The Birth of Insurance Contracts - The Ataturk Institute for Modern ...

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cost characteristics. Proposition 2, which is proven in Appendix B, follows. Proposition 2 If the sea loan sustains all the allocations in the core under hidden information, the commenda supports the corresponding allocations under full information. 2.6 Optimal Risk-sharing with k1 > k From the observation that debt-like sea loans and equity-like commenda contacts are corner so- lutions when the venture is highly costly and risky, it follows that a well-endowed entrepreneur will not raise funds for such a venture in whole through either of these contracts. Rather, he will optimally finance part of the costly and risky venture himself, bear the liability of loss for the corresponding part, and resort to limited-liability sea loans or commenda contracts for the remaining part, thereby effectively receiving less insurance against the marine risk. In other words, the model delivers an optimal capital structure where inside equity held by the merchant, debt-like sea loans and outside-equity-like commenda contracts coexist. Proposition 3 If the venture is highly risky and costly, the optimal event-contingent allocation of consumption when k1 > k can be attained by letting the merchant finance part of the venture, φ ∗ ∈ (0, 1) and raising the remaining capital, τ ∗ = − (1 − φ ∗ ) k, through a debt-like sea loan or an equity-like commenda, one or the other depending on the information structure. This result is novel in the literature. For the last fifty years or so Corporate Finance has focused on various departures from the Modigliani and Miller’s theorem that make capital structure relevant to a firm’s value under the assumption that economic agents are risk neutral (Harris and Raviv, 1991). Some models take the form of the securities (contracts) issued by the firm, mainly debt and equity, as exogenously given; others endogenously derive the characteristics of debt and equity in terms of cash flows and/or control rights; but all predict a maximum inside participation rate to the firms’ investments (φ = 1 in the model). Since contracts are chosen or designed exclusively to minimize the costs associated with agency relations, information asym- metries, signaling, incomplete contracting or transacting, the best an entrepreneur can do is to finance the project he manages in its entirety, unless restricted to rely on external funds because 14
of budget constraints (k1 = 0). However, the evidence indicates that both medieval merchants and today’s entrepreneurs/firms are risk averse and resort to external funds before investing 100 percent of their own wealth. 11 A notable exception is Leland and Pyle (1977). They exploit managerial risk aversion to obtain a signaling equilibrium in which entrepreneurs retain a higher fraction of (inside) equity than they would hold in the absence of adverse selection, but still rely on external funds because of diversification. Leland and Pyle thus rationalize the observed fact that entrepreneurs self-finance only a part of their ventures, but do not address the fundamental question of why debt and equity are designed the way they are. 2.6.1 Graphical analysis The proof of proposition (3) is developed in appendix 3. Lets here adressed it graphically. When the merchant is initially endowed with k1 > k > 0, there are more resources in the economy than when he does not have any initial wealth, k1 = 0, so that the corresponding Edgeworth Box is larger. Figure 5 represents both the Edgeworth Boxes for parameters λk1=0 (with k1 = 0) and λk1>k (with k1 > k > 0), although for ease of exposition the noncontractible area is not depicted under the hidden information scenario. 12 Because of DARA, the indifference curves of the merchant become flatter as he receives more initial wealth, while those of the financier are unaltered by any increase of the merchant’s wealth. Therefore, the contract curve for interior points for parameters λk1>k lies below the contract curve for λk1=0. The previous subsections shows that the contract curve for k1 = 0 can be represented by CCλk 1 =0 in figure 5 when a venture is risky and costly and both agents are risk-averse. Therefore, the contract curve for k1 > k will be characterized by CCλk 1 >k in figure 5. 11 For medieval evidence, see section 3 below. For today’s evidence, see Zingales (2000) and (1995, table IV, p. 1439). 12 Alternatively, figure 5 can be thought of as representing a face of the Edgeworth Boxes for a given value of c2(¯x) under full information. In this case there are three events for both agents and the contract curve must be represented in a 3-dimensional Edgeworth Box. However, as we are looking at a binding restriction for only one event, we can abstract from the optimal relationship between c2(¯x) and c2(x) given by the Kuhn-Tucker conditions of program 3 (in the appendix) and draw the optimal allocation in an intuitive 2-dimensional Edgeworth Box with coordinates ci(y), ci(x). 15
Page 1 and 2: 1 Introduction The Birth of Insuran
Page 3 and 4: of hostile people, and to the inves
Page 5 and 6: utility from second-date consumptio
Page 7 and 8: in his enterity. In return for some
Page 9 and 10: ci(s) ≥ 0 ∀i, ∀s (3) ci(s)
Page 11 and 12: financier for the entire capital re
Page 13: power U 2. 10 It is worth to note,
Page 17 and 18: project is highly costly and risky
Page 19 and 20: parties commit part of their wealth
Page 21 and 22: commenda) because the high risk and
Page 23 and 24: the agents’ ability to diversify,
Page 25 and 26: It is proved below that at a soluti
Page 27 and 28: Show that dc2(y) d(k2−k) = −
Page 29 and 30: Program 3 is concave so that Kuhn-T
Page 31 and 32: When the entrepreneur lacks the wea
Page 33 and 34: [10] González de Lara, Y. “The S
Page 35 and 36: FIGURE 1 (Hidden Information, k1 =
Page 37: c1(y) ✛ FIGURE 5 (k1 > k, Two-sid

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