A By-Line Cointegration Analysis of Underwriting Margins and Interest Rates in the Property-Liability Insurance Industry

By Haley, Joseph D. | Journal of Risk and Insurance, December 1995 | Go to article overview

A By-Line Cointegration Analysis of Underwriting Margins and Interest Rates in the Property-Liability Insurance Industry


Haley, Joseph D., Journal of Risk and Insurance


Introduction

The theoretical relationship between interest rates and property-liability insurance underwriting margins is negative. Each of the three most well-known insurance pricing models - the capital asset pricing model, the discounted cash flow model, and the option pricing model - has, as a general result, this negative relationship (Haley, 1993).(1)

Haley (1993) empirically verified that the aggregate underwriting margin for the property-liability insurance industry from 1930 through 1989 was indeed negatively cointegrated with the 90-day Treasury bill yield for new issues (risk-free interest rate).

This article extends the work of Haley by determining whether the cointegrating relationship that was found at the aggregate level also exists at the micro level - that is, for individual lines of insurance coverage. Venezian (1985) reports that individual lines of coverage have profit cycles which differ in length from that of the industry, as well as from each other. Fields and Venezian (1989) show that the relationship between the risk-free interest rate and individual lines of insurance from 1960 through 1985 varies across lines. They caution against treating profit cycles as a singular industry-wide phenomenon, as such treatment would result in aggregation bias.

In general, for an aggregated time series to be integrated of order one - that is, nonstationary and denoted as I(1) - only one component of the aggregation needs to be I(1). It will be shown below that, of the 17 property-liability coverage lines analyzed here, nine are stationary and eight are nonstationary. Three of the nonstationary lines are significantly, negatively cointegrated with the risk-free interest rate, and two lines show weak evidence of a negative cointegrating relationship. The time period of this study, with some variation across lines, is 1949 through 1992. The underwriting profits are for U.S. stock property-liability insurers and were obtained from Best's Aggregates and Averages (A.M. Best, 1949-1992); the interest rate data (90-day Treasury bill yield for new issues) were obtained from the Survey of Current Business (U.S. Department of Economic Analysis, 1949-1992).

This article first very briefly discusses unit root testing and the results of the tests performed on the individual coverage lines. Second, a cointegration analysis is performed with the nonstationary lines and the risk-free interest rate. The final section presents concluding remarks.

Unit Root Testing

In order to make this work a congruent extension of the aggregate results mentioned above, it must be acknowledged that the aggregate underwriting margin is a weighted average of the individual lines. So the underwriting margin of each line of coverage is not the time series to be evaluated for a unit root; rather, what needs to be tested is a series of weighted values from each line. This is seen in equation (1) as

[r.sub.u] = [w.sub.1][r.sub.1] + [w.sub.2][r.sub.2] + ... + [w.sub.i][r.sub.i], (1)

where [r.sub.u] = the aggregate underwriting margin,

[r.sub.i] = the underwriting margin for line i, and

[w.sub.i] = the industry market share of line i.

The market share, [w.sub.i], is computed as earned premiums for line i over total earned premiums for the industry. For the purposes of unit root testing, the [w.sub.i][r.sub.i] time series are used. The series can also be written as

[w.sub.i][r.sub.i] = underwriting profits of line i/total industry earned premiums. (2)

An argument could be made for using written premiums in equation (2) instead of earned premiums. Written premiums, as a cash flow measure, are more immediately sensitive to price changes than earned premiums. Earned premiums, due to the overlapping of policies sold, reflect a weighted average of premium rates for the current year and the preceding year. Earned premiums were chosen because it is the figure reported on the insurer's statement of income, and it was used in the previously cited aggregate calculations. …

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