# Goal

Prior posts in this series: Part 1, Part 2

In this post, we will test whether using earnings coefficient of variation (CV) as a categorical variable in our regression improves the model performance. Specifically, we will split earnings CVs by company into buckets (quartiles) and build a hierarchical regression model with a slope parameter that varies by earnings CV bucket.

# Data

The table below summarizes the data required for this analysis, which is the same as used in the prior posts. This table shows the data for the “P&C Commercial” lines sector, but global data across 10 P&C sectors are used in the analysis.

By company input data - P&C commercial lines | ||||||

Sector | Company | Market Cap ($b) | P:B Ratio | P:TBV Ratio | 2018 ROAE | 20 qrt EPS CV |

P&C_Comm | Allianz SE | 103.5 | 1.35x | 1.69x | 10.4% | 16.1% |

P&C_Comm | The Chubb Corporation | 69.0 | 1.37x | 2.45x | 8.9% | 28.9% |

P&C_Comm | American International Group, Inc. | 53.4 | 0.74x | 0.74x | 5.5% | 164.9% |

P&C_Comm | Zurich Financial Services AG | 46.1 | 1.49x | 2.05x | 10.2% | 35.0% |

P&C_Comm | The Travelers Companies, Inc. | 36.9 | 1.56x | 1.9x | 9.7% | 25.5% |

P&C_Comm | The Hartford Financial Services Group, Inc. | 19.9 | 1.16x | 1.2x | 8.0% | 27.7% |

P&C_Comm | Fairfax Financial Holdings Limited | 15.3 | 1.25x | 2.52x | 11.4% | 334.2% |

P&C_Comm | CNA Financial Corporation | 14.4 | 1.18x | 1.2x | 6.9% | 47.6% |

P&C_Comm | Cincinnati Financial Corporation | 12.2 | 1.62x | 1.62x | 6.6% | 25.9% |

P&C_Comm | XL Group Plc. | 9.3 | 0.93x | 1.2x | 9.0% | 218.4% |

P&C_Comm | Old Republic International Corporation | 5.5 | 1.16x | 1.2x | 9.2% | 43.7% |

P&C_Comm | The Hanover Insurance Group | 4.4 | 1.47x | 1.57x | 10.0% | 72.6% |

The data elements include: current P:B ratio, 2018 prospective ROE, and historical EPS CV over the past 20 quarters. The data used in this analysis is as of December 15, 2017.

The table below summarizes the input data by price-to-book value quartiles. It highlights the relationship between P:B ratio, ROAE, and EPS CV. As the P:B ratio increases, ROAE increases and EPS CV decreases. These are the effects that we want to capture in our model.

Summary of metrics by P:B quartiles | |||||

pb_ntile | # of companies | Median P:B Ratio | Median P:TBV Ratio | Median 2018 ROAE | Median EPS CV |

1 | 26 | 0.9x | 1.1x | 8.4% | 84.3% |

2 | 25 | 1.2x | 1.4x | 9.1% | 51.7% |

3 | 25 | 1.6x | 1.8x | 10.2% | 47.1% |

4 | 25 | 2.7x | 3.1x | 16.7% | 34.7% |

# Current model

The best model from the prior posts used ROE and an indicator variable for EPS volatility. A company was deemed “high” volatility if their 20 quarter EPS CV from greater than the sector median.

The graph below summarizes the current model. You can see that EPS volatility impacts P:B ratio as the gray line (high volatility companies) is lower than the teal line (low volatility companies) in every sector. The magnitude of the impact varies by sector - larger impact for P&C_SmallSpec and smaller for WEur_Large.

# Alternative model

For the alternative model, we use the 20 quarter EPS CV quartile that each company falls into. This provides more granularity on the level of volatility for each company - one of four buckets, instead of just high or low volatility. This allows use to make more useful statements about the cost of volatility on valuation.

The graph below shows the fitted line for each sector, for each earnings volatility quartile. The lowest volatility companies have the highest valuation and the highest volatility companies have the lowest valuation, as expected.

The leave-one-out cross-validation results from the loo package indicate that this alternative model performs better than the current model.

The table below summarizes the impact to P:B ratio by sector of being in each EPS CV quartile, assuming at 10% ROE. The impact is greatest moving from the 4th quartile to the 3rd and from the 2nd to the 1st.

Summary of results by sector - model with EPS CV Quartile Parameter | ||||||||

Fitted P:B at 10% ROE by EPS CV Quartile |
| % Impact on P:B Ratio | ||||||

Sector | 1st quartile | 2nd quartile | 3rd quartile | 4th quartile |
| 1st to 2nd | 2nd to 3rd | 3rd to 4th |

APAC | 1.79x | 1.45x | 1.38x | 1.21x |
| 24% | 5% | 14% |

London_Spec | 1.94x | 1.63x | 1.55x | 1.34x |
| 19% | 5% | 16% |

P&C_Comm | 1.65x | 1.34x | 1.25x | 1.08x |
| 23% | 7% | 16% |

P&C_FL | 1.57x | 1.26x | 1.18x | 1x |
| 24% | 7% | 18% |

P&C_LargeSpec | 1.88x | 1.56x | 1.46x | 1.28x |
| 20% | 7% | 14% |

P&C_Pers | 2x | 1.71x | 1.6x | 1.42x |
| 17% | 7% | 13% |

P&C_Reins | 1.52x | 1.25x | 1.18x | 0.99x |
| 21% | 6% | 19% |

P&C_SmallSpec | 1.94x | 1.64x | 1.53x | 1.36x |
| 18% | 7% | 12% |

WEur_Large | 1.54x | 1.22x | 1.14x | 0.98x |
| 26% | 7% | 17% |

WEur_Mid | 1.7x | 1.41x | 1.29x | 1.13x |
| 21% | 9% | 14% |

# Conclusion

Using EPS CV quartile as a variable in our regression improves the model performance versus a simple binary variable for earnings volatility. This result allows us to make more granular statements about the cost of earnings volatility on a company’s valuation.