Financial guarantors’ executive compensation, charter value and risk-taking

Research in International Business and Finance 26 (2012) 387–397

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Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Financial guarantors’ executive compensation, charter value and risk-taking夽 Van Son Lai a,∗, Issouf Soumaré a,1, Yan Sun b a b

Department of Finance, Insurance and Real Estate, Laval University, 2325 rue de la Terrasse, Québec, QC G1V 0A6, Canada Xi’an Jiaotong University, China

a r t i c l e

i n f o

Article history: Received 31 January 2012 Accepted 6 March 2012 Available online 22 March 2012 JEL classification: G13 G22 G28 G32 Keywords: Charter value Financial guarantee Managerial compensation Optimal risk Principal-agent problem

a b s t r a c t Financial guarantees have been extensively used recently as part of rescue packages to bail out troubled institutions and governments around the world. We propose a new incentive compensation model for studying agency conflict between the shareholders and the manager of a typical financial guarantor. In our model, the manager chooses the guarantor’s risk level, with disutility to reduce risk (i.e., reducing the risk of the guarantor incurs a direct cost to the manager). Moral hazard causes the manager to select a level of risk that is higher than the level chosen in an otherwise first-best environment with no conflict of interest between the shareholders and the manager. However, in our proposed framework, charter value plays a self-disciplining role on the manager’s appetite for risk, therefore it helps mitigate the extent of the deviation from first best with agency conflict found previously (e.g., Jensen and Meckling, 1976; Cadenillas et al., 2004, 2007). This suggests that researchers should study charter value, managerial compensation

夽 We gratefully acknowledge financial support from the Institut de Finance Mathématique of Montréal (IFM2), the Fonds Québecois de la Recherche sur la Société et la Culture (FQRSC), the Social Sciences and Humanities Research Council of Canada (SSHRC) and the Fonds Conrad-Leblanc. Yan Sun gratefully acknowledges support from the State Key Program of National Natural Science of China (Grant No. 71032002). The usual disclaimer applies. This work was undertaken while Lai was visiting the Risk Management Institute, National University of Singapore, Singapore. Lai thanks Professor Jin-Chuan Duan for his hospitality. It was finalized while Issouf Soumaré was visiting the Guanghua School of Management at Peking University (Beijing, China). Soumaré would like to thank Professor Li Liu, Professor Longkai Zhao, and the other members of the Department of Finance of the Guanghua School of Management for their hospitality. ∗ Corresponding author. Tel.: +1 41656 2131; fax: +1 418 656 2624.

E-mail addresses: [email protected] (V.S. Lai), [email protected] (I. Soumaré), [email protected] (Y. Sun). 1 Tel.: +1 41656 2131; fax: +1 418 656 2624. 0275-5319/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ribaf.2012.03.002

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and risk decisions within a unified framework and not separately, as all studies have done in the past. © 2012 Elsevier B.V. All rights reserved.

1. Introduction We have witnessed an unprecedented financial crisis—the biggest since the Great Depression. The so called subprime credit crisis, following a misuse of complex structured financial products and securitization, had repercussions worldwide. Further, turmoil caused by sovereign, state and municipality deficits worldwide threatens the increasing integrated world economy (e.g., Gurdgiv et al., 2011). Several large institutions, some hitherto thought to be unshakable, have gone bankrupt. Indeed, no financial institution seems to be ‘too big to fail’. American International Group (AIG), the world’s biggest insurer has been placed under public oversight. Lehman Brothers, the oldest U.S. investment bank, has gone bankrupt. The list is obviously not limited to AIG and Lehman Brothers. One might also mention Dexia, Fortis, Société Générale, Royal Bank of Scotland (RBS), Northern Rock, Lloyds TBS and HBOS in Europe, to name a few. Also, the credit trouble of PIIGS (Portugal, Italy, Ireland, Greece and Spain) countries threatens even more the world financial stability and economic performance. Executive compensation in the financial services industry, known to encourage excessive risktaking by managers, is often cited as a cause of the subprime crisis and the current European sovereign debt crisis, creating havoc worldwide. Furthermore, in the wake of the undergoing social revolution, executive compensation has become a very sensitive issue worldwide. Albeit complex, there are variety of papers treating some aspects of executive compensation, e.g., Li et al. (2007) and Hearn (2012). Despite the role of the financial services industry in the economy, very few research works focus on executive compensation in this special and heavily regulated sector. This paper proposes a new model for studying the incentive alignment compensation schemes offered to the managers of financial guarantor firms (hereafter called guarantors), assuming that managers have the latitude to determine the risk to which guarantors are exposed. Financial guarantees are used to resolve financial crises and other liquidity shortfalls. Recent examples include mainly the US and European governments rescue plans to bail out troubled institutions and governments.2 Given the pervasive importance of financial guarantees as tools for credit enhancement or as part of bailout vehicles to rescue distressed entities (e.g., Merton and Bodie (1992)), it is appropriate to study the executive compensation of managers of such institutions granting financial guarantees. We consider the guarantor to be the party that insures a debt from a representative firm (the guaranteed firm). As in Cadenillas et al. (2004, 2007), we assume that the guarantor’s manager chooses the portfolio: in doing so, he determines the portfolio’s overall risk. To align the manager’s interests with those of the guarantor’s shareholders, the guarantor uses a compensation scheme that is sensitive to performance: i.e., the guarantor pays the manager a fixed salary and grants him shares in the guarantor. Since the manager is responsible for managing the guarantor’s overall portfolio risk, we assume that he exhibits disutility from costly actions to reduce risk (e.g., Guo and Ou-Yang, 2006). As in Jin (2002) and Garvey and Milbourn (2003), we assume that systematic risk is outside the manager’s control and that the manager’s actions can only influence idiosyncratic risk. We also assume bankruptcy to be costly to shareholders (see Ju et al., 2005; Leland, 2004; Parrino et al., 2005). We hold that charter or franchise value acts as a self-disciplining influence on the manager’s appetite for risk. On one hand, since the guarantor’s overall risk level affects the charter value—an effect that impacts both the shareholders and manager if the guarantor survives—then when the charter value is sufficiently high, the manager takes fewer risks to not compromise the charter value and thus decrease his stake (e.g., Keeley, 1990; Galloway et al., 1997; Cebenoyan et al., 1999; Palia and Porter, 2004). In this way, higher charter value induces the manager to take fewer risks, even if he is given less equity. On the other hand, from the shareholders’ viewpoint, there is an incentive to give the

2 See for example: The Economist, “Europe’s rescue plan” (Oct 29, 2011), and The Financial Times, “Europe agrees rescue package” (May 10, 2010).

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manager more shares to lessen his appetite for risk (since he owns part of the firm): this view reflects shareholders’ fear of losing charter value or the license to operate the financial company. These two phenomena indicate that charter value, a crucial driver of agents’ behavior in financial institutions, cannot be ignored when designing models that encompass managerial compensation. In other words, charter value, risk and incentive compensation should be studied jointly and not separately, as the literature has done to date. As such, to our knowledge, this paper is the very first to address these three dimensions in an integrated new framework. In our incentive compensation framework, the manager chooses a higher level of risk than in an otherwise first-best case with no agency conflict. However, in our proposed framework, charter value plays a self-disciplining role on the manager’s appetite for risk, therefore it helps mitigate the extent of the deviation from first best with agency conflict found previously (e.g., Jensen and Meckling, 1976; Cadenillas et al., 2004, 2007). This excessive risk-taking in the presence of shareholder-manager conflict is mainly due to (i) misalignment between manager and shareholders’ interests and (ii) the moral hazard caused by the unobservable risk-control costs the manager must bear to reduce the guarantor’s overall risk. We also find that high leverage on the part of the guarantor boosts the manager’s appetite for risk. This is intuitive, because high debt makes the guarantor’s residual value looks like an out-of-the-money option. Since the manager’s performance-based compensation is linked to the residual value, high debt encourages the manager to gamble for an unlimited upside payoff with limited downside loss. This finding is in line with the various current regulatory proposals to limit excessive leverage in financial institutions. Our work suggests that these new regulations should not only prevent excessive leverage by financial institutions, but also take the compensation design into consideration. Indeed, as argued by Bebchuk and Spamann (2010), the performance tied compensation itself might contribute to the meltdown of a financial institution. However, when the correlation between the existing guaranteed portfolio and the new firm to be included in the portfolio is high, the manager tends to adhere to a position of risk diversification. The rest of this paper is structured as follows. Section 2 presents our incentive compensation model in the financial guarantee business. Section 3 presents the results and our interpretations. We conclude in Section 4.

2. The model We consider two firms with a simple capital structure composed of equity (Ei ) and zero-coupon debt (Di ). Neither firm pays dividends and neither makes intermediate payments on its debt before maturity. The debt of the first firm—hereafter called the guaranteed firm, with capital structure (EV , DV )—is guaranteed by the second firm, hereafter called the guarantor. We denote by i = V the guaranteed firm and by i = W the guarantor. The initial asset value of the guaranteed firm (net of the premium paid) is V0 . We define by LV the leverage ratio of the guaranteed firm, i.e. LV = DV /V0 . As in Angoua et al. (2008), the relationship between the guaranteed debt value DV and its face value FV is given by FV = DV eRT , where R = r +  V + ı W is a linear formulation of the yield to maturity as a function of the risk-free interest rate r and the assets risks of the two firms.  V and  W are the asset return volatility of the guaranteed firm and the asset return volatility of the guarantor, respectively. T is the maturity of the guaranteed risky debt and  and ı are constant parameters. The guarantor has senior debt with face value FW and initial asset value W0 . As in Merton (1974), LW is the quasi-debt ratio of the guarantor’s existing portfolio before adding the guaranteed firm and is defined as LW = FW e−rT /W0 , i.e., the present value of the debt face value (instead of the market value of the debt) divided by the initial asset value. The guarantor is vulnerable to default by the guaranteed firm. We make the standard assumptions of contingent claims analysis. The assets of the guaranteed firm and of the guarantor, net of all other costs (for instance, for the guaranteed firm, the insurance premium paid to the guarantor; and for the guarantor, the overhead costs) and the market index, follow geometric Brownian motions: dWt = W dt + ˇW M dZM (t) + W dZW (t), Wt

(1)

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dVt = V dt + ˇV M dZM (t) + V dZV (t), Vt

(2)

dMt = M dt + M dZM (t), Mt

(3)

where i ,  i , ˇi and i are the instantaneous mean returns, the asset return volatility, beta coefficients with the market index, and volatilities of idiosyncratic risk components, respectively. The standard Wiener processes ZM , ZW and ZV capture sources of common market risk, guarantor’s idiosyncratic risk and the guaranteed firm’s idiosyncratic risk, respectively. They are correlated as follows: E[dZM (t)dZV (t)] = E[dZM (t)dZW (t)] = 0 and E[dZW (t)dZV (t)] = cWV dt; meaning that there is zero correlation between sources of risk for the common market and the two firms’ sources of idiosyncratic risk, but that the latter two sources of risk are correlated. specified in (1) With the asset return processes  2  2 + 2 . 2  2 +  2 and  = and (2), the firms’ total return volatilities are W = ˇ ˇW V M W V M V Following Merton (1977), when the debt reaches maturity, the maximum guarantee provided by a default-free guarantor is the expected shortfall GT = max(FV − VT , 0). This is equivalent to a put option for which the underlying corresponds to the total asset of the guaranteed firm and the exercise price is equal to the face value of the guaranteed debt. The present value of this shortfall is: G0 = FV e−rT N(−d2 ) − V0 N(−d1 ),

(4) √ √ where d1 = (ln(V0 /FV ) + (r T , d2 = d1 − V T , and N(·) is the cumulative distribution function of the standard normal distribution. We assume that the guarantor charges the amount , as follows, to guarantee the debt of the client firm: + V2 /2)T )/V

 = (1 + ε)G0 ,

(5)

where G0 is the pure premium equal to the present value of the expected loss on the risky debt (see Eq. (4)) and ε is a loading factor that captures all other costs in the transaction. This guarantee premium is added to the guarantor’s existing wealth as an initial investment such that the guarantor’s initial asset value becomes W0 + . The guarantor’s net asset is determined by the risk-neutral expectation of the present value of the final payoff as follows:



EW0 = e−rt

(max(WT − FW − max(FV − VT , 0), 0) + WT 1{WT >FW +max(FV −VT ,0)}

− hWT 1{WT
(6)

2 a + bW + cW

where  = represents the charter or franchise value coefficient and can be seen as future benefits that the guarantor’s shareholders will lose in the event of bankruptcy (e.g., Angoua et al., 2008; Keeley, 1990). The charter value function  is defined as a quadratic function of the guarantor’s asset return volatility. As in Angoua et al. (2008), we assume that a > 0, b > 0 and c < 0.3 h is the bankruptcy cost coefficient. 1{·} is the indicating variable with respect to the realization set {·}. The explicit formulas for Eq. (6) are provided in Appendix A. We assume that the guarantor is run by a manager who maximizes the following utility function:



max W

sT + EW0 − ˛

1 2 TW



 ,

where W =

2 − ˇ2  2 , W W M

(7)

subject to shareholders’ participation constraints (1 − )EW0 − sT ≥ P¯ and P¯ ≥ W0 − FW e−rT ≥ 0, where sT and are, respectively, the constant salary over period T and the proportion of shares granted to the manager to align his incentives to the interests of the guarantor’s shareholders. ˛ is the manager’s risk-control effort cost coefficient. The components of the manager’s compensation (s, ) are obtained

3 The values of these parameters exhibit, among other things, the impact of different external environments (the regulatory environment, investment opportunities, competition, etc.).

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Table 1 Payoffs to the guarantor’s shareholders, manager and debtholders. Scenarios

Payoff to guarantor’s shareholders

Payoff to guarantor’s manager

Payoff to guarantor’s debtholders

Case 1: WT ≥ FW , VT ≥ FV

(1 − )[(1 + )WT − FW ] − sT

[(1 + )WT − FW ] + sT − ˛ 12

FW

(1 − )[(1 + )WT − FW − (FV − VT )] − sT

[(1 + )WT − FW − (FV − VT )] + sT − ˛ 12

T

W

Case 2:

WT > FW , VT < FV , WT − FW ≥ FV − VT

FW

T

WT ≥ FW , VT < FV , WT − FW < FV − VT Case 4: WT < FW Case 3:

W

−(1 − )hWT − sT

− hWT + sT − ˛

1 T2

FW

−(1 − )hWT − sT

− hWT + sT − ˛

1 T2

(1 − h)WT

W W

This table summarizes the payoffs to the guarantor’s shareholders, manager and debtholders at the maturity of the guaranteed debt. V and W denote the asset value of the guarantor and the guaranteed firm, respectively. They are characterized by the following processes: (dWt /Wt ) = W dt + ˇW  M dZM (t) + W dZW (t), (dVt /Vt ) = V dt + ˇV  M dZM (t) + V dZV (t), where i ,  i , ˇi and i are the instantaneous mean returns, the asset return volatility, beta coefficients with the market index, and volatilities of idiosyncratic risk components, respectively. The standard Wiener processes ZM , ZW and ZV capture sources of common market risk, guarantor’s idiosyncratic risk and the guaranteed firm’s idiosyncratic risk, respectively. FV and FW represent the face value of the guarantor’s debts and those of the guaranteed firm, respectively; is the proportion of shares granted to the manager as incentive compensation; sT is the amount of cash compensation over the period T;  is the parameter for the charter value; h is the bankruptcy cost coefficient; and ˛ is the manager’s risk-control effort cost coefficient.

from the shareholders’ incentive compatibility conditions as (s∗, ∗) ∈ arg max{(1 − )EW0 − sT }, with (1 − )EW0 − sT ≥ 0. As stated earlier, the manager is responsible for setting the guarantor’s overall risk level. The coefficient ˛ in the manager’s disutility function represents the manager’s skill at managing risk, especially idiosyncratic risk (as we also mentioned earlier, the manager’s actions do not affect systematic risk). For a skilled manager, this coefficient is small. The magnitude of the coefficient determines the importance of the disutility to the manager of setting the idiosyncratic risk, and thus affects the manager’s optimal risk choice. The cost is inversely proportional to the square of the size of the guarantor’s idiosyncratic risk. Thus, even if low risk prevents the guarantor from going bankrupt, which may be optimal from shareholders’ viewpoint, the manager may choose high risk because it is less costly to him. Table 1 gives the payoffs to the guarantor’s shareholders, manager and debtholders. In cases 1 and 2, the guarantor is able to make the required repayment on the guaranteed debt at maturity T and the manager and shareholders receive their positive payoffs consequently. In case 1, neither the guarantor nor the client firm defaults. In case 2, the guaranteed firm defaults on its debt and the guarantor is able to cover the shortfall after paying its own senior debt. In cases 3 and 4, the guarantor’s net asset value after paying its senior debt is insufficient to reimburse the remaining guaranteed debt. In case 3, the guaranteed firm defaults on its debt and the guarantor is unable to cover the shortfall on the guaranteed debt after paying its own senior debt, causing the guarantor to go bankrupt and lose its charter value. In case 4, the guarantor defaults both on its own senior debt and the guaranteed debt. Here, all stakeholders share the “indirect cost” upon bankruptcy: the guarantor loses part of its extra wealth and the shareholders and the manager are left to bear additional bankruptcy costs in proportion to their equity ownership. 3. Results analysis Table 2 presents our results. In Panel A, we show the results for the case without incentive compensation. This corresponds to the first-best case. In Panel B, we table results with our proposed incentive compensation scheme. Since the parameters of the charter value function have a significant impact on the optimal policies, we present the results for four sets of values for the parameters of the charter value function. The first row in the tables is used as base case for the other rows, in which we vary key parameter values.

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Table 2 Optimal compensation and risk choice. Panel A: No agency conflict T

LV

LW

cWV

ˇV

2 3 2 2 2 2 2

60% 60% 50% 60% 60% 60% 60%

80% 80% 80% 90% 80% 80% 80%

0.3 0.3 0.3 0.3 0.4 0.3 0.3

0.3 0.3 0.3 0.3 0.3 0.5 0.3

a = 0.1, b = 1, c=−2 ∗ W

a = 0.15, b = 1, c=−2 ∗ W

a = 0.045, b = 1.2, c = − 2 ∗ W

a = 0.145, b = 0.8, c=−2 ∗ W

0.3 0.3 0.3 0.3 0.3 0.3 0.5

0.3636 0.4033 0.3496 0.4255 0.3625 0.3659 0.3627

0.3614 0.4043 0.3451 0.4281 0.3602 0.364 0.3605

0.4266 0.4581 0.4174 0.475 0.4256 0.4284 0.4259

0.2794 0.3416 0.096 0.3738 0.2787 0.2837 0.2793

ˇW

a = 0.1, b = 1, c=−2

a = 0.15, b = 1, c=−2

a = 0.045, b = 1.2, c = − 2

a = 0.145, b = 0.8, c = − 2

∗ W

*

∗ W

*

∗ W

*

∗ W

*

0.3736 0.4075 0.3618 0.4305 0.3726 0.3757 0.3752

0.1878 0.1887 0.2112 0.3254 0.1936 0.1811 0.1896

0.3721 0.4085 0.3586 0.4330 0.3709 0.3744 0.3737

0.2612 0.2549 0.2821 0.3937 0.2662 0.2553 0.2628

0.4320 0.4606 0.4234 0.4784 0.4310 0.4337 0.4323

0.2251 0.2314 0.2440 0.3751 0.2302 0.2194 0.2266

0.3081 0.3497 0.2891 0.3817 0.3072 0.3108 0.3151

0.1528 0.1435 0.1837 0.2679 0.1594 0.1448 0.1543

ˇW

Panel B: Incentive compensation T

LV

2 3 2 2 2 2 2

60% 60% 50% 60% 60% 60% 60%

LW

80% 80% 80% 90% 80% 80% 80%

cWV

0.3 0.3 0.3 0.3 0.4 0.3 0.3

ˇV

0.3 0.3 0.3 0.3 0.3 0.5 0.3

0.3 0.3 0.3 0.3 0.3 0.3 0.5

∗ This table presents the manager’s optimal risk choice, W , and the optimal incentive compensation, *, granted by shareholders to the manager. The first panel gives results for the case with no agency conflict, i.e., when the interests of the shareholders and the manager are perfectly aligned. The second panel gives results for our model, i.e., when there is agency conflict between the manager and shareholders. The first row of each panel represents the base parameter. The other rows are obtained by changing certain parameter values (underlined) and keeping others constant. We consider two firms with a simple capital structure composed of equity (Ei ) and zero-coupon debt (Di ), with the guaranteed firm indexed by i = V and the guarantor denoted by i = W. The relationship between the guaranteed debt value DV and its face value FV is given by FV = DV eRT , where R = r +  V + ı W , where r is risk-free interest rate and  V and  W are the asset return volatility of the guaranteed firm and the asset return volatility of the guarantor, respectively. T is the maturity of the guaranteed risky debt and  and ı are constant parameters. The initial asset value of the guaranteed firm is V0 . The guarantor has senior debt with face value FW and initial asset value W0 . The assets of the guaranteed firm and of the guarantor, net of all other costs (for instance, for the guaranteed firm, the insurance premium paid to the guarantor; and for the guarantor, the overhead costs) and the market index, follow geometric Brownian motions: (dWt /Wt ) = W dt + ˇW  M dZM (t) + W dZW (t); (dVt /Vt ) = V dt + ˇV  M dZM (t) + V dZV (t); (dMt /Mt ) = M dt +  M dZM (t); where i ,  i , ˇi and i are the instantaneous mean returns, the asset return volatility, beta coefficients with the market index, and volatilities of idiosyncratic risk components, respectively. The standard Wiener processes ZM , ZW and ZV capture sources of common market risk, guarantor’s idiosyncratic risk and the guaranteed firm’s idiosyncratic risk, respectively. They are correlated  as follows: E[dZM (t)dZ  V (t)] = E[dZM (t)dZW (t)] = 0 and E[dZW (t)dZV (t)] = cWV dt. The firms’ total return volatilities are W = 2 2 2 ˇW M + W and V =

2 ˇV2 M + V2 . At the maturity of the guaranteed debt, the maximum guarantee provided by a default-

−rT free guarantor is the expected shortfall √ GT = max(FV − √VT , 0), which yields its present value: G0 = FV e N(− d2 ) − V0 N(− d1 ), where d1 = (ln(V0 /FV ) + (r + V2 /2)T )/V T , d2 = d1 − V T , and N(·) is the cumulative distribution function of the standard normal distribution. We assume that the guarantor charges the amount , as follows, to guarantee the debt of the client firm:  = (1 + ε)G0 , where ε is a loading factor that captures all other costs in the transaction. The guarantor’s net asset is given by 2 }, where Eq. (6) in the main text. The guarantor manager maximizes the following utility function: max{sT + EW0 − ˛(1/)TW

W =



W

2 2 2 W − ˇW M , subject to shareholders’ participation constraints (1 − )EW0 − sT ≥ P¯ and P ≥ W0 − FW e−rT ≥ 0, where sT

and are, respectively, the constant salary and the proportion of shares granted to him. ˛ is the manager’s risk-control effort cost coefficient. The components of the manager’s compensation (s, ) are obtained from the shareholders’ incentive compatibility conditions as (s∗ , ∗ ) ∈ arg max{(1 − )EW0 − sT }, with (1 − )EW0 − sT ≥ 0. LV is the leverage ratio of the guaranteed firm: LV = DV /V0 LW is the quasi-debt ratio of the guarantor’s existing portfolio before adding the guaranteed firm: LW = FW e−rT /W0 . The coefficients a, b and c characterize the charter value function of the guarantor, i.e.,  = a + b W + c W 2 . The baseline parameters values are W0 = 2000, EV = 1200, LV = 60%, LW = 80%, r = 0.05,  M = 0.30, V = 0.30, ˇW = 0.30, ˇV = 0.30,  = 0.01, ı = 0.02, ˛ = 2, a = 0.1, b = 1, c = −2, T = 2, h = 0.25, ε = 0. We set the pecuniary reservation price of shareholders as P = 200 + W0 − FW e−rT and the fixed salary portion of the manager’s compensation as s ≤ 20. This allows us to keep the incentive portion of the compensation at about 80% of total compensation. (Murphy (1998) documents equity-based compensation at almost 95% of total compensation: the fixed salary portion is thus small. Statistically, the average incentive compensation in the largest 24 banks is about 80% (see http://www.qvmgroup.com/invest/archives/626).)

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In Panel A of Table 2, there is no agency conflict between the guarantor’s shareholders and its manager. Thus, the risk level is that which maximizes the guarantor’s residual asset value. This risk level is the first-best risk choice for the guarantor. In Panel B of Table 2, where there is agency conflict between the manager and the shareholders, there is moral hazard as in the standard incentive compensation framework, because the manager chooses risk that maximizes his net worth and not that of shareholders. This leads to a choice of risk that deviates from first-best. The comparison of Panel A (no incentive compensation—first-best) to Panel B (incentive compensation) indicates that the latter case (with shareholder-manager conflict) always yields higher risk levels than the first case (no agency conflict). With an incentive compensation scheme that grants the manager shares to better align his interests with those of shareholders, the manager still deviates from the first-best choice, because reducing risk is costly to him. This excess risk-taking in the case with agency conflict is mainly due to moral hazard from the unobservable riskcontrol costs born by the manager and the misalignment between the manager’s and shareholders’ interests. In this way, we see that in determining a manager’s compensation, shareholders face a tradeoff between the benefits of better aligning their interests with those of the manager and the costs of the manager’s compensation. If the benefits of giving the manager greater incentive compensation exceed the costs of doing so, then shareholders will give such compensation: if not, they will offer the manager a higher fixed salary. Regarding the optimal risk, the manager maximizes his own utility and chooses the level of risk that reduces his risk-control costs: this can undermine the intended effects of the incentive compensation. This dynamic helps explain why both the incentive portion of the manager’s compensation and the risk level chosen by the manager can be high. In our study, charter value disciplines the manager’s risk-taking behavior. Since the guarantor’s overall level of risk affects the charter value and the manager obtains part of the charter value if the guarantor survives, then when the charter value is large, the manager is cautious in risk-taking so as not to jeopardize his gains from the charter value, even if he is granted fewer shares. At the same time, shareholders who wish to lock up their charter gains have an incentive to grant the manager more shares, as a way to encourage him to take less risk. These results indicate that charter value, a predominant stake in the financial institution setting, cannot be ignored in models that incorporate the dynamics of managerial compensation. Rather, models must examine the relationship between charter value, risk, and incentive compensation, instead of studying them separately as has been done in most literature so far. Comparing the results with different coefficients for the charter value in Table 2, we find different relationship between manager’s risk choice and his incentive compensation. For instance, when the maturity of the debt increases from 2 to 3 years, with charter value coefficients a = 0.10, b = 1 and c = −2, the shareholders grant more incentive compensation to the manager who prefers to take more risk. While with charter value coefficients a = 0.15, b = 1 and c = −2, i.e. increasing the value of the intercept a, the shareholders grant less incentive and the manager prefers to take even more risk. This then stresses the importance to account for charter value effect in examining the relationship between manager’s risk taking and his incentive compensation. We perform sensitivity analyses by varying the values of some parameters while keeping others constant. For instance, when the maturity of the guaranteed debt increases, the manager takes more risk. This is because the guarantor’s net asset value (shared by the shareholders and the manager) has an imbedded option, and the longer the maturity of the guaranteed debt, the higher the time value of the imbedded option. Furthermore, this time value increases for the manager as he takes on more risk. Therefore, granting the manager more shares (that is, equity) incites him to take on even more risk. In our framework, there are two ways to increase the guarantor’s leverage: by increasing the leverage of the existing portfolio or by adding a more leveraged firm to the guaranteed portfolio. Our results indicate that in both cases, the manager’s appetite for risk increases with the magnitude of the guarantor’s leverage ratio. Intuitively, higher leverage makes the guarantor’s residual value looks like an out-of-the-money option. In terms of utility, it is therefore more valuable for

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the manager to take more risk: by doing so, he gambles for an unlimited upside payoff with a limited downside loss. In that case, granting him more shares does not necessary alter his risk-taking behavior. The correlation between the guarantor’s existing portfolio and its new guaranteed client-firm is crucial for overall risk diversification. Unlike the leverage ratio, when this correlation is high, the manager tends to choose lower risk to decrease overall portfolio risk. 4. Conclusion This paper considers charter value in developing a new and rich model for the incentive-based compensation of the managers of the guarantors of firms’ risky debt. In this model, the manager makes costly portfolio investment and risk decisions on behalf of the guarantor. Comparing our results to the first-best case of no agency conflict, we find that in our model, the manager takes more risk than the first-best case without agency conflict would suggest. Moreover, we find that charter value has a disciplinary effect on the manager’s risk-taking behavior. This suggests that scholars should study charter value, managerial compensation and risk decisions within a unified framework and not separately, as all studies have done in the past. Appendix A. If two stochastic variables (X, Y) follow a bivariate lognormal distribution, then their transformation (ln(X), ln(Y)) are bivariate normal distributed with the following probability density function: f (X, Y ) =

1

2X Y



(1 − 2 )XY



× exp

A2 + B2 − 2 AB − 2(1 − 2 )



,

(A.1)

where A = (ln(X) − X )/ X , B = (ln(Y) − Y )/ Y , and is the correlation between the variables. The marginal distribution of the variables ln(X) and ln(Y) are N(X , X2 ) and N(Y , Y2 ), respectively. The following expressions follow:



+∞



+∞

f (X, Y )dX dY = 1 − N(l) − N(m) + N(l, m, ), l



l



+∞

f (X, Y )dX dY = N(l) − N(l, m, ), −∞



(A.2)

m

l

(A.3)

m



m

f (X, Y )dX dY = N(l, m, ), −∞

(A.4)

−∞

where N(x) is the cumulative distribution function of the standard normal distribution and N(x, y, ) is the cumulative distribution function of the standard bivariate normal distribution with correlation

between the variables. The guarantor’s net asset value at the maturity of the guaranteed firm debt is: EWT = max(WT − FW − max(FV − VT , 0), 0) + WT 1{WT >FW +max(FV −VT ,0)} − hWT 1{WT
(A.5)

Using the risk-neutral measure, the expectation of the present value of the above equation is: EW0 = E[e−rT {max(WT − FW − max(FV − VT , 0), 0) + WT 1{WT >FW +max(FV −VT ,0)}



− hWT 1{WT
+∞



+∞

((1 + )WT − FW )f (V, W )dW dV FV

FW

V.S. Lai et al. / Research in International Business and Finance 26 (2012) 387–397



+∞

− e−rT h



FV



FW

FV

WT f (V, W )dW dV + e−rT

0



− FW )f (V, W )dW dV − e−rT h

FV



+∞

((1 + )WT + VT − FV FW +FV −VT

0



395

FW +FV −VT

WT f (V, W )dW dV 0

(A.6)

0

We divide formula (A.6) into six parts as follows: EW0 = G1 − G2 + G3 − G4 − C1 − C2, where



+∞

G1 = e−rT (1 + )

 

FV



+∞

(A.7)

+∞

f (V, W )dW dV

(A.8)

((1 + )WT + VT )f (V, W )dW dV,

(A.9)

FW



+∞

FW +FV −VT

0

 G4 = e

WT f (V, W )dW dV,

FV

G3 = e−rT

+∞

FW

FV

G2 = e−rT FW



FV

−rT



+∞

(FW + FV )f (V, W )dW dV,

(A.10)

FW +FV −VT

0



+∞

C1 = e−rT h



FW

WT f (V, W )dW dV, FV



FV

C2 = e−rT h



(A.11)

0 FW +FV −VT

WT f (V, W )dW dV, 0

(A.12)

0

and f(V, W) is the joint probability density function given by (ref. Eq. (A.1)): f (V, W ) =



V0 (W0 + )



2V W TVW

 +



1 − 2

1 2(1 − 2 )

exp −

2 /2)T ln(W/W0 + ) − (r − (W √ W T



2

 − 2

2 /2))T ln(W/(W0 + )) − (r − (W √ W T



ln(V/V0 ) − (r − (V2 /2))T √ V T

ln(V/V0 ) − (r − (V2 .2))T √ V T

2



.

Next we compute the integrals to obtain the explicit expressions of Eqs. (A.7)–(A.12). We provide the detailed calculations for one integral for illustrative purpose, as the other integrals are computed similarly. Let us consider formula (A.7). We can rewrite it as follows:



G1 = e−rT (W0 + )

+∞



Z

+∞



√ YW T +



U

r−

2 W

2

  T

g(X, Y, )dY dX,

with X =

ln(V/V0 ) − (r − (V2 /2))T , √ V T Z=

Y=

2 /2))T ln(W/(W0 + )) − (r − (W , √ W T

ln(FV /V0 ) − (r − (V2 /2))T , √ V T

g(X, Y, ) =

1

2



1 − 2

U=

e−(1/2(1−

2 /2))T ln(FW /(W0 + )) − (r − (W , √ W T

2 ))(X 2 +Y 2 −2 XY )

(A.13)

396

V.S. Lai et al. / Research in International Business and Finance 26 (2012) 387–397

√ To simplify √ the calculations, we make the following change of variables: X1 = X − W T and Y1 = Y − W T , then formula (A.13) becomes:





+∞

+∞

G1 = (W0 + )

f (X1 , Y1 , )dX1 dY1 , Z1

U1

√ √ where Z1 = Z − W T = d3, U1 = U − W T = d4 and f(X1 , Y1 ) is the bivariate normal density function given in (A.1). For Eqs. (A.8)–(A.10), we use the same method as above, and obtain:



G2 = e−rT FW

+∞



+∞

f (X, Y, )dY dX, d5

d6



d3



 G4 = e



+∞

G3 = (1 + )(W0 + )

−rT

(A.14) d8



+∞

f (X, Y, )dY dX + V0 −∞ d5

f (X, Y, )dY dX, −∞

d7(x)



+∞

(FW + FV )

f (X, Y, )dY dX, −∞

(A.16)

d10(x)

with d5 =

ln(FV /V0 ) − (r − (V2 /2))T , √ V T

d6 =

2 /2))T ln(FW /(W0 + )) − (r − W , √ W T

√ √ d3 = d5 − W T , d4 = d6 − W T ,

d7 =

2 /2))T √ ln((FW + FV − V2 (X))/(W0 + )) − (r − (W − W T , √ W T

 V2 (X) = V0 exp

r−

V2



2

√ T + V T X + W V T

 ,

√ d8 = d5 − V T ,

d9 =

2 /2))T √ ln((FW + FV − V3 (X))/(W0 + )) − (r − (W − V T , √ W T

 V3 (X) = V0 exp

d10 =

r−

V2



2

√ T + V T X + V2 T

 ,

2 /2))T ln((FW + FV − V1 (X))/(W0 + )) − (r − (W , √ W T

 V1 (X) = V0 exp

r−

V2 2

(A.15)

d9(x)



√ T + V T X

 .

V.S. Lai et al. / Research in International Business and Finance 26 (2012) 387–397

397

Using the expressions (A.2), (A.3) and (A.4), we obtain the explicit expressions for Eqs. (A.7)–(A.12) as follow: G1 = (1 + )(W0 + )[1 − N(d3) − N(d4) + N(d3, d4, )], G2 = e−rT FW [1 − N(d5) − N(d6) + N(d5, d6, )], G3 = (1 + )(W0 + )[N(d3) − N(d3, d7, )] + V0 [N(d8) − N(d8, d9, )], G4 = e−rT (FW + FV )[N(d5) − N(d5, d10, )], C1 = h(W0 + )[N(d4) − N(d3, d4, )], C2 = h(W0 + )N(d3, d7, ). Finally, the expectation of the present value of the guarantor net asset is: EW0 = G1 − G2 + G3 − G4 − C5 − C6 = (1 + )(W0 + )[1 − N(d4) + N(d3, d4, ) − N(d3, d7, )] + V0 [N(d8) − N(d8, d9, )] − e−rT FW [1 − N(d6) + N(d5, d6, ) − N(d5, d10, )] − e−rT FV [N(d5) − N(d5, d10, )] − h(W0 + )[N(d4) − N(d3, d4, ) + N(d3, d7, )].

(A.17)

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