Crisis risk prediction with concavity from Polymodel

Yao Kuang; Raphael Douady

doi:10.3934/jdg.2021027

Article Contents

2022, Volume 9, Issue 1: 97-115. Doi: 10.3934/jdg.2021027

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Crisis risk prediction with concavity from Polymodel

Yao Kuang^1, and
Raphael Douady^2,

1.
State University of New York at Stony Brook, Stony Brook, NY, USA
2.
Sorbonne Economics Center, University Paris 1-Sorbonne, CNRS, France

Received: October 2020

Revised: August 2021

Early access: October 2021

Published: January 2022

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Abstract

Financial crises are an important research topic because of their impact on the economy, businesses, and populations. However, prior research tends to generate reactive systemic risk measures, in the sense that the measure surges after the crisis starts. Few of them succeed in warning of financial crises in advance. In this paper, we first sketch a toy model that produces normal mixture distributions based on a dynamic regime switching model. We derive that the relative concavity among various indices tends to increase before a crisis. Using Polymodel theory, we introduce a measure of concavity as a crisis risk indicator, and test it against known crises observed in the past. We validate this indicator by a trading strategy holding long or short positions on the S & P 500 Index, depending on the indicator value.

Keywords:

Mathematics Subject Classification: 62P05, 62P20, 91G10, 91G15, 91G70.

Citation:

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Figure 1. Graphically Nonlinear Relationship between $ Y $ and $ X $

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Figure 2. Financial Crises

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Figure 3. Concavity in Polymodel v.s. S & P 500 Index (monthly)

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Figure 4. Comparing concavity with its $ 90^{th} $ percentile (monthly)

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Figure 5. Comparing concavity with its $ 80^{th} $ percentile (monthly)

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Figure 6. Concavity in Polymodel v.s. S & P 500 Index (bi-weekly)

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Figure 7. If Concavity Increases v.s. S & P 500 Index (bi-weekly)

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Figure 8. Concavity in Polymodel v.s. Russell 2000 Index (monthly)

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Figure 9. If Concavity Increases v.s. Russell 2000 Index (monthly)

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Figure 10. Crisis Indicator (monthly S & P 500 Index)

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Figure 11. Concavity Strategy (monthly S & P 500 Index)

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Table 1. Sample Indices Factors

Category	Ticker	Description
Equity	SHCOMP Index	SSE Composite Index
Equity	STI Index	Singapore Stock Market Index
Equity	DAX Index	30 Major German Stocks Index
Currency	DXY Index	US Dollar Index
Currency	USDCNY Curncy	USD to Chinese Yuan Exchange
Currency	USDJPY Curncy	USD to Japanese Yen Exchange
Bound & Yield	IRX	US 13 Week Treasury Bill Yield
Bound & Yield	USGG3M Index	US Government 3-Month Bond Yield
Bound & Yield	USGG5YR Index	US Government 5-year Bond Yield
Commodity	BCOMCN Index	Corn
Commodity	BCOMAG Index	Agriculture
Commodity	BCOMNG Index	Natural Gas
Volatility	VXO Index	CBOE S & P 100 Volatility Index
Note: Those factors are referred to in Ye and Douady [15].

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Table 2. Crises List

Price peak month	Price bottom month	Drawdown from peak to trough
June, 1998	August, 1998	15.57%
August, 2000	September, 2002	46.28%
October, 2007	February, 2009	52.56%
May, 2015	September, 2015	8.89%
September, 2018	December, 2018	13.97%
December, 2019	March, 2020	20%

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Table 3. Strategies Annual Statistics (with monthly data)

Annual	log-r (%)	std	Sharpe	r (%)	MDD (%)	Calmar
S & P 500	7.06	0.154	0.457	7.08	52.6	0.135
Concavity	10.57	0.146	0.725	10.62	24.0	0.443

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