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Small Business Economics

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01-06-2013

Optimum pricing of mutual guarantees for credit

Authors: Yoram Kroll, Assaf Cohen

Published in: Small Business Economics | Issue 1/2013

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Abstract

The main finding of this paper is that under financial market impediments and asymmetric information, a mutually guaranteed and correctly schemed and priced insurance credit contract should have an abnormal actuarial profit. Such a contract improves welfare by simultaneously eliminating underinvestment (UI) and overinvestment (OI) and by reducing the probability of the insurer’s ruin. This solution is relevant for mutual credit insurance agencies and international or governmental agencies interested in increasing the value creation of small and medium enterprises that suffer from limited access to equity and debt markets.

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See a review by De Gobbi (2002) and Independent Expert Group reports (2003, 2005) and some recent empirical findings by Columba et al. (2010) and Bartoli et al. (2010).

Methods for measuring the effectiveness of guarantees are given by Riding et al. (2007). The effectiveness of guarantees in India are discussed and analyzed by Suran (2008).

There is a voluminous literature that analyzes the different reasons for such phenomena, for example, Jensen and Meckling (1976), Galai and Masulis (1976), Myers (1977), Myers and Majluf (1984), and Jensen (1986).

Although not within the scope of this paper, one can also assume that the firm selects more than one project at a time and ranks projects by NPV.

This behavior of small firms is consistent with Petersen and Rajan’s (1994) findings that 82 % of SME debt is in the form of bank loans and that, on average, small firms borrow from one bank whereas large firms borrow from three banks.

It can be assumed that the bank knows more through the due-diligence stage in which the bank learns more about the specific borrower. This two-stage lending process can reduce the gap between the information of the bank and the borrower.

Due diligence and milestone lending can improve the knowledge of the bank regarding the expected effort and the ability of the lender to select or pinpoint good quality projects.

Following Stiglitz and Weiss (1981), if the bank faces a surplus of demand for debt over supply of debt at a given interest rate, then, because of the negative effect of high interest on the quality of lenders, the bank may have an incentive to ration debt rather than to increase the interest of debt.

Kroll and Cohen (2000) analyzed these methods as alternative solutions for UI problems.

In the case where the insurer is a mutual guarantee institute (MI) that belongs to a group of borrowers, it is possible that the information of the MI is better than that of the bank.

Note that for costless competitive markets, Eq. (7) can be an equality rather than an inequality.

Adding a cost to the insurer will cause a reduction in the benefits of the credit insurance but will not change the direction of the analysis and the main conclusion.

For example, it is reasonable to assume that “subprime” borrowers devoted less effort in their fight for better prices when they purchased homes with close to 100 % nonrecourse loans.

One can also assume random cash flow in each realization of a future state and then consider the expected cash flow in the realized future state.

Kroll (1984) gives an example of state-contingent stochastic dominance analysis.

Analysis of the option value of a leveraged stock is given originally by Galai and Masulis (1976).

In practice, other welfare and social considerations may also affect these critical values.

An exact analysis of the consideration to join the MI is beyond the scope of this paper.

We assume that, because of competition, the NPV_B of the bank is zero. Therefore, we obtain \( {\text{NPV}} = {\text{NPV}}_{\text{MI}} + {\text{NPV}}_{\text{S}} = 10.1 + 13.8 = 23.9 \).

For example, consider the costless credit insurance (C = 0) contract with β = 100 %, which was in use among the more than 300 “kibbutz” firms in Israel until 1986. As a result, at the end of the eighties, 80 % of the “kibbutz” firms were in default and, later, almost 50 % of the small industrial plants that were owned by the kibbutzim had to be closed. Since 1990, the guarantees have not been without cost, and they cover at most 50 % of the defaulted amount. As a result, since 1990 very few plants in the kibbutzim have defaulted.

Bartoli, F., Ferri, G., & Murro, P. (2010). Bank-firm relations and the role of mutual guarantee institutions during crisis. Working paper on SSRN.

Columba, F., Gambacorta, L., & Misrulli, P. E. (2010). Mutual guarantee institutions and small business finance. Journal of Financial stability, 6, 45–54.CrossRef

De Gobbi, M. S. (2002). Making social capital work: Mutual guarantee societies for artisans. Working Paper, ILO.

Galai, D., & Masulis, W. (1976). The option pricing model and the risk factor of stock. Journal of Financial Economics, 3, 53–81.CrossRef

Ghatak, M., & Guinnane, T. W. (2008). The economics of lending with joint liability: Theory and practice. Journal of Development Economics, 60, 195–228.CrossRef

Independent Expert Group. (2003). Raising EU R&D. A Report to the European Commission.

Independent Expert Group. (2005). Guarantees and Mutual Guarantees. Best Report: To the European Commission.

Jensen, M. (1986). Agency costs of free cash flow, corporate finance and take-overs. American Economic Review, 76, 323–329.

Jensen, M., & Meckling, W. (1976). Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics, 3, 305–360.CrossRef

Kroll, Y. (1984). The analysis of risky investments: A state contingent approach. Journal of Banking & Finance, 8, 509–524.CrossRef

Kroll, Y., & Cohen, A. (2000). Alternative solutions to under-investment and credit rationing. Journal of Business Finance and Accounting, 27, 393–419.CrossRef

Myers, S. (1977). Determinants of corporate borrowing. Journal of Financial Economics, 5, 146–175.CrossRef

Myers, S., & Majluf, J. (1984). Corporate financing and investment decision when firms have information that investors do not have. Journal of Financial Economics, 13, 187–221.CrossRef

Petersen, A. M., & Rajan, R. G. (1994). The benefits of lending relationships: Evidence from small business data. Journal of Finance, 49, 3–37.CrossRef

Riding, A., Madill, J., & Haines, G. (2007). Incrementality of SME loan guarantees. Small Business Economics, 29, 47–61.CrossRef

Stieglitz, J. E. (1990). Peer monitoring credit markets. The World Bank economics review, 4, 351–366.CrossRef

Stiglitz, J. E., & Weiss, A. (1981). Credit rationing in markets with imperfect information. American Economic Review, 71, 393–409.

Suran, B. S. (2008). Leveraging mutual guarantees for gaining financial access: Joint liability groups as collateral substitutes. In K. J. Karmakar (Ed.), Microfinance in India (pp. 409–424). Sage Publications (available also through SSRN).

Zhang, W. (2008). Ex anta moral hazard and repayment performance under group lending. Journal of East Asia Studies, 6, 145–171.

Title: Optimum pricing of mutual guarantees for credit
Authors: Yoram Kroll
Assaf Cohen
Publication date: 01-06-2013
Publisher: Springer US
Published in: Small Business Economics / Issue 1/2013
Print ISSN: 0921-898X
Electronic ISSN: 1573-0913
DOI: https://doi.org/10.1007/s11187-012-9430-3

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