# Distributional Bounds for Portfolio Risk with Tail Dependence

Kunio So, Junichi Imai

Research output: Contribution to journalArticle

### Abstract

The present paper proposes a new method for estimating portfolio risk by applying the concept of bounds to a dependence structure. We introduce four tail dependence measures as partial dependence information and derive bounds on the distribution of a non-decreasing function to obtain bounds on risk measures. We show that bounds on risk measures can be tightened significantly in the probability levels with which we are concerned, those for financial risk management. In the present paper, we provide theorems describing the distributional bounds of the proposed method and prove that these bounds are pointwise best-possible bounds. Furthermore, we calculate risk measures, i.e., value at risk and expected shortfall, from empirical return data and compare the effectiveness of the proposed model with that of typical parametric copula models.

Original language English 795-816 22 Methodology and Computing in Applied Probability 17 3 https://doi.org/10.1007/s11009-014-9396-5 Published - 2014 Feb 14

### Fingerprint

Tail Dependence
Risk Measures
Expected Shortfall
Copula Models
Financial Risk
Value at Risk
Dependence Structure
Risk Management
Parametric Model
Partial
Calculate
Theorem

### Keywords

• Copulas
• Fréchet bounds
• Market risks
• Risk management
• Tail dependence

### ASJC Scopus subject areas

• Mathematics(all)
• Statistics and Probability

### Cite this

In: Methodology and Computing in Applied Probability, Vol. 17, No. 3, 14.02.2014, p. 795-816.

Research output: Contribution to journalArticle

@article{b29f81711739405fa85770b86c55246b,
title = "Distributional Bounds for Portfolio Risk with Tail Dependence",
abstract = "The present paper proposes a new method for estimating portfolio risk by applying the concept of bounds to a dependence structure. We introduce four tail dependence measures as partial dependence information and derive bounds on the distribution of a non-decreasing function to obtain bounds on risk measures. We show that bounds on risk measures can be tightened significantly in the probability levels with which we are concerned, those for financial risk management. In the present paper, we provide theorems describing the distributional bounds of the proposed method and prove that these bounds are pointwise best-possible bounds. Furthermore, we calculate risk measures, i.e., value at risk and expected shortfall, from empirical return data and compare the effectiveness of the proposed model with that of typical parametric copula models.",
keywords = "Copulas, Fr{\'e}chet bounds, Market risks, Risk management, Tail dependence",
author = "Kunio So and Junichi Imai",
year = "2014",
month = "2",
day = "14",
doi = "10.1007/s11009-014-9396-5",
language = "English",
volume = "17",
pages = "795--816",
journal = "Methodology and Computing in Applied Probability",
issn = "1387-5841",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - Distributional Bounds for Portfolio Risk with Tail Dependence

AU - So, Kunio

AU - Imai, Junichi

PY - 2014/2/14

Y1 - 2014/2/14

N2 - The present paper proposes a new method for estimating portfolio risk by applying the concept of bounds to a dependence structure. We introduce four tail dependence measures as partial dependence information and derive bounds on the distribution of a non-decreasing function to obtain bounds on risk measures. We show that bounds on risk measures can be tightened significantly in the probability levels with which we are concerned, those for financial risk management. In the present paper, we provide theorems describing the distributional bounds of the proposed method and prove that these bounds are pointwise best-possible bounds. Furthermore, we calculate risk measures, i.e., value at risk and expected shortfall, from empirical return data and compare the effectiveness of the proposed model with that of typical parametric copula models.

AB - The present paper proposes a new method for estimating portfolio risk by applying the concept of bounds to a dependence structure. We introduce four tail dependence measures as partial dependence information and derive bounds on the distribution of a non-decreasing function to obtain bounds on risk measures. We show that bounds on risk measures can be tightened significantly in the probability levels with which we are concerned, those for financial risk management. In the present paper, we provide theorems describing the distributional bounds of the proposed method and prove that these bounds are pointwise best-possible bounds. Furthermore, we calculate risk measures, i.e., value at risk and expected shortfall, from empirical return data and compare the effectiveness of the proposed model with that of typical parametric copula models.

KW - Copulas

KW - Fréchet bounds

KW - Market risks

KW - Risk management

KW - Tail dependence

UR - http://www.scopus.com/inward/record.url?scp=84938952698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938952698&partnerID=8YFLogxK

U2 - 10.1007/s11009-014-9396-5

DO - 10.1007/s11009-014-9396-5

M3 - Article

AN - SCOPUS:84938952698

VL - 17

SP - 795

EP - 816

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 3

ER -