Relative valuation of U.S. insurance companies

Abstract

This study examines the accuracy of relative valuation methods in the U.S. insurance industry, using price as a proxy for intrinsic value. The approaches differ in terms of the fundamentals used, the adjustments made to the fundamentals, the use of conditioning variables, and the selection of comparables. Selected findings include the following. First, over the last decade, book value multiples have performed significantly better than earnings multiples in valuing insurance companies. Second, inconsistent with the practice of many analysts, excluding accumulated other comprehensive income from book value worsens rather than improves valuation accuracy. Third, as expected, using income before special items, instead of reported income, improves valuation accuracy, but, surprisingly, excluding realized investment gains and losses does not. An exception to this latter result occurred during the financial crisis, likely due to an increase in “gains trading.” Fourth, conditioning the price-to-book ratio on return on equity significantly improves the valuation accuracy of book value multiples. Finally, while valuations based on analysts’ earnings forecasts outperform those based on reported earnings or book value, the gap between the valuation performance of forecasted EPS and the conditional price-to-book approach was relatively small during the last decade.

Appendices

Appendix 1: Derivation of the residual income model

The value of any financial claim is the present value of expected net flows to the owners of that claim. Accordingly, the value of common equity (equity value or EV) is the present value of expected net flows to common equity holders (net equity flow or NEF):

$$ {\text{EV}}_{0} = \frac{{{\text{E}}[{\text{NEF}}_{1} ]}}{{1 + {\text{r}}_{\text{e}} }} + \frac{{{\text{E}}[{\text{NEF}}_{2} ]}}{{(1 + {\text{r}}_{\text{e}} )^{2} }} + \cdots = \sum\limits_{{{\text{t}} = 1}}^{\infty } {{\text{E}}\left[ {{\text{NEF}}_{\text{t}} } \right]} \times \left( {1 + {\text{r}}_{\text{e}} } \right)^{{ - {\text{t}}}} $$

(7)

where r_e is the cost of common equity capital. Equation (7) assumes that NEF is paid at the end of each year.

Theoretically, to value existing common equity, NEF should only include flows associated with currently existing common shares. However, this definition of NEF is impractical because future dividends and share repurchases will be paid not only to existing shares but also to shares that will be issued in the future. An alternative approach is to assume that all future share issuance transactions will be at fair value; that is, the present value of the cash or other assets or services that will be received when new shares are issued is equal to the present value of the subsequent dividends and share repurchases associated with those shares. Under this assumption, NEF is redefined as the total of all common dividends, common share repurchases, and noncash distributions, minus the fair value of assets or services to be received in exchange for issuance of common shares.

Valuation model (7) can be restated in terms of comprehensive income attributable to common equity (comprehensive income or CI) and the book value of common equity (common equity or CE) by substituting the following relation for NEF_t:

$$ {\text{NEF}}_{\text{t}} = {\text{CI}}_{\text{t}} - {\text{CE}}_{\text{t}} + {\text{CE}}_{{{\text{t}} - 1}} $$

(8)

This relation postulates that changes in common equity are due to either comprehensive income attributable to common equity or to net equity flows. Given the definitions of NEF (discussed above) and comprehensive income (net income plus other comprehensive income), Eq. (8) accounts for essentially all changes in common equity and therefore provides a reasonable approximation for the actual relationship between net equity flows, earnings, and book value.

Substituting Eq. (8) into (7),

$$ {\text{EV}}_{0} = \frac{{{\text{E}}[{\text{CE}}_{0} + {\text{CI}}_{1} - {\text{CE}}_{1} ]}}{{1 + {\text{r}}_{\text{e}} }} + \frac{{{\text{E}}[{\text{CE}}_{1} + {\text{CI}}_{2} - {\text{CE}}_{2} ]}}{{(1 + {\text{r}}_{\text{e}} )^{2} }} + \cdots $$

For each t = 1, 2, …, adding and subtracting r_e × CE_t−1

$$ {\text{EV}}_{0} = \frac{{{\text{E}}[{\text{CE}}_{0} + {\text{CI}}_{1} - {\text{CE}}_{1} + {\text{r}}_{\text{e}} \times {\text{CE}}_{0} - {\text{r}}_{\text{e}} \times {\text{CE}}_{0} ]}}{{1 + {\text{r}}_{\text{e}} }} + \frac{{{\text{E}}[{\text{CE}}_{1} + {\text{CI}}_{2} - {\text{CE}}_{2} + {\text{r}}_{\text{e}} \times {\text{CE}}_{1} - {\text{r}}_{\text{e}} \times {\text{CE}}_{1} ]}}{{(1 + {\text{r}}_{\text{e}} )^{2} }} + \cdots $$

Rearranging terms

$$ {\text{EV}}_{0} = \frac{{{\text{E}}[{\text{CE}}_{0} \times (1 + {\text{r}}_{\text{e}} ) + ({\text{CI}}_{1} - {\text{r}}_{\text{e}} \times {\text{CE}}_{0} ) - {\text{CE}}_{1} ]}}{{1 + {\text{r}}_{\text{e}} }} + \frac{{{\text{E}}[{\text{CE}}_{1} \times (1 + {\text{r}}_{\text{e}} ) + ({\text{CI}}_{2} - {\text{r}}_{\text{e}} \times {\text{CE}}_{1} ) - {\text{CE}}_{2} ]}}{{(1 + {\text{r}}_{\text{e}} )^{2} }} + \cdots $$

And, finally, cancelling offsetting terms, we get

$$ {\text{EV}}_{0} = {\text{CE}}_{0} + \sum\limits_{{{\text{t}} = 1}}^{\infty } {{\text{E}}\left[ {{\text{CI}}_{\text{t}} - {\text{r}}_{\text{e}} {\text{CE}}_{{{\text{t}} - 1}} } \right]} \times \left( {1 + {\text{r}}_{\text{e}} } \right)^{{ - {\text{t}}}} $$

(9)

That is, equity value is equal to current book value (CE₀) plus the present value of expected residual income in all future years, where residual income is earnings in excess of the return required by common equity investors given the amount (CE) and cost (r_e) of common equity capital, that is, CI_t − r_e CE_t−1.³⁵

Appendix 2: Constructing trailing four quarters (TFQ) data

In quarterly reports, companies provide income statement data in two formats: quarterly and year-to-date. Before 1995, Compustat collected only the quarterly data. Starting in 1995, both forms of data are available in Compustat. In contrast, companies report quarterly cash flow information using the year-to-date format only. Cash flow data are available since 1988.

I measure most trailing four quarters (TFQ) data as the year-to-date value plus the previous year annual value minus the previous year’s year-to-date value for the same quarter. For the period 1988–1994, this requires that I first estimate the income statement year-to-date values; I do so by aggregating the relevant quarterly data.

For some variables, particularly those related to per share calculations, the process of calculating TFQ data is more complicated. For example, to calculate the weighted average shares outstanding, the data have to be adjusted with respect to stock splits and stock dividends as well as for the fraction of the period to which they relate (for example, year-to-date data for the third quarter have to by multiplied by ¾ before applying the TFQ calculation).