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The Relationship between the US Economy’s Information Processing and Absorption Ratios: Systematic vs Systemic Risk^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- AR = Absorption Ratio
- N = number of assets
- n = number of eigenvectors in the numerator of the absorption ratio
- ${\sigma}_{{E}_{i}}^{2}$ variance of the i-th eigenvector
- ${\sigma}_{{A}_{i}}^{2}$ variance of the j-th asset.

_{1}and σ are adjustment constants as described in Burnashev [8] and Parker [6], respectively. Burnashev’s error exponent p determines the relative influence of the true distribution compared to the error distribution in the entropic yield curve, as explained in Parker [6].

## 3. Results

#### 3.1. AR Uses and Performance as Described by Kritzman et al.

“…1. Most significant U.S. stock market drawdowns were preceded by spikes in the absorption ratio.2. Stock prices, on average, depreciated significantly following spikes in the absorption ratio and, on average, appreciated significantly in the wake of sharp declines in the absorption ratio.3. The absorption ratio was a leading indicator of the U.S. housing market bubble.4. The absorption ratio systematically rose in advance of market turbulence.5. Important milestones throughout the global financial crisis coincided with shifts in the absorption ratio…”.Kritzman et al. [5], p. 113

#### 3.2. R/C and Polycyclic Portfolio Rebalancing

#### Theoretical and Practical Limitations of Traditional Regime Based Strategies

#### 3.3. The R/C Model and Polycyclic Portfolio Rebalancing (PPR)

#### 3.4. Polycyclic Portfolio Rebalancing (PPR) using R/C and the Variance of R/C over Financial Cycles

_{A}/CC

_{L}) approaches 1.00, the behavior of the information processing variable R/C transitions from a normally distributed variable to a Cauchy distributed variable. This would imply that as R/C approaches 1.00, the variance of R/C should also experience a transition to more extreme values.) Just as Kritzman [5] cautioned for AR, R/C triggers should be seen as more of a “near necessary condition for a significant drawdown, just not a sufficient condition”. The R/C measure indicates the high probability and not the certainty of a market decline, despite the impressive performance indicated in Figure 4.

#### 3.5. Simple Example Using the R/C-Cycle Systematic Risk Triggers (Bear Market Emergence)

#### 3.6. Summary of the Tradeoffs between the Example Triggers

## 4. Discussion

#### 4.1. AR and R/C Strengths and Weaknesses

#### 4.2. The Combined use of AR and R/C to Mitigate Systemic and Systematic Risks

## Supplementary Materials

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Trigger Level 3: (Bear Market Emergence Signals: 1/4/1988 through 6/18/2018). Activated 50 total days before 3/24/2000 SP500 peak and 43 total days before 10/9/2007 SP500 peak (total days indicates nontrading days included); Logic: R/C <1.02 and VAR(R/C) > 11 times the average variance of R/C in a 10-day window.

**Figure 5.**Trigger Level 1: (Bear Market Emergence Signals: 1/4/1988 through 6/18/2018). Began 2 years, 5 months or 882 total days before 3/24/2000 SP500 peak (Includes nontrading days); Began 2 years, 3.5 months or 834 total days before 10/9/2007 SP500 peak (Includes nontrading days); Logic: R/C <1.065 and VAR(R/C) > 0.5 times the average variance of R/C in a 10-day window.

**Figure 6.**Portfolio Adjustment at Trigger Level 1: Begin exponential increasing shift of portfolio from Equity to Fixed (Most shift occurs in later periods).

**Figure 7.**Trigger Level 2: (Bear Market Emergence Signals: 1/4/1988 through 6/18/2018). Began 1 years, 5.3 months or 533 days before 3/24/2000 SP500 peak; Began 1 years, 7.9 months or 603 days before 10/9/2007 SP500 peak; Logic: R/C <1.065 and VAR(R/C) > 4 times the average variance of R/C in a 10-day window.

**Figure 8.**Portfolio Adjustment at Trigger Level 2: Begin exponential increasing shift of portfolio from Equity to Fixed (Most shift occurs in later periods).

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## Share and Cite

**MDPI and ACS Style**

Parker, E. The Relationship between the US Economy’s Information Processing and Absorption Ratios: Systematic vs Systemic Risk. *Entropy* **2018**, *20*, 662.
https://doi.org/10.3390/e20090662

**AMA Style**

Parker E. The Relationship between the US Economy’s Information Processing and Absorption Ratios: Systematic vs Systemic Risk. *Entropy*. 2018; 20(9):662.
https://doi.org/10.3390/e20090662

**Chicago/Turabian Style**

Parker, Edgar. 2018. "The Relationship between the US Economy’s Information Processing and Absorption Ratios: Systematic vs Systemic Risk" *Entropy* 20, no. 9: 662.
https://doi.org/10.3390/e20090662