# The Entropic Linkage between Equity and Bond Market Dynamics

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods (Entropic Yield Curve)

#### 2.1. Entropic Yield Curve Initial Derivation

#### 2.2. Entropic Yield Curve, Kullback–Leibler Divergence, and the Implied Information Processing Rate

#### 2.3. The Entropic Yield Curve vs. the Nelson–Siegel Specification

_{2}) produced most of the typical shapes of the yield curve as seen in the reproduction below. This parameter had no true economic, financial or other interpretation, other than its demonstrated utility in adjusting the curve to fit those observed in reality.

_{2}) has an equivalent representation (in terms of function) in the Entropic Yield Curve. This equivalent parameter is the ratio at the heart of this paper R/C. As the values of R/C vary from 1.9 to 0.1 (bottom to top) the resulting curves appear nearly identical to the variety and style produced by varying Nelson–Siegel’s nondescript parameter as seen below in Figure 3 using the parameter settings in Table 1:

#### 2.4. The Various Regimes of the Entropic Yield Curve

#### 2.5. Simulation: Level of R/C vs. Variance of R/C

#### 2.6. Harbinger of the Bears

…that ratio of these rates R/C or (CC_{A}/CC_{L}) can determine different regimes of normal and “anomalous” behaviors for security returns”. As this ratio evolves over a continuum of values, security returns can be expected to go through phase transitions between different types of behavior. These dramatic phase transitions can occur even when the underlying information generation mechanism is unchanged. Additionally when the information arrival and processing rates are assumed to fluctuate independently and normally, the resulting ratio (CC_{A}/CC_{L}) is shown to be Cauchy distributed and thus fat tailed…—Edgar Parker [8]

## 3. Results

_{1}, and σ all equal to 1 and the long term factor B

_{0}= 30 year rate. R is then estimated by minimizing the RMSE of the estimated (1, 3, 6) monthly yield rates, and (1, 2) year yields rates vs. the corresponding true yield rates. See the Supplementary Materials for a copy of the excel file with the macro used to estimate R/C. More precise curve fitting methods such as those commonly used for Nelson–Siegel (and other models) could be utilized, but this simple method is sufficient for the purposes of the demonstration that follows:

## 4. Discussions

## Supplementary Materials

## Acknowledgments

## Conflicts of Interest

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R | C | σ | C_{1} | B_{0} |
---|---|---|---|---|

1.9 to 0.1 | 1 | 1.1 | 0.9 | 2 |

Time Period | Mean | Variance |
---|---|---|

Total (1990–2016) | 0.10 | 267.61 |

I | 3.41 | 0.41 |

II | −56.78 | 1097.03 |

III | 3.88 | 0.35 |

IV | −24.35 | 1302.45 |

V | 4.07 | 0.10 |

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**MDPI and ACS Style**

Parker, E. The Entropic Linkage between Equity and Bond Market Dynamics. *Entropy* **2017**, *19*, 292.
https://doi.org/10.3390/e19060292

**AMA Style**

Parker E. The Entropic Linkage between Equity and Bond Market Dynamics. *Entropy*. 2017; 19(6):292.
https://doi.org/10.3390/e19060292

**Chicago/Turabian Style**

Parker, Edgar. 2017. "The Entropic Linkage between Equity and Bond Market Dynamics" *Entropy* 19, no. 6: 292.
https://doi.org/10.3390/e19060292