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Crisis risk prediction with concavity from Polymodel

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  • 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.

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


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  • 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].
     | Show Table
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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%
     | Show Table
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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
     | Show Table
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