# Goal

In a prior post we explored the impact of earnings volatility on P&C (re)insurers stock valuation. The analysis concluded that earnings volatility - as measured by 20 quarter earnings coefficient of variation worse than sector median - is a significant driver of valuation when included in a price-to-book value versus prospective return on equity regression framework.

In this post, we will explore:

- Is price-to-tangible book value a better metric to estimate than price-to-book value?
- Is the spread of prospective ROE over a company’s cost of equity capital a better variable to use than just ROE?

# Data

The table below summarizes the data required for this analysis, which is the same as used in the prior post. 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 | Cost of Equity | Spread | 20 qrt EPS CV |

P&C_Comm | Allianz SE | 103.5 | 1.35x | 1.69x | 10.4% | 10.2% | 0.2% | 16.1% |

P&C_Comm | The Chubb Corporation | 69.0 | 1.37x | 2.45x | 8.9% | 7.9% | 1.0% | 28.9% |

P&C_Comm | American International Group, Inc. | 53.4 | 0.74x | 0.74x | 5.5% | 10.3% | -4.8% | 164.9% |

P&C_Comm | Zurich Financial Services AG | 46.1 | 1.49x | 2.05x | 10.2% | 10.1% | 0.1% | 35.0% |

P&C_Comm | The Travelers Companies, Inc. | 36.9 | 1.56x | 1.9x | 9.7% | 8.3% | 1.4% | 25.5% |

P&C_Comm | The Hartford Financial Services Group, Inc. | 19.9 | 1.16x | 1.2x | 8.0% | 9.0% | -1.0% | 27.7% |

P&C_Comm | Fairfax Financial Holdings Limited | 15.3 | 1.25x | 2.52x | 11.4% | 5.3% | 6.1% | 334.2% |

P&C_Comm | CNA Financial Corporation | 14.4 | 1.18x | 1.2x | 6.9% | 8.4% | -1.5% | 47.6% |

P&C_Comm | Cincinnati Financial Corporation | 12.2 | 1.62x | 1.62x | 6.6% | 8.0% | -1.4% | 25.9% |

P&C_Comm | XL Group Plc. | 9.3 | 0.93x | 1.2x | 9.0% | 9.5% | -0.5% | 218.4% |

P&C_Comm | Old Republic International Corporation | 5.5 | 1.16x | 1.2x | 9.2% | 7.9% | 1.3% | 43.7% |

P&C_Comm | The Hanover Insurance Group | 4.4 | 1.47x | 1.57x | 10.0% | 7.8% | 2.2% | 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 sector. This summary data by sector is used below to identify which companies are “high” or “low” volatility companies.

Summary of input data by sector | |||||||

Sector | # of companies | Median P:B Ratio | Median P:TBV Ratio | Median 2018 ROAE | Median Cost of Equity | Median Spread | Median EPS CV |

APAC | 12 | 1.5x | 2x | 10.9% | 11.6% | -1.3% | 62.3% |

London_Spec | 3 | 2.2x | 2.4x | 11.9% | 7.1% | 3.5% | 37.5% |

P&C_Comm | 12 | 1.3x | 1.6x | 9.1% | 8.4% | 0.2% | 39.4% |

P&C_FL | 5 | 1.4x | 1.7x | 15.2% | 13.9% | 3.0% | 88.7% |

P&C_LargeSpec | 11 | 1.6x | 1.8x | 9.1% | 8.9% | -1.2% | 47.1% |

P&C_Pers | 11 | 1.7x | 2x | 8.2% | 8.0% | 1.2% | 48.9% |

P&C_Reins | 12 | 1.1x | 1.2x | 9.1% | 8.4% | -0.4% | 120.0% |

P&C_SmallSpec | 9 | 1.4x | 1.5x | 6.7% | 9.4% | -2.2% | 70.2% |

WEur_Large | 9 | 1.4x | 2x | 10.4% | 12.1% | 0.1% | 35.0% |

WEur_Mid | 19 | 1.8x | 2.3x | 11.6% | 10.6% | 2.0% | 33.2% |

# Baseline model

We will use the same baseline model as in the prior post - price-to-book value vs. prospective ROE.

# Alternative models

The alternative models use price-to-tangible book ratio instead of price-to-book value. One model uses prospective ROE (same as baseline), while one uses spread of ROE over estimated cost of equity. The cost of equity is estimated using a CAPM-style methodology. The logic is that investors should more highly value companies that are able to earn their cost of equity, so explicitly incorporating cost of equity should improve our model. Of course estimating cost of equity is impossible and a CAPM-style model is hardly adequate…but that discussion is for another time.

However, that is not the case when using this data set. Neither of the alternative models perform better than the baseline model. The table below shows the Bayesian r-squared values for each model. The baseline model has a higher r-squared in most sectors. The model that uses tangible book value and ROE produces similar results as the baseline model. The TBV and spread model does not perform as well as the other two models.

Comparison of Bayesian R2 by model | |||

Sector | Baseline | P:TBV | P:TBV vs. Spread |

APAC | 74% | 41% | 26% |

London_Spec | 38% | 59% | 20% |

P&C_Comm | 16% | 36% | 36% |

P&C_FL | 30% | 32% | 26% |

P&C_LargeSpec | 3% | 4% | 6% |

P&C_Pers | 46% | 39% | 24% |

P&C_Reins | 5% | 8% | 6% |

P&C_SmallSpec | 29% | 38% | 20% |

WEur_Large | 92% | 83% | 61% |

WEur_Mid | 78% | 75% | 62% |

# Conclusion

Using price-to-tangible book value produces similar results as using price-to-book value. It is worth further exploring how each model has performed over time.

Based on this data, using spread over cost of equity instead of ROE does not improve model performance. Additionally, cost of equity is an another data element that would need to be collected in order to perform back-testing.