Academic journal article Journal of Risk and Insurance

Solvency Risk and the Tax Sheltering Behavior of Property-Liability Insurers

Academic journal article Journal of Risk and Insurance

Solvency Risk and the Tax Sheltering Behavior of Property-Liability Insurers

Article excerpt

Introduction

Property-liability insurers are major participants in the market for tax-exempt (municipal) bonds. Since tax-exempt bonds almost always yield less than comparable taxable bonds in pretax terms, insurers are faced with the problem of optimally allocating investable funds between taxable and tax-exempt bonds. The allocation will depend on the tax-exempt yield relative to the taxable yield, a well known result in the literature. This article examines this relation between the relative yield of taxable and tax-exempt bonds and the use of tax-exempt bonds by property-liability insurers when solvency risk is explicitly taken into account.

The problem of optimally allocating the investable funds between taxable and tax-exempt securities has been analyzed in a certainty framework by Hendershott and Koch (1980) and Gleeson and Lenrow (1987). Later, Cummins and Grace (1994) extended the analysis to an uncertainty framework, taking premiums and the level of insurer assets as given; they also assume that insurance risks are fully diversifiable, so that expected profit maximization is appropriate. When insurance risks are not fully diversifiable, the allocation between taxable and tax-exempt securities will affect the competitive premium and/or the solvency risk. Hence, treating the premiums as given ignores the effect of the allocation (between taxable and tax-exempt securities) on the premium. This article uses a partial equilibrium framework; we assume that the securities and insurance markets are competitive, allowing the premiums to adjust.

In Hendershott and Koch's certainty model, the insurer invests in tax-exempt bonds whenever the tax-exempt yield exceeds the after-tax yield from taxable bonds and the underwriting losses are matched by income from taxable bonds. In our model, the insurer may optimally refrain from investing in tax-exempt bonds, if the spread between taxable and tax-exempt yields is sufficiently large, even if the tax-exempt yield is greater than the after-tax yield from taxable bonds. However, if the spread between taxable and tax-exempt yields is sufficiently small, the insurer may optimally refrain from investing in taxable bonds, even though the taxable yield is strictly greater than the tax-exempt yield. Cummins and Grace (1994) derive a similar result when insurers are subject to alternative minimum taxes. Our partial equilibrium model shows that the above result is true when the tax function is much simpler.

The Model

To study the insurer's investment choice, we work with a one-period model and make the following assumptions.

Assumption 1: Premiums are collected by the insurer at the beginning of the period and claims are paid at the end of the period. Assumption 1 is based on Smith's (1989) one-period model, which assumes that all underwriting expenses are incurred at the beginning of the period and claims are defined to include claims-adjustment expenses.

Assumption 2: The probability distribution of the claims at the end of the period is log normal. We will use the notation [L.sub.1] for the level of liabilities at the end of the period and the mean and standard deviation of log ([L.sub.1]) will be represented by [micro]-[[Sigma].sup.2]/2 and [Sigma], respectively.(1) The uncertainty in claims, [Sigma], is the only source of uncertainty that has not been eliminated in the portfolio of policies through diversification. The level of assets at the beginning and end of the period will be denoted [A.sub.0] and [A.sub.1], respectively. At the end of the period, if [L.sub.1] [is greater than] [A.sub.1], the insurer is said to be in default.

Assumption 3: The insurer invests in riskless assets only. Restricting the investment to riskless assets simplifies the model and yet allows it to capture the essence of the tax sheltering problem of the insurers. Often insurers use risky assets, such as common stocks and long-term bonds, for tax sheltering. …

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