# A New Measure of Market Inefficiency

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## Abstract

**:**

## 1. Introduction

## 2. When Are Returns “Excessive” or “Abnormal”?

#### ETR as a Stochastic Variable

## 3. ETR and Measures of Relative Inefficiency between Agents

**Definition**

**1.**

## 4. A New Measure of Market Inefficiency

**Definition**

**2.**

## 5. Applying the Inefficiency Matrix to Empirical Data

#### 5.1. Artificial Financial Market

#### 5.1.1. Characterization of Efficient Markets

#### 5.1.2. Characterisation of Inefficient Markets

#### 5.2. Experimental Markets

## 6. Applications to Real-World Commercial Stock Markets

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Benink and Bossaerts (2001) have applied the work of Hayek and related Neo-Austrian theory specifically to financial markets. |

2 | For a recent discussion of these issues, see Pastor and Veronesi (2009). |

3 | A related notion—the return gap—was considered in Kacperczyk et al. (2008) in the context of measuring mutual fund performance. |

4 | Of course, we are here neglecting considerations of any costs, such as trading costs, information costs etc. |

5 | In the case of a market with fixed trading periods then one would be updating ETR every trading period. |

6 | In the context of entire markets it has been suggested in Farmer and Lo (1999) that “relative” efficiency of markets is a more useful notion than that of absolute efficiency. |

7 | Details can be found in Benink et al. (2010). |

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**Figure 1.**Histogram of ETR for 100 (90, 10) traders (

**top**) and Graph of ${I}_{ij}(t,0)$ for a fixed random subgroup of 50 noise traders in a homogeneous market (

**bottom**).

**Figure 2.**Histogram of excess profits for 50 (90, 10) traders and 50 (50, 50) traders after 3001 ticks (

**top**) and graph of ${I}_{ij}(t,0)$ for markets with 50 $j=(50,50)$ traders and 50 $i=(100-x,x)$ traders. In the legend, 50:65, for example, corresponds to a market with 50 noise traders and 50 (65:35) traders.

**Figure 3.**Inefficiency ${I}_{ij}(t,0)$ for two agent groups in the in-sample (first half) set. On the (

**top**), two randomly chosen groups and on the (

**bottom**) the decile of agents with the highest ETR against the rest of the market.

**Figure 4.**Inefficiency ${I}_{ij}(t,0)$ for two agent groups in the out-of-sample (second half) set. On the (

**top**), two randomly chosen groups and on the (

**bottom**) the decile of agents with the highest ETR against the rest of the market.

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**MDPI and ACS Style**

Stephens, C.R.; Benink, H.A.; Gordillo, J.L.; Pardo-Guerra, J.P.
A New Measure of Market Inefficiency. *J. Risk Financial Manag.* **2021**, *14*, 263.
https://doi.org/10.3390/jrfm14060263

**AMA Style**

Stephens CR, Benink HA, Gordillo JL, Pardo-Guerra JP.
A New Measure of Market Inefficiency. *Journal of Risk and Financial Management*. 2021; 14(6):263.
https://doi.org/10.3390/jrfm14060263

**Chicago/Turabian Style**

Stephens, Christopher R., Harald A. Benink, José Luís Gordillo, and Juan Pablo Pardo-Guerra.
2021. "A New Measure of Market Inefficiency" *Journal of Risk and Financial Management* 14, no. 6: 263.
https://doi.org/10.3390/jrfm14060263