Abstract
We study capital management and investment decisions of a value-maximizing insurance firm with a broad ownership base in a discrete-time setting. We highlight that the valuation measure used to determine the value of the cash flows to shareholders should reflect two economically sound requirements: market-consistency and indifference to idiosyncratic risk. We provide a rigorous construction of this economic valuation measure and use it to derive the optimal capital-management and investment strategies that realize the economic value of the firm. Our objective is to shed light on the controversial question of whether insurers should invest in liquidly-traded risky assets. Decomposing firm value into net tangible value, default option value, and franchise value, we find that whether to take investment risk is optimal or not essentially depends on the tradeoff between the impact of investment risk on the owner’s option to default and on the firm’s franchise value. A variety of numerical examples illustrate how changes in the regulatory and financial environment can result in materially different optimal investment strategies.
Highlights
This paper revisits questions related to the capital and investment strategies of publicly-traded, limited-liability insurance firms with a diffuse shareholder base
Our work shows that if we account for the limited liability when specifying cash flows to shareholders and use the right valuation measure, value-maximizing insurance firms will exhibit widely different optimal behaviors depending on the environment in which they operate
We have studied a dynamic model for a value-maximizing insurance firm that takes decisions on its capital and investment strategies, including the possibility of liquidation
Summary
This paper revisits questions related to the capital and investment strategies of publicly-traded, limited-liability insurance firms with a diffuse shareholder base. Our work shows that if we account for the limited liability when specifying cash flows to shareholders and use the right valuation measure, value-maximizing insurance firms will exhibit widely different optimal behaviors depending on the environment in which they operate. As pointed out in the section embedding our work in the literature, if the valuation rule is not market consistent, it may be optimal to invest in the risky asset even when the value function is concave. Froot (2007) derives the optimal financial strategies of an insurer under a marketconsistent valuation While their model accounts for deadweight cost of capital, it does not contemplate the possibility of firm default, as we do. Our objective is different, some of the valuation measures put forward for valuing insurance contracts coincide with the economic valuation measure advocated in this paper. In particular, Artzner et al (2020) use the concept of ‘‘insurance arbitrage’’ to justify the valuation of insurance liabilities using essentially the same probability measure that we propose.
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