Supply chain finance risk management

Definition 1

Given the fixed contract (q, ξ), the value γ ( q , ξ ) = u h ( q , ξ ) − u l ( q , ξ ) refers to the benefit of being a high-type operator compared with a low-type operator.

For the two contracts ( q h , ξ h ) and ( q l , ξ l ) in a contract menu, γ ( q h , ξ h ) = u h ( q h , ξ h ) − u l ( q h , ξ h ) = − ( ξ h + c ) q h + ( ξ h + c + 1 ) θ h + min ( φ + c − ξ h , μ + c − ξ h ) q h and γ ( q l , ξ l ) = u h ( q l , ξ l ) − u l ( q l , ξ l ) = − ( φ + c ) q l + ( φ + c + 1 ) θ h + min ( φ + c − ξ l , μ + c − ξ l ) q l . The value γ may be positive or negative. The operators lose their incentive to disguise the truth when γ is insignificant.

To evaluate the optimal contract design, a truth-telling mechanism can be implemented by applying the revelation principle and envelope theorem (Dasgupta et al., 1979; Myerson, 1981, 2008). Two stages of games are involved in this mechanism, namely, contracting and executing. Operators hold private information on their payment ability at the beginning of the contracting stage and provide claimed information regarding their types. For an operator with a tendency-to-pay θ_i, the hotel expects an income of U ( q i , ξ i , y i , θ i ) = y i + ξ i ( q i − y i ) + sgn ( θ i ) , which is equal to an immediate payment plus a credit payment from high-type operators. The hotel cannot receive any credit payment from low-type operators by definition; thus, the second term is zero on sgn ( θ l ) = 0 . The hotel designs a menu of contracts to collect information that could reveal the true type of an operator while maximizing the expected value of profit π ( y ) = max ( q ( θ ) , ξ ( θ ) ) E [ U ( q , ξ , y , θ ) ] . Therefore, the combined informatics game is given as follows:

π ( y ) = max ( q i , ξ i ) i ∈ { H , L } { ∑ i α [ y i + ξ i ( q i − y i ) + sgn ( θ i ) ] }

1

s . t . u i ( q i , ξ i ) ≥ u i ( q j , ξ j ) , ∀ i ≠ j , (IC)

2

u i ( q i , ξ i ) ≥ 0 , ∀ i . (IR)

3

The incentive compatibility (IC) constraints (equation (2)) make the contracts ( q i , ξ i ) satisfying to ensure that the designed contracts induce self-selection. Note that the term self-selection refers to the situation that high-type operators only select a high-type contract, whereas low-type operators select a low-type contract. The benefit of an i-type operator accepting an i-contract must be higher than that of accepting other contracts. Individual rationality (IR) constraints (equation (3)) make the contracts ( q i , ξ i ) satisfying to ensure participation. The benefit of accepting a contract must be higher than that of not accepting any contract. Problem (1) yields a second-best contract, which is less optimal because the hotel surrenders a part of its profit to satisfy the IC constraints and exchange for operators’ private information. By contrast, obtaining the best contract under information symmetry is possible, and the profit of the hotel is fully maximized because the contracts are tailored to each type of operator. Therefore, an operator selecting contracts that are not designed for the operator is impossible. Following mechanism design theory and given the freedom of choice and sufficient incentives provided in the contract terms, a self-selection contract enables each operator to follow the expectation of credit-principals and self-select a designated contract capable of revealing their tendency to pay, which is otherwise hidden from the hotel.

Proposition 1

The optimal contracts { ( q h ° , ξ h ° ) , ( q l ° , ξ l ° ) } and optimal profits π° for the hotel under information symmetry are listed in Table 3.

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Table 3.

Solutions of the optimal contracts for the hotel under information symmetry.

Regimes	Conditions	q h °	ξ h °	q l °	ξ l °	π°
(I)	μ ≥ φ	p φ + c + θ h	φ	p φ	c	α ( θ h + φ p φ + c ) + ( 1 − α ) p φ
(II)	μ < φ	p φ + c + θ h	φ	p μ	c	α ( θ h + φ p φ + c )

Table 3 shows the optimal contract design { ( q h ° , ξ h ° ) , ( q l ° , ξ l ° ) } , which is represented by the superscript (⋅)°, and benchmark profits when operators truthfully report their types. The hotel makes the most profit with knowledge of the types of operators. The hotel tends to grant credit to high-type operators but encourages low-type operators to pay in full immediately because the latter are known to be less trustworthy. The hotel manager can easily maximize its profits according to the suggestion (see Figure 1) because information related to the types of operator is transparent. In an ideal world, the hotel manager can see through each agent’s true payment intention (high or low) and the agents do not hide any information. Therefore, the manager knows all high-type operators will pay and all low-type operators intend to default. In regime (I) of Figure 1, the hotel in a healthy business environment can allow high-type operators to defer payment to earn profit and motivate low-type operators to pay immediately to avoid income loss. In regime (II), the hotel in a speculative environment continues to trust high-type operators but refuses to transact with low-type ones because the default intention is known to everyone.

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Figure 1.

Optimal business strategies under information symmetry.

An optimal contract in this ideal world suggests a lower price q_l to low-type operators compared with q_h offered to high-type operators. A hotel can unilaterally design an “optimal” contract that extracts all profits from operators without worrying about high-type operators selecting an l-type contract because high- and low-type operators can only accept h-type and l-type contracts, respectively. That is, the operators’ profits become u h h = p − ( φ + c ) ( q h − θ h ) = 0 and u l l = p − min ( φ + c − ξ l , μ + c − ξ l ) q l = p − p = 0 , where u_ij represents the utility for i-type agents accepting a j-type contract.

However, without an effective mechanism, self-selection would not be guaranteed under the contracts in Table 2 if operators were free to select the best contracts for improved profits. High-type operators will unexpectedly choose l-type contracts, under which the agents maximize their profits. In proposition 1, if the hotel knows the types of operators but cannot ensure self-selection from a contract mechanism, this model implies double marginalization: The total profit of the hotel and tour operators is less than the one under self-selection. The utility in situations where cross-selection is allowed, under which an h-type operator chooses an l-contract, becomes u h l = ( φ + c ) θ h − c φ p ≥ 0 when p c φ ( φ + c ) < θ h . Therefore, high-type operators obtain incentives by disguising themselves as low-type ones without exposing their financial conditions. On the part of low-type operators, u l h = p − min ( φ + c − ξ l , μ + c − ξ l ) q h = p − min ( φ , μ ) ( p φ + c + θ h ) = φ + c − min ( φ , μ ) φ + c p − min ( φ , μ ) θ h < 0 , such that low-type operators prefer to remain who they are and hide nothing about their type. Hotel profits diminish from θ h + φ p φ + c (Table 3) to p φ (Table 4) once all operators disguise themselves as low-type operators.

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Table 4.

Profits and utility when all operators pretend as low type.

Regimes	uhl	ulh	π (Disguise)
(I)	( φ + c ) θ h − c φ p > 0	c φ + c p − φ θ h < 0	α p φ + ( 1 − α ) p φ
(II)	( φ + c ) θ h − c φ p > 0	φ + c − μ φ + c p − μ θ h < 0	α p φ

The contract solutions in Tables 3 and 4 reveal a counterintuitive reaction: Untrustworthy operators tell the truth, whereas reliable ones deceive. This disguising phenomenon is generally attributed to the relatively high contract price for high-type operators in the first design of contract optimization. All operators appear to be low-type ones when they can select from the contracts in Table 3. In this case, low-type operators do not worry about exposing themselves because the hotels are unable to distinguish between the good and bad ones. Thus, the hotel performs risk management blindly or based on probability. The hotel has no reliable method of identifying operator types before a truth-revealing contract menu can be designed properly, and anyone is equally likely to incur bad debts or generate revenue streams. A rough idea in urging high-type operators to select the h-type contract is to reduce the price and increase credit rate. However, determining the extent of price reduction is not straightforward because a poorly designed contract may conversely enable low-type operators to disguise themselves as high-type ones. Therefore, the discovery of operators’ true types is the key in devising an effective set of risk management strategies.

Proposition 2

The optimal contracts { ( q h * , ξ h * ) , ( q l * , ξ l * ) } for the hotel under information asymmetry are listed in Table 5. The condition discriminating regimes (i) and (iii) is as follows

φ = 1 2 ( 1 − α α + 3 − c )

5

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Table 5.

Solution of the optimal contracts for the hotel under information asymmetry.

Regimes	Conditions	q h *	ξ h *	q l *	ξ l *
(i)	μ ≥ φ ≥ 1 2 ( 1 − α α + 3 − c )	p c	φ	p φ + c + θ h	θ h ( φ + c ) q l
(iii)	min ( μ , 1 2 ( 1 − α α + 3 − c ) ) ≥ φ	q l φ + c − 1	1	p φ + c + θ h	φ + c − 1
(ii)	μ < φ	p c	φ	p φ + c + θ h	θ h ( μ + c ) q l

Table 5 shows the optimal contract design when operators hide their types from the hotel and where the optimization values are represented by the superscript (⋅)*. The contract allows the hotel to surrender the least share of benefits to the operators and effectively eliminate any disguise. Therefore, IC constraints are satisfied under the informatics game (5). Thus, high-type operators lose motivation to disguise themselves as low-type ones because the incentives received from the hotel are higher than those provided if they pretend to be low-type operators. In proposition 2, the hotel manager does not know the types of operators. As a result, self-selection surely will not be guaranteed without an effective mechanism. In this disguised world, the service provider makes the same contract with all types of operators without knowing their types.

Self-selected tour operators could benefit from either price discounts or delayed payments for an improved cash flow. The solutions in Table 5 achieve the goal of mechanism design and yield a menu of self-selection contracts, thereby effectively preventing both types of operators from disguising themselves. The contract ( q h * , ξ h * ) provides a low credit rate ξ h * that fits the profile of reliable operators but a high price q h * can exclude false selection from low-type operators. By contrast, the contract ( q l * , ξ l * ) offers a low price q l * before bad debts occur to encourage immediate payment of less trustworthy operators, but a high credit rate ξ l * can prevent unexpected selection from high-type operators.

This study’s optimal contract design can also prevent certain unprofitable actions by hotels. Hotels that are unaware of the true financial condition of operators often act over-prudently on most business transactions, including asking for a high wholesale price q or a high credit rate ξ. This reaction may not be desirable in a speculative business world. Regimes (i) and (iii) of Table 5 show that a sufficiently low q_l can induce immediate payment from less trustworthy operators. Therefore, the money that could otherwise disappear can be collected.

A guideline for risk mitigation strategies can be devised based on the contract design in Table 5. Because we are in a disguised world, the hotel manager cannot know the agent’s true payment intention (high or low) and the agents have motives to hide their types. With the use of a truth-telling tool, we summarize our strategies in Figure 2 by subdividing regime (I) in Figure 1 of a healthy business environment into regimes (i) and (iii), whereas the speculative business environment remains in regime (ii). The hotel manager is unaware of operator types; thus, a concession of profit between the hotel and the operators results in the latter’s confession of private information. Figure 2 explicitly shows the types of operators resulting from the revelation of the designed contract. To ensure self-selection, that is, the high types selecting a high-type contract and not pretending to be the low types to enjoy the benefit for inducing the truth, the hotel must pay extra incentives to the high types to let them stick to a high-type contract.

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Figure 2.

Optimal payment strategies under information asymmetry.

If the goodwill loss when defaulting is higher than that of borrowing from a bank to pay off debts, or μ > φ, as shown in regimes (i) and (iii) of Figure 2, then low-type operators borrow money to pay all debts. By contrast, high-type operators defer a portion of payment, that is, y l * = q l and y h * = θ h . The condition discriminating regimes (i) and (iii) lies in the difference between φ and α. If φ is low, then the hotel should sacrifice a portion of its income to keep high-type operators from borrowing by offering a contract with a low trade credit rate. Thus, the hotel can consistently judge the types of operators based on their credit behavior. High-type and low-type operators in regime (ii) of Figure 2 are also well distinguished by the contract menu. However, the hotel does not risk cooperating with low-type operators because they are highly likely to incur bad debts.

The hotel should incur additional cost to compensate for the motivation of deception because operators tend to pretend to be of low type to enjoy discounted payment if paid immediately. Therefore, this additional cost paid to high-type operators is defined as information rent γ ≡ γ h − γ l , which is also the high-type operators’ gain in u h h from information symmetry to information asymmetry.

Figure 3 suggests risk attitudes for the hotel manager facing business uncertainty α given the results of proposition 2. Figure 3 mirrors the regime setting of Figure 2 but changes the coordinates to bank rate φ and the percentage of high types α, respectively. Note that the high types have incentives to become low-types to enjoy better terms. Therefore, the higher the percentage of the high types exists in a market, the more the cost the hotel needs to bear. Therefore, the hotel becomes less profitable and it must conduct its business more conservatively. The extent of willingness to pay high information rent γ in exchange for the truth and certain returns is an attitude that accommodates risk. The value γ and ( q h , ξ h ) in regime (i) are higher compared with that in regime (iii). Therefore, the risk attitudes in regimes (i) and (iii) are termed as conservatism and progressivism, respectively. Regime (i) is conservatism and regime (iii) is progressivism because hotels in regime (iii) pay a larger q_i amount than the q_i at the same level of uncertainty in regime (i). The risk attitude of progressivism is associated with low information rent, and the benefit of acquiring true information does not exceed the cost of offering a contract. Therefore, a progressivism attitude may lead to high profit in a risky business environment.

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Figure 3.

Risk attitudes toward business uncertainty.

However, low-type operators tend to defer payment at high credit rates. The hotel in regime (ii) should reject doing business with low-type operators because of their evident default intention. The risk attitude in regime (ii) is called differentiation.

Proposition 3

The optimal profit π* earned by the hotel, information rent γ, and value of information δ to the hotel are listed in Table 6.

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Table 6.

Optimal profits of the hotel for each contract under information asymmetry.

Regimes	π h * and γ	π l * and δh	δl
(i)	α ( φ p c + ( 1 − φ ) θ h ) and ( φ + c ) ( p φ + c + θ h − p c )	( 1 − α ) ( p φ + c + θ h ) and φ ( p φ + c + θ h − p c )	p φ − ( p φ + c + θ h )
(iii)	α ( p φ + c − ( φ + c − 3 ) θ h ) and ( 1 + c ) ( φ + c − 2 φ + c − 1 ( p + θ h ) + p φ + c )	( 1 − α ) ( p φ + c + θ h ) and ( φ − 1 ) p φ + c + ( φ + c − 2 ) θ h	p φ − ( p φ + c + θ h )
(ii)	α ( θ h + φ ( φ p c − θ h ) and ( φ + c ) ( p φ + c + θ h − p c )	0 and φ ( p c − ( p φ + c + θ h ) )	0

The various types of benefits that each type of operator brings to the hotel under information asymmetry are presented in Table 6, which shows that the hotel earns less as compared with Table 3 although the total channel profits increase. Part of the profit loss for the hotel is transferred to the operators, who are the information holders. Thus, the hotel should reduce the motivation of operators to disguise themselves while maintaining the maximum profitability of the hotel to uncover the types of the operators.

The targeted risk event is a payment default from the tour operators. Risk management refers to the implementation of actions in reducing the consequences of possible risk events. Most businesses do not simply walk away from all risk because doing so also precludes potential income. Most existing risk management practices are based solely on a risk value that is determined by the estimated likelihood of a risk occurrence and the financial consequence in a risk event. For risk assessment modeling, the percentage of less trustworthy operators and the selling price of hotel rooms are set as the likelihood and the consequence, respectively. However, this study’s risk assessment maximizes the use of hidden information in the decision-making process.

Proposition 4

Retail price p must be confined within the range of φ + c φ + c − 1 θ h ≤ p ≤ φ c ( φ + c ) θ h based on the optimal solutions in Table 5. Moreover, the hotel surrenders substantial profits to high-type operators if α ≥ 1 1 + φ and α ≥ θ h − c φ ( φ + c ) p ( φ + c − 1 ) θ h − c φ ( φ + c ) p for regimes (i) and (iii), respectively. The change rates in profit in regimes (i) and (iii) satisfy ∂ π ( i ) ∂ α ≤ 0 for p ≤ c ( φ + c ) ( φ + c ) − c φ θ h and ∂ π ( i i i ) ∂ α ≤ 0 under all conditions.

Proposition 4 elaborates the key decision framework in this study. Figure 4 summarizes the resulting risk mitigation strategies. Decision-making is straightforward for a sufficiently high p. When the retail price p is high, the operators’ reward increases and business transactions tend to shift toward cooperation for all types of operators, regardless of risk. This situation is considered a high-reward event in risk assessment. When α is high, a high percentage of reliable operators are available in the market and the hotel anticipates a low probability of payment default. Therefore, a considerably high α results in a low risk of payment default. The situation is a low-risk event in risk assessment.

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Figure 4.

Risk mitigation strategies.

High-type operators lose the motivation to disguise themselves as low-type ones when p is high, such as p > φ c ( φ + c ) θ h . Self-selection becomes automatic; thus, profit is maximized. Figure 4 shows a strategy called Euphoria because the hotel does not need to do anything to gain the maximum profits. However, all parties cease to transact if p becomes too low to be attractive or p < φ + c φ + c − 1 θ h . This strategy is called Rejection because of the existence of an extremely unfavorable business environment. Other risk strategies derived from this study’s contracts are presented excluding the two extreme cases of Euphoria and Rejection.

Four risk mitigation strategies are adopted in relation to the analytic results: avoidance, acceptance, transfer, and sharing (cf. Norrman and Jansson, 2004). Risk avoidance eliminates events that can trigger risks. Risk prediction and credit screening of customers are examples of risk avoidance strategies. Risk acceptance refers to the self-absorption of risks and its consequences. Preparing a reserve fund is an example of risk acceptance strategies. The ambiguous situations of low-reward, low-risk and high-reward, high-risk are considered in four detailed transfer and sharing strategies through information-inductive tools. Risk transfer often refers to the use of mechanisms to transfer risks to other parties or financial institutions, such as insurance companies, supply chain partners, and customers. Therefore, this study further distinguishes between the case of paying premium as risk transfer and the case of providing collateral as liability transfer. Finally, a general risk sharing strategy emphasizes the reduction of a risk impact by distributing risks to multiple parties or objects, such as business diversification. This study also views revenue sharing as risk sharing and business opportunity as liability sharing, because the former uses money and the latter uses the tool of making money to trade financial safety. Several hotels can perform risk sharing by sharing a credit loss collectively or performing liability sharing by collaboratively offering hotel rooms to complete a single transaction. The conditions in proposition 4 are further applied to concrete risk mitigation strategies through the following arguments. Proposition 4 shows that our focus is on the price range [ φ + c φ + c − 1 θ h , φ c ( φ + c ) θ h ] . A risk acceptance strategy is suggested when the price is sufficiently high, such as when φ + c φ + c − 1 θ h ≤ c ( φ + c ) ( φ + c ) − c φ θ h ≤ p ≤ φ + c φ + c − 1 θ h . The hotel can control the risk at an acceptable level because the probability of receiving a bad debt is low. Risk in a risk acceptance strategy is acknowledged and cooperation can be established without controlling for consequent loss. Although the hotel may have to bear profit cuts to pay information rent in this price range, all parties can still earn considerable profits because of their cooperation (Table 6). Thus, the hotel can obtain high profit and maintain business relationships with prospective operators by adopting the acceptance strategy under favorable conditions.

The process of decision-making becomes ambiguous when business transactions are conducted in high-reward, high-risk or low-reward, low-risk situations because both situations are endowed with similar risk values in terms of quantitative steps of most-risk assessment processes. Determining a suitable mitigation strategy solely on the basis of the risk value is difficult without referring to other factors. The two boundary prices indicated in proposition 4 characterize an interesting region in Figure 4, which includes regimes (i) and (iii), and are divided by the discriminating α value in equation (5). High-reward, high-risk and low-reward, low-risk agents occupy the left and right wings of the region, respectively. In regime (i), the hotel is dealing with a low-reward, low-risk operator if α ≥ 1 1 + φ and φ + c φ + c − 1 θ h ≤ p ≤ c ( φ + c ) ( φ + c ) − c φ θ h (proposition 4). Thus, paying a positive value for information is necessary, that is, δ ( i ) ≥ 0 .

Low-type operators would prefer to borrow when the interest rate imposed on borrowing from a bank is lower than that imposed on delayed payment. Thus, the hotel encourages low-type operators to pay immediately by reducing prices that are lower than the h-type price and adapting transfer strategies by transferring risks to a third-party institution. The hotel’s accountability, responsibility, and authority under the transfer strategies are reassigned to another stakeholder (i.e. the bank) who is willing to accept the risks. Thus, the hotel earns high profits from transactions with reduced risks. Given that most agents are reliable in regime (i) and hotel profit is reduced slightly, the hotel exercises the risk transfer strategy by sharing a small amount of income, which is equivalent to an insurance premium. Conversely, if α < 1 1 + φ , then the hotel receives the value of information, that is, δ ( i ) < 0 . The hotel should adopt the liability sharing strategy by sharing business opportunities with other partners because the hotel remains profitable in a moderate-risk environment.

Only a small percentage of operators in regime (iii) is reliable. Therefore, the hotel should focus on collecting revenues from low-type operators and pay information rent to high-type ones, that is, ∂ π ( i i i ) ∂ α ≤ 0 (proposition 4). Hotels in the region with α ≥ θ h − c φ ( φ + c ) p ( φ + c − 1 ) θ h − c φ ( φ + c ) p and a negative δ ( i i i ) should adopt a liability transfer strategy by transferring debt ownership to financial institutions. Conversely, the region characterized by α < θ h − c φ ( φ + c ) p ( φ + c − 1 ) θ h − c φ ( φ + c ) p represents a situation that involves high-reward, high-risk partners. Hence, the hotel should design contracts based on a risk sharing strategy by pooling a reserved fund to cover credit losses from low-type operators because most of them obtain high rewards.

Regime (ii) is excluded in Figure 4 because it does not involve α. Therefore, avoidance strategy is clearly associated with regime (ii). The hotel should exercise avoidance strategy when detecting profit loss tendency because of defaulting from low-type operators to prevent risky transactions in which rewards and well-being drop to unacceptable levels. The hotel can design a contract to enable the low-type operator to voluntarily terminate the cooperation. Contract terms or constraints are adjusted to eliminate or reduce risks. These adjustments can be accommodated by changing the funding, schedule, or technical requirements.

Discovering the truth behind operators’ minds is considered the most difficult component of risk management. This study’s trade credit tool can overcome this challenge. The operator types are manifested, and business operation strategies are determined. Thus, the hotel can engage effectively with agents who can bring additional profits. The hotel earns profits with mitigated financial risks by paying information rent to discourage operators with low tendency-to-pay from opting for payment default. Existing due diligence measures, such as enhancing the rating for quality, qualifications, or credit of an enterprise, can be applied as strategic supplements.

Proposition 5

A high bank rate results in high information rent, thereby diminishing the gap between the values of high- and low-type information to hotel profits. That is, ∂ γ ∂ φ ≥ 0 except if θ h < 1 c p in regimes (i) and (iii), ∂ δ h ∂ φ ≥ 0 except if θ h < φ c ( φ + c ) φ + 2 c φ + c p in regimes (i) and (iii), and ∂ δ l ∂ φ ≤ 0 .

Proposition 5 implies that the cost of implementing an effective contract depends on the bank borrowing rate, which is generally a standard indicator in measuring economic prosperity. In terms of the changes in hotel profit, both loss in high-type operators and gain in low-type operators decrease in high bank rate cases. The value of high-type information to hotel profit is negative, whereas that of low-type information is positive. Therefore, the net effort of the hotel in extracting type information decreases when the bank rate is high. Our risk mitigation strategies require limited effort under good economic conditions. However, paying high costs in the case of low bank rates is suggested because the loss and gain of the hotel are not transferred completely to the operators. Low-type operators with a positive value of information to hotel profit should not be disregarded automatically. A good risk management strategy can ensure profitability, even in a risky environment, when information is revealed.

Proposition 6

A high tendency level of high-type operators (θ_h) leads to high values of information to tourism channel profit, that is, ∂ Δ ∂ θ h > 0 if 1 < φ < 2. The values of information to the hotel and channel profit also increase with the percentage of high-type operators, that is, ∂ δ ∂ α ≥ 0 and ∂ Δ ∂ α ≥ 0 .

Proposition 6 indicates that the profit of the entire tourism channel increases with a high tendency-to-pay (θ_h) when the proposed risk management strategies are implemented in a moderate business environment. Extreme pricing conditions, which are higher or lower than the two price boundaries, should be excluded because hotel losses are unlikely to be converted into channel profits. Therefore, engaging with operators with a high tendency-to-pay should be encouraged regardless of information rent losses. An increasing number of high-type operators may similarly lead everyone to have a positive risk attitude. Thus, a healthy business environment leads to profitability for all business participants.