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doi: 10.3934/jdg.2021027
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Crisis risk prediction with concavity from Polymodel

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

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.

Citation: Yao Kuang, Raphael Douady. Crisis risk prediction with concavity from Polymodel. Journal of Dynamics & Games, doi: 10.3934/jdg.2021027
References:
[1]

B. K. Adhikari and J. E. Hilliard, The VIX, VXO and realised volatility: A test of lagged and contemporaneous relationships, Internat. J. Financial Markets Derivatives, 3 (2014), 222-240.  doi: 10.1504/IJFMD.2014.059637.  Google Scholar

[2]

A. Ang and J. Chen, Asymmetric correlations of equity portfolios, J. Finance Econ., 63 (2002), 443-494.  doi: 10.1016/S0304-405X(02)00068-5.  Google Scholar

[3]

A. Ang and A. Timmermann, Regime changes and financial markets, Ann. Rev. Finance Econ., 4 (2011), 313-337.  doi: 10.3386/w17182.  Google Scholar

[4]

C. Aschwanden, Not even scientists can easily explain p-values, FiveThirtyEight, (2015). Available from: https://web.archive.org/web/20190925221600/https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/. Google Scholar

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L. E. Baum and T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist., 37 (1966), 1554-1563.  doi: 10.1214/aoms/1177699147.  Google Scholar

[6]

C. Brownlees and R. F. Engle, SRISK: A conditional capital shortfall measure of systemic risk, Rev. Financial Stud., 30 (2017), 48-79.  doi: 10.1093/rfs/hhw060.  Google Scholar

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A. S. Cherny, R. Douady and S. A. Molchanov, On measuring hedge fund risk, SSRN Electric J., (2008). doi: 10.2139/ssrn.1113620.  Google Scholar

[8]

R. CumbyS. Figlewski and J. Hasbrouck, Forecasting volatility and correlations with EGARCH models, J. Derivatives, 1 (1993), 51-63.  doi: 10.3905/jod.1993.407877.  Google Scholar

[9]

A. Gil, J. Segura and N. M. Temme, Numerical Methods for Special Functions, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007. doi: 10.1137/1.9780898717822.  Google Scholar

[10]

E. Helleiner, Understanding the 2007–2008 global financial crisis: Lessons for scholars of international political economy, Ann. Rev. Polit. Sci., 14 (2011), 67-87.  doi: 10.1146/annurev-polisci-050409-112539.  Google Scholar

[11]

F. Longin and B. Solnik, Extreme correlation of international equity markets, J. Finance, 56 (2002), 649-676.  doi: 10.1111/0022-1082.00340.  Google Scholar

[12]

D. K. PatroM. Qi and X. Sun, A simple indicator of systemic risk, J. Financial Stabil., 9 (2013), 105-116.  doi: 10.2139/ssrn.1569805.  Google Scholar

[13]

D. Sornette and J. V. Andersen, A nonlinear super-exponential rational model of speculative financial bubbles, Internat. J. Modern Phys. C, 13 (2002), 171-187.  doi: 10.1142/S0129183102003085.  Google Scholar

[14]

R. Tibshirani, Regression shrinkage and selection via the lasso, J. Roy. Statist. Soc. Ser. B., 58 (1996), 267-288.  doi: 10.1111/j.2517-6161.1996.tb02080.x.  Google Scholar

[15]

X. Ye and R. Douady, Systemic risk indicators based on nonlinear PolyModel, J. Risk Financial Manag., 12 (2018). doi: 10.3390/jrfm12010002.  Google Scholar

[16]

H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B Stat. Methodol., 67 (2005), 301-320.  doi: 10.1111/j.1467-9868.2005.00503.x.  Google Scholar

show all references

References:
[1]

B. K. Adhikari and J. E. Hilliard, The VIX, VXO and realised volatility: A test of lagged and contemporaneous relationships, Internat. J. Financial Markets Derivatives, 3 (2014), 222-240.  doi: 10.1504/IJFMD.2014.059637.  Google Scholar

[2]

A. Ang and J. Chen, Asymmetric correlations of equity portfolios, J. Finance Econ., 63 (2002), 443-494.  doi: 10.1016/S0304-405X(02)00068-5.  Google Scholar

[3]

A. Ang and A. Timmermann, Regime changes and financial markets, Ann. Rev. Finance Econ., 4 (2011), 313-337.  doi: 10.3386/w17182.  Google Scholar

[4]

C. Aschwanden, Not even scientists can easily explain p-values, FiveThirtyEight, (2015). Available from: https://web.archive.org/web/20190925221600/https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/. Google Scholar

[5]

L. E. Baum and T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist., 37 (1966), 1554-1563.  doi: 10.1214/aoms/1177699147.  Google Scholar

[6]

C. Brownlees and R. F. Engle, SRISK: A conditional capital shortfall measure of systemic risk, Rev. Financial Stud., 30 (2017), 48-79.  doi: 10.1093/rfs/hhw060.  Google Scholar

[7]

A. S. Cherny, R. Douady and S. A. Molchanov, On measuring hedge fund risk, SSRN Electric J., (2008). doi: 10.2139/ssrn.1113620.  Google Scholar

[8]

R. CumbyS. Figlewski and J. Hasbrouck, Forecasting volatility and correlations with EGARCH models, J. Derivatives, 1 (1993), 51-63.  doi: 10.3905/jod.1993.407877.  Google Scholar

[9]

A. Gil, J. Segura and N. M. Temme, Numerical Methods for Special Functions, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007. doi: 10.1137/1.9780898717822.  Google Scholar

[10]

E. Helleiner, Understanding the 2007–2008 global financial crisis: Lessons for scholars of international political economy, Ann. Rev. Polit. Sci., 14 (2011), 67-87.  doi: 10.1146/annurev-polisci-050409-112539.  Google Scholar

[11]

F. Longin and B. Solnik, Extreme correlation of international equity markets, J. Finance, 56 (2002), 649-676.  doi: 10.1111/0022-1082.00340.  Google Scholar

[12]

D. K. PatroM. Qi and X. Sun, A simple indicator of systemic risk, J. Financial Stabil., 9 (2013), 105-116.  doi: 10.2139/ssrn.1569805.  Google Scholar

[13]

D. Sornette and J. V. Andersen, A nonlinear super-exponential rational model of speculative financial bubbles, Internat. J. Modern Phys. C, 13 (2002), 171-187.  doi: 10.1142/S0129183102003085.  Google Scholar

[14]

R. Tibshirani, Regression shrinkage and selection via the lasso, J. Roy. Statist. Soc. Ser. B., 58 (1996), 267-288.  doi: 10.1111/j.2517-6161.1996.tb02080.x.  Google Scholar

[15]

X. Ye and R. Douady, Systemic risk indicators based on nonlinear PolyModel, J. Risk Financial Manag., 12 (2018). doi: 10.3390/jrfm12010002.  Google Scholar

[16]

H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B Stat. Methodol., 67 (2005), 301-320.  doi: 10.1111/j.1467-9868.2005.00503.x.  Google Scholar

Figure 1.  Graphically Nonlinear Relationship between $ Y $ and $ X $
Figure 2.  Financial Crises
Figure 3.  Concavity in Polymodel v.s. S & P 500 Index (monthly)
Figure 4.  Comparing concavity with its $ 90^{th} $ percentile (monthly)
Figure 5.  Comparing concavity with its $ 80^{th} $ percentile (monthly)
Figure 6.  Concavity in Polymodel v.s. S & P 500 Index (bi-weekly)
Figure 7.  If Concavity Increases v.s. S & P 500 Index (bi-weekly)
Figure 8.  Concavity in Polymodel v.s. Russell 2000 Index (monthly)
Figure 9.  If Concavity Increases v.s. Russell 2000 Index (monthly)
Figure 10.  Crisis Indicator (monthly S & P 500 Index)
Figure 11.  Concavity Strategy (monthly S & P 500 Index)
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].
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].
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%
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%
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
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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