Impediments to Communication in Financial Institutions: Implications for the Risk Management Organization

Abstract

This article investigates the question of how risk management should be embedded in a financial firm’s hierarchy. We answer this question by combining capital market theory with game-theoretic thinking. We develop a theory for the integration of risk management into an organization, based on private information and differences in preferences. Our model compares the payoffs from uninformed decision-making, solo decision-making, joint voting decision-making, and coordinated decision-making when information about a project’s expected return and risk is dispersed in the organization. Our findings have a number of implications for the organization of risk management.

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Notes

  1. 1.

    See New York Times (2011).

  2. 2.

    See KPMG (2009, p. 7).

  3. 3.

    Roy (2008, pp. 128–129).

  4. 4.

    Senior Supervisor Group (2008, p. 9).

  5. 5.

    Meulbroek (2002, p. 55).

  6. 6.

    Sharpe (1964).

  7. 7.

    Lintner (1965).

  8. 8.

    Mehr and Forbes (1973).

  9. 9.

    Froot and Stein (1998).

  10. 10.

    Boyer et al. (2013).

  11. 11.

    Mehr and Forbes (1973, p. 398).

  12. 12.

    Tufano (1998, p. 75).

  13. 13.

    Fatemi and Luft (2002).

  14. 14.

    Bloos (2009).

  15. 15.

    Aghion and Tirole (1997).

  16. 16.

    Bolton and Farrell (1990).

  17. 17.

    Hart and Moore (2005).

  18. 18.

    Garicano (2000).

  19. 19.

    Dessein (2002).

  20. 20.

    Harris and Raviv (2005).

  21. 21.

    Marino and Matsusaka (2005).

  22. 22.

    Liberti and Mian (2009).

  23. 23.

    See, for example, Aghion and Tirole (1997), Dessein (2002), and Alonso et al. (2008).

  24. 24.

    Crawford and Sobel’s (1982).

  25. 25.

    See Dessein (2002).

  26. 26.

    See, e.g., Alonso et al. (2008), based on Grossman and Hart (1986) and Hart and Moore (1990). See Hori (2008) for an analysis of how incentive contracts are used to motivate private information gathering and truthful reporting.

  27. 27.

    The agency conflict between business managers and shareholders is discussed in Jensen (1986). Empirical research documenting the empire-building and expense preferences of managers includes Edwards (1977), Hannan and Mavinga (1980), Masulis et al. (2007), Hope and Thomas (2008), and Xuan (2009). For anecdotic evidence, see Oliver Wyman (2012, p. 59).

  28. 28.

    Anecdotic evidence for this bias can be found in Oliver Wyman (2012, p. 59).

  29. 29.

    In the lower case, \(\tilde{\alpha } - \sigma_{\text{R}} \le \varDelta_{\text{R}} \le 0\) implies \(\left( {\tilde{\alpha } - \sigma_{\text{R}} } \right)^{2} \ge \varDelta_{\text{R}}^{2}\).

  30. 30.

    This threshold is always positive, since we assume that \(\tilde{\alpha } - RP \cdot \sigma_{\text{S}} < 0\) (the expected payoff is negative when the highest possible project risk realizes).

  31. 31.

    We have checked that the relation between \(\varDelta_{\text{R}}\) and \(\varDelta_{\text{S}}\) solving \({\text{Payoff}}_{\text{ID}} = {\text{Payoff}}_{\text{RD}}\) is in general not polynomial.

  32. 32.

    Pagach and Warr (2011).

  33. 33.

    The importance of contracting in two-tier and three-tier hierarchies has been studied, for example, by Melumad et al. (1992) and Villadsen (1995).

  34. 34.

    See Lindorff (2009).

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Correspondence to Helmut Gründl.

Appendices

Appendix A: Solo decision-making by the business manager

If \(\tilde{\alpha } - \sigma_{\text{R}} \le \varDelta_{\text{R}} \le 0\), then \(R_{\text{P}}^{*} = R_{\text{f}} + \varDelta_{\text{R}} + RP \cdot \mu_{\text{S}}\) is within the interval of the uniform distribution \(\left[ {\mu_{\text{R}} - \sigma_{\text{R}} ,\mu_{\text{R}} + \sigma_{\text{R}} } \right]\) and the expected payoff is obtained as

$$ \begin{aligned} {\text{Payoff}}_{\text{BMD}} & ={ \,E\left( {\alpha_{\text{P}} |R_{\text{P}} > R_{\text{P}}^{*} } \right) \cdot { \Pr }\left( {R_{\text{P}} > R_{\text{P}}^{*} } \right)} \\&= \left( {\frac{{\mu_{\text{R}} + \sigma_{\text{R}} + R_{\text{P}}^{*} }}{2} - R_{\text{f}} - R_{\text{P}} \cdot \mu_{\text{S}} } \right) \cdot \frac{{\mu_{\text{R}} + \sigma_{\text{R}} - R_{\text{P}}^{*} }}{{2\sigma_{\text{R}} }} \\ & = \frac{{\mu_{\text{R}} - RP \cdot \mu_{\text{S}} - R_{\text{f}} + \sigma_{\text{R}} + \varDelta_{\text{R}} }}{2} \cdot \frac{{\mu_{\text{R}} - RP \cdot \mu_{\text{S}} - R_{\text{f}} + \sigma_{\text{R}} - \varDelta_{\text{R}} }}{{2 \cdot \sigma_{\text{R}} }} \\&= \frac{{\left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \varDelta_{\text{R}}^{2} }}{{4 \cdot \sigma_{\text{R}} }} \\ \end{aligned}. $$

If \(\varDelta_{\text{R}} < \tilde{\alpha } - \sigma_{\text{R}}\), then \(R_{\text{P}}^{*}\) lies left from the interval \(\left( {\mu_{\text{R}} - \sigma_{\text{R}} ,\mu_{\text{R}} + \sigma_{\text{R}} } \right)\), meaning that the business manager approves all projects and the expected profit is \(\tilde{\alpha }\).

Appendix B: Solo decision-making by the risk manager

If \(\varDelta_{\text{S}} \le \tilde{\alpha } + RP \cdot \sigma_{\text{S}}\), then \(S_{\text{P}}^{*} = \frac{1}{RP}\left( {\mu_{\text{R}} - R_{\text{f}} - \varDelta_{\text{S}} } \right)\) is within the interval of the uniform distribution \(\left[ {\mu_{\text{S}} - \sigma_{\text{S}} ,\mu_{\text{S}} + \sigma_{\text{S}} } \right]\) and the expected payoff is obtained as

$$\begin{aligned} {\text{Payoff}}_{\text{RMD}} &= {\text{E}}\left( {\alpha_{\text{P}} |S_{\text{P}} < S_{\text{P}}^{*} } \right) \cdot { \Pr }\left( {{\text{S}}_{\text{P}} < {\text{S}}_{\text{P}}^{ *} } \right) \\&= \left( {\mu_{\text{R}} - R_{\text{f}} - R_{\text{P}} \cdot \frac{{\mu_{\text{S}} - \sigma_{\text{S}} + S_{\text{P}}^{*} }}{2}} \right) \cdot \frac{{{\text{S}}_{\text{P}}^{ *} - \mu_{\text{S}} + \sigma_{\text{S}} }}{{2\sigma_{\text{S}} }} \\ & = \frac{{\mu_{\text{R}} - R_{\text{f}} - RP \cdot \mu_{\text{S}} + RP \cdot \sigma_{\text{S}} + \varDelta_{\text{S}} }}{2} \cdot \frac{{\mu_{\text{R}} - R_{\text{f}} - RP \cdot \mu_{\text{S}} + RP \cdot \sigma_{\text{S}} - \varDelta_{\text{S}} }}{{2 \cdot RP \cdot \sigma_{\text{S}} }} = \frac{{\left( {\tilde{\alpha } + RP \cdot \sigma_{\text{S}} } \right)^{2} - \varDelta_{\text{S}}^{2} }}{{4 \cdot RP \cdot \sigma_{\text{S}} }} \\ \end{aligned}.$$

If \(\tilde{\alpha } + RP \cdot \sigma_{\text{S}} < \varDelta_{\text{S}}\), then \({\text{S}}_{\text{P}}^{ *}\) is left from the interval \(\left( {\mu_{\text{S}} - \sigma_{\text{S}} ,\mu_{\text{S}} + \sigma_{\text{S}} } \right)\), i.e., the risk manager rejects all projects and the expected profit is 0.

Appendix C: Comparison of solo decision-making by business manager vs risk manager

If \(\varDelta_{\text{R}}^{2} \le \left( {\sigma_{\text{R}} - \tilde{\alpha }} \right)^{2} - \frac{{\sigma_{\text{R}} }}{{RP \cdot \sigma_{\text{S}} }} \cdot \left( {\tilde{\alpha } - RP \cdot \sigma_{\text{S}} } \right)^{2}\), then

$$\begin{aligned} {\text{Payoff}}_{\text{BMD}} & \ge \frac{{\left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \left( {\sigma_{\text{R}} - \tilde{\alpha }} \right)^{2} + \frac{{\sigma_{\text{R}} }}{{RP \cdot \sigma_{\text{S}} }} \cdot \left( {\tilde{\alpha } - RP \cdot \sigma_{\text{S}} } \right)^{2} }}{{4 \cdot \sigma_{\text{R}} }} = \frac{{4 \cdot \sigma_{\text{S}} \cdot RP \cdot \tilde{\alpha } + \tilde{\alpha }^{2} - 2 \cdot \tilde{\alpha } \cdot RP \cdot \sigma_{\text{S}} + \left( {RP \cdot \sigma_{\text{S}} } \right)^{2} }}{{4 \cdot \sigma_{\text{S}} \cdot RP}} \\ {\kern 1pt} \quad & = \frac{{\left( {\tilde{\alpha } + RP \cdot \sigma_{\text{S}} } \right)^{2} }}{{4 \cdot RP \cdot \sigma_{\text{S}} }} \ge {\text{Payoff}}_{\text{RMD}} \\ \end{aligned}.$$

If \(\varDelta_{\text{R}} < \tilde{\alpha } - \sigma_{\text{R}} < 0\) and \(\varDelta_{\text{S}} > - \left( {\tilde{\alpha } - RP \cdot \sigma_{\text{S}} } \right)\), then

$${\text{Payoff}}_{\text{BMD}} \ge \frac{{\left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \left( {\tilde{\alpha } - \sigma_{\text{R}} } \right)^{2} }}{{4 \cdot \sigma_{\text{R}} }} = \tilde{\alpha } = \frac{{\left( {\tilde{\alpha } + RP \cdot \sigma_{\text{S}} } \right)^{2} - \left( {\tilde{\alpha } - RP \cdot \sigma_{\text{S}} } \right)^{2} }}{{4 \cdot RP \cdot \sigma_{\text{S}} }} \ge {\text{Payoff}}_{\text{RMD}}.$$

If \(\tilde{\alpha } - \sigma_{\text{R}} \le \varDelta_{\text{R}} \le 0\) and \(\varDelta_{\text{S}} > \sqrt[{}]{{\left( {\tilde{\alpha } + RP \cdot \sigma_{\text{S}} } \right)^{2} - \frac{{RP \cdot \sigma_{\text{S}} }}{{\sigma_{\text{R}} }} \cdot \left[ {\left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \varDelta_{\text{R}}^{2} } \right]}}\), then

$$\begin{aligned} {\text{Payoff}}_{\text{RMD}} & \le \frac{{\left( {\tilde{\alpha } + RP \cdot \sigma_{\text{S}} } \right)^{2} - \left( {\tilde{\alpha } + RP \cdot \sigma_{\text{S}} } \right)^{2} + \frac{{RP \cdot \sigma_{\text{S}} }}{{\sigma_{\text{R}} }} \cdot \left[ {\left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \varDelta_{\text{R}}^{2} } \right]}}{{4 \cdot RP \cdot \sigma_{\text{S}} }} = \frac{{4 \cdot \tilde{\alpha } \cdot \sigma_{\text{R}} + \left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \varDelta_{\text{R}}^{2} }}{{4 \cdot \sigma_{\text{R}} }} = \frac{{\left( {\tilde{\alpha } - \sigma_{\text{R}} } \right)^{2} - \varDelta_{\text{R}}^{2} }}{{4 \cdot \sigma_{\text{R}} }} \\ \quad & \le \frac{{\left( {\tilde{\alpha } + \sigma_{\text{R}} } \right)^{2} - \varDelta_{\text{R}}^{2} }}{{4 \cdot \sigma_{\text{R}} }} = {\text{Payoff}}_{\text{BMD}} \\ \end{aligned}.$$

Appendix D: Nash equilibrium for joint voting decision-making

Under the assumption that the cut-off levels in the Nash Equilibrium lie in the interior of the uniform distributions, they are derived as follows:

$$R_{\text{P}}^{\text{N}} = R_{\text{f}} + \varDelta_{\text{R}} + RP \cdot \frac{{\mu_{\text{S}} - \sigma_{\text{S}} + S_{\text{P}}^{\text{N}} }}{2}$$
(A.1)
$$S_{\text{P}}^{\text{N}} = \frac{1}{RP} \cdot \left( {\frac{{R_{\text{P}}^{\text{N}} + \mu_{\text{R}} - \sigma_{\text{R}} }}{2} - R_{\text{f}} - \varDelta_{\text{S}} } \right).$$
(A.2)

Inserting (A.1) into (A.2) and solving for \(S_{\text{P}}^{\text{N}}\) leads to

$$S_{\text{P}}^{\text{N}} = \frac{1}{RP} \cdot \left( {\frac{{R_{\text{f}} + \varDelta_{\text{R}} + RP \cdot \frac{{\mu_{\text{S}} - \sigma_{\text{S}} + S_{\text{P}}^{\text{N}} }}{2} + \mu_{\text{R}} - \sigma_{\text{R}} }}{2} - R_{\text{f}} - \varDelta_{\text{S}} } \right)$$
$$\Leftrightarrow \frac{3}{4}S_{\text{P}}^{\text{N}} = \frac{1}{RP} \cdot \left( {\frac{{ - {\text{R}}_{\text{f}} + \mu_{\text{R}} - \sigma_{\text{R}} + \varDelta_{\text{R}} - 2\varDelta_{\text{S}} }}{2}} \right) + \frac{{\mu_{\text{S}} - \sigma_{\text{S}} }}{4}$$
$$\Leftrightarrow S_{\text{P}}^{\text{N}} = \frac{1}{RP} \cdot \left( {\frac{{ - 2{\text{R}}_{\text{f}} + 2\mu_{\text{R}} - 2\sigma_{\text{R}} + 2\varDelta_{\text{R}} - 4\varDelta_{\text{S}} }}{3}} \right) + \frac{{\mu_{\text{S}} - \sigma_{\text{S}} }}{3}.$$

Inserting the solution into (A.1) and simplifying yields

$$R_{\text{P}}^{\text{N}} = \frac{2}{3}R_{\text{f}} + \frac{4}{3}\varDelta_{\text{R}} - \frac{2}{3}\varDelta_{\text{S}} + \frac{1}{3} \cdot \left( {\mu_{\text{R}} + \sigma_{\text{R}} } \right) + \frac{2}{3} \cdot RP \cdot \left( {\mu_{\text{S}} - \sigma_{\text{S}} } \right).$$

The expected payoff in the interior Nash equilibrium is obtained as

$$\begin{aligned} {\text{Payoff}}_{\text{JVD}} & = {\text{E}}\left( {\alpha_{\text{P}} |\left\{ {R_{\text{P}} \ge R_{\text{P}}^{\text{N}} } \right\}\mathop \cap \nolimits \left\{ {S_{\text{P}} \le S_{\text{P}}^{\text{N}} } \right\}} \right) \cdot \Pr \left( {R_{\text{P}} \ge S_{\text{P}}^{\text{N}} } \right) \cdot \Pr \left( {S_{\text{P}} \le S_{\text{P}}^{\text{N}} } \right) \\ & = \left( {\frac{{\mu_{\text{R}} + \sigma_{\text{R}} + R_{\text{P}}^{\text{N}} }}{2} - R_{\text{f}} - R_{\text{P}} \cdot \frac{{\mu_{\text{S}} - \sigma_{\text{S}} + S_{\text{P}}^{\text{N}} }}{2}} \right) \cdot \frac{{\mu_{\text{R}} + \sigma_{\text{R}} - R_{\text{P}}^{\text{N}} }}{{2\sigma_{\text{R}} }} \cdot \frac{{S_{\text{P}}^{\text{N}} - \mu_{\text{S}} + \sigma_{\text{S}} }}{{2\sigma_{\text{S}} }} \\ & = \frac{{\left( {\tilde{\alpha } - 2\varDelta_{\text{R}} + \varDelta_{\text{S}} } \right) \cdot \left( {\tilde{\alpha } + \varDelta_{\text{R}} - 2\varDelta_{\text{S}} } \right) \cdot \left( {\tilde{\alpha } + \varDelta_{\text{R}} + \varDelta_{\text{S}} } \right)}}{{27 \cdot RP \cdot \sigma_{\text{R}} \cdot \sigma_{\text{S}} }} \\ \end{aligned}.$$

If \(S_{\text{P}}^{\text{N}} < \mu_{\text{S}} - \sigma_{\text{S}}\), then the risk manager considers all projects as too risky and rejects them. The condition is equivalent to \(\varDelta_{\text{S}} > \frac{{\varDelta_{\text{R}} + \mu_{\text{R}} + \sigma_{\text{R}} - R_{\text{f}} - RP \cdot \left( {\mu_{\text{S}} + 2\sigma_{\text{S}} } \right)}}{2} = :\varDelta_{{{\text{S}},2}}\). In this case, the expected payoff is zero. If \(R_{\text{P}}^{\text{N}} < \mu_{\text{R}} - \sigma_{\text{R}}\), then the business manager accepts all projects. This condition is equivalent to \(\varDelta_{\text{S}} > 2\varDelta_{\text{R}} + R_{\text{f}} - \mu_{\text{R}} + 0.5\sigma_{\text{R}} + RP \cdot \left( {\mu_{\text{S}} - \sigma_{\text{S}} } \right) = :\varDelta_{{{\text{S}},1}}\). If in addition \(\varDelta_{\text{S}} \le \varDelta_{{{\text{S}},2}}\), then the selection of projects is identical to the risk manager’s solo decision-making. Hence, the expected payoffs coincide. In total, an interior solution only occurs if the latter two cases are both ruled out, i.e., if \(\varDelta_{\text{S}} \le { \hbox{min} }\left\{ {\varDelta_{{{\text{S}},1}} ,\varDelta_{{{\text{S}},2}} } \right\}\).

Appendix E: Comparison of joint voting and solo decision-making for \(\varDelta_{\text{R}} = \varDelta_{\text{S}} = 0\)

For \(\varDelta_{\text{R}} = \varDelta_{\text{S}} = 0\), both solo and joint voting decision-making setups assume interior solutions. We first verify \({\text{Payoff}}_{\text{JVD}} \ge {\text{Payoff}}_{\text{BMD}}\). To this end, we define

$$f\left( {\sigma_{\text{S}} } \right) = \frac{{27\sigma_{\text{s}} RP}}{4} \cdot \left( {{\text{Payoff}}_{\text{JVD}} - {\text{Payoff}}_{\text{BMD}} } \right) = 4\left( {\tilde{a} + \sigma_{\text{R}} + RP\sigma_{\text{S}} } \right)^{3} - 27\sigma_{\text{s}} RP\left( {\tilde{a} + \sigma_{\text{R}} } \right)^{2}$$
$$f^{\prime}\left( {\sigma_{\text{S}} } \right) = 12\left( {\tilde{a} + \sigma_{\text{R}} + RP \cdot \sigma_{\text{S}} } \right)^{2} - 27RP\left( {\tilde{a} + \sigma_{\text{R}} } \right)^{2} = 0 \Leftrightarrow \sigma_{\text{S}} = \frac{{\tilde{a} + \sigma_{\text{R}} }}{2RP}.$$

Due to \(f^{\prime\prime}\left( {\sigma_{\text{S}} } \right) = 24\left( {\tilde{a} + \sigma_{\text{R}} + RP \cdot \sigma_{\text{S}} } \right) > 0,\,f\left( {\sigma_{\text{R}} } \right)\) has a global minimum at \(\sigma_{\text{S}} = \frac{{\tilde{a} + \sigma_{\text{R}} }}{2RP}\) with \(f\left( {\frac{{\tilde{a} + \sigma_{\text{R}} }}{2RP}} \right) = 0\). In order to show \({\text{Payoff}}_{\text{JVD}} \ge {\text{Payoff}}_{\text{BMD}}\), we define

$$g\left( {\sigma_{\text{R}} } \right) = \frac{{27 \cdot \sigma_{\text{R}} }}{4} \cdot \left( {{\text{Payoff}}_{\text{JVD}} - {\text{Payoff}}_{\text{RMD}} } \right) = 4\left( {\tilde{a} + \sigma_{\text{R}} + RP \cdot \sigma_{\text{S}} } \right)^{3} - 27\sigma_{\text{R}} \left( {\tilde{a} + RP \cdot \sigma_{\text{S}} } \right)^{2}$$
$$g^{\prime}\left( {\sigma_{\text{R}} } \right) = 12\left( {\tilde{a} + \sigma_{\text{R}} + RP \cdot \sigma_{\text{S}} } \right)^{2} - 27\left( {\tilde{a} + RP \cdot \sigma_{\text{S}} } \right)^{2} = 0 \Leftrightarrow \sigma_{\text{R}} = \frac{{\tilde{a} + RP \cdot \sigma_{\text{S}} }}{2}.$$

Analogously to the above, \(g\left( {\sigma_{\text{R}} } \right)\) is minimal at this point with \(g\left( {\frac{{\tilde{a} + RP \cdot \sigma_{\text{S}} }}{2}} \right) = 0\).

Appendix F: Coordinated decision-making

The expected payoff is determined as

$${\text{Payoff}}_{\text{CD}} = E\left[ {\alpha_{\text{P}} \cdot \text{1}_{{\left\{ {\alpha_{\text{P}} \ge \varDelta } \right\}}} } \right] = \int_{\varDelta }^{{\tilde{\alpha } + \sigma_{\text{R}} + RP \cdot \sigma_{S} }} {x \cdot f\left( x \right){\text{d}}x},$$

where \(\text{1}\) denotes the indicator function and

$$f\left( x \right) = \frac{1}{{\left( {\sigma_{\text{R}} + RP \cdot \sigma_{\text{S}} } \right)^{2} }} \cdot \left\{ {\begin{array}{*{20}c} {x - \left( {\tilde{\alpha } - \sigma_{\text{R}} - RP \cdot \sigma_{\text{S}} } \right) \quad {\text{if }}\,x \le \tilde{\alpha }} \\ { - x + \tilde{\alpha } + \sigma_{\text{R}} + RP \cdot \sigma_{\text{S}} \quad {\text{if }}\,x > \tilde{\alpha }} \\ \end{array} } \right.$$

is the density function of \(\alpha_{\text{P}}\), resulting from the convolution of the two uniform distributions. The rest follows from calculating the integral.

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Höring, D., Gründl, H. & Schlütter, S. Impediments to Communication in Financial Institutions: Implications for the Risk Management Organization. Geneva Risk Insur Rev 41, 193–224 (2016). https://doi.org/10.1057/s10713-016-0015-y

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Keywords

  • risk management
  • organization structure
  • financial institutions