitt, Jaan Kalda |
|---|---|
| Categories | |
| ArXiv ID | physics/0504122 |
| URL | https://arxiv.org/abs/physics/0504122 |
| DOI | 10.1140/epjb/e2006-00062-8 |
| Journal | Eur. Phys. J. B 50, 141-145 (2006) |
Abstract
The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurtic, because it minimises the effects from "fat tails" of returns. The leptokurtic portfolio theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the "noise kernel" -- an ellipsoidal cloud of points in the space of asset returns. The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return are accepted for investors as normal fluctuations. The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America, Europe and Pacific total return stock indices.
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"abstract": "The question of optimal portfolio is addressed. The conventional Markowitz\nportfolio optimisation is discussed and the shortcomings due to non-Gaussian\nsecurity returns are outlined. A method is proposed to minimise the likelihood\nof extreme non-Gaussian drawdowns of the portfolio value. The theory is called\nLeptokurtic, because it minimises the effects from \"fat tails\" of returns. The\nleptokurtic portfolio theory provides an optimal portfolio for investors, who\ndefine their risk-aversion as unwillingness to experience sharp drawdowns in\nasset prices. Two types of risks in asset returns are defined: a fluctuation\nrisk, that has Gaussian distribution, and a drawdown risk, that deals with\ndistribution tails. These risks are quantitatively measured by defining the\n\"noise kernel\" -- an ellipsoidal cloud of points in the space of asset returns.\nThe size of the ellipse is controlled with the threshold parameter: the larger\nthe threshold parameter, the larger return are accepted for investors as normal\nfluctuations. The return vectors falling into the kernel are used for\ncalculation of fluctuation risk. Analogously, the data points falling outside\nthe kernel are used for the calculation of drawdown risks. As a result the\nportfolio optimisation problem becomes three-dimensional: in addition to the\nreturn, there are two types of risks involved. Optimal portfolio for\ndrawdown-averse investors is the portfolio minimising variance outside the\nnoise kernel. The theory has been tested with MSCI North America, Europe and\nPacific total return stock indices.",
"arxiv_id": "physics/0504122",
"authors": [
"Robert Kitt",
"Jaan Kalda"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1140/epjb/e2006-00062-8",
"journal_ref": "Eur. Phys. J. B 50, 141-145 (2006)",
"title": "Leptokurtic Portfolio Theory",
"url": "https://arxiv.org/abs/physics/0504122"
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