Explicit Contingent Liabilities in Debt Management*
IV. Valuation and pricing of government guarantees Introduction
The current value and nature of guarantees should be reported publicly. Such a system supports transparency and sound decision-making and encourages use of guarantees only in situations where other forms of support are less efficient.
IV. Valuation and pricing of government guarantees
government’s role in the economy, market-related fees should thus be the point of departure whenever government guarantees might otherwise put companies at an unequal footing.
Box 6.1. Illustration of the risk of a loan guarantee
Figure 6.1 below shows a hypothetical probability distribution of the net assets of a given company. Net assets are defined as the market value of the underlying assets of the company (equal to the market value of equity and debt) less the face value of debt. The face value of debt is assumed to be 100.
Figure 6.1. Probability distribution of net assets
If the company is profitable and net assets are positive, the creditors will receive the full amount of 100, while the excess asset value accrues to shareholders (pink part of distribution). On the other hand, if equity has become worthless, the company will only be able to service the debt in amounts equal to the liquidation value of assets, i.e.the market value of debt will fall short of the face value (blue part of distribution). In the worst case, the market value of underlying assets is zero and the company defaults on the full debt obligation of 100.
If the debt is covered by a government guarantee, the lenders will receive 100 regardless of the performance of the company, and the credit risk is transferred to the government, i.e.the potential losses in the red part of the distribution must be borne by the government. In the case of positive net assets, the government does not stand to gain apart from any fees received for issuing the guarantee if the government is not a shareholder. If the government is a shareholder, both potential losses and gains should be part of an overall risk assessment.
9
-100 8 7 6 5 4 3 2 1
0 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Per cent
Creditor/guarantor loss Shareholder value
Net asset value
Application of market-related fees by the government raises the question of why the government should issue guarantees at terms identical to the private market in the first place. The reason may be that private agents are in fact not willing to provide certain guarantees, which would constitute a market failure that legitimises government intervention. Of course, in this case a market-related fee will be a hypothetical concept. Irrespective of the possibility of market failures, it is appropriate to establish the principles and the context for application of market-related fees in a budget act to prevent illicit state aid and ensure disclosure.
If state aid is not an issue, the calculation of collected or budget-funded fees needs not be based on market values. Indeed, the expected cost is the
“best” assessment in average terms of the fiscal burden from the guarantee portfolio and thus provides a sensible yardstick for fiscal/budgetary planning.
It should be pointed out, however, that government guarantees are an attractive form of subsidy relative to, for example, comparable direct money transfers when expected values are applied – both from the perspective of the recipient of the subsidy and the decision makers in the government. This points to the possibility of excessive guarantee issuance, raising the risk exposure of the government, if the guarantee portfolio is not subject to prudent risk management.
For example, assume that the government issues a loan guarantee with an expected value of 100 and a market value of 120. The recipient will prefer a guarantee to a direct appropriation of 100, since the real value to the recipient of a guarantee is 120. Also, by issuing a loan guarantee the government can provide more support for a given amount of budget appropriations. The actual costs of the individual guarantee are the same irrespective of the rule used to set aside budget means. But since a given budget will permit issuance of more guarantees under expected cost pricing, the government may end up with more guarantees and higher risks in its overall balance sheet in this case.
Box 6.1. Illustration of the risk of a loan guarantee (cont.)
In this example the government will experience a loss of 20 or more with a probability of around 12 per cent by guaranteeing the debt obligations of the firm. The expected loss from the guarantee is calculated as the sum of potential losses weighted with their respective probabilities, and thus expresses a risk neutral valuation of the credit risk. The expected loss in this example is 5.9. If the government in fact suffers a loss under the guarantee, it may be much larger than the expected loss, possibly as high as 100, implying that the whole loan has to be written off.
Given the size of government balance sheets, risk neutrality may apply to the assessment of any single guarantee. However, depending on the magnitude of risk in the overall guarantee portfolio, and the risk tolerance in general, it might be appropriate for the government to set a mark-up on the expected costs to protect against unexpected outcomes even if state aid is not a concern.
Pricing methods
Pricing government guarantees requires an assessment of the contingencies where the asset value of the guaranteed company will fall short of the government guaranteed obligations. A number of factors thus may come into play, including project or company specific risks, the course of the general macro economy, the initial equity/debt ratio, and the actions of the management. In some cases relevant information may be readily available. In other cases a fundamental analysis of the risk characteristics of the guarantee may be required.
Implicit guarantee pricing
Bond prices reflect the credit risk of the borrower. If the potential recipient of a guarantee has issued actively traded bonds, the bond price thus contains information on the value of a guarantee.
If the government issues a guarantee, the guaranteed debt should trade at a price equivalent to risk-free bonds. Therefore, the implicit market value of a guarantee can be calculated as the difference between the market value of a risk-free government bond and the market value of bonds issued by the potential recipient of the guarantee.6 A larger credit risk decreases the bond price and increases the value of the guarantee.
If the potential recipient of the guarantee has not issued traded bonds, bond price information from comparable companies may serve as a substitute. Similarly, if it is possible to attach a specific rating to the recipient, the yield spread of that rating category to government bonds could be used to price the guarantee.
This implicit valuation methodology provides the market value of the guarantee and can be used to set market-related fees. The market value comprises the expected or risk-neutral value of the guarantee. But in addition, it will most likely include a risk premium, which reflects the market’s required premium for being exposed to unexpected contingencies. If fees are set on the basis of the expected value of the guarantee, it is therefore necessary to estimate the size of the risk premium and subtract this amount from the market-related fee.
It is possible to obtain estimates of the risk premium attached to various rating categories. Different rating agencies compile historical default and recovery rates, which can be used to obtain an (historical) estimate of the expected loss on rated issues. By comparing this information to the actual yield spread, comprising both the expected loss and the risk premium, it is thus possible to infer the estimated size of the risk premium. This may serve as a reference for fixing the market value of a guarantee on the basis of the expected value and vice versa.
Option models
Information needed to apply the implicit guarantee pricing approach may not be readily available. In that case, it may be necessary to apply more fundamental methods, trying to price the guarantee directly. One possibility is to use an option model.
Issuing a guarantee is like issuing a put option. A put option entitles but does not oblige the holder of the option to sell a particular asset at a price agreed in advance. A government guarantee can thus be compared to a put option because it effectively gives the lender the right to sell the loan at par value to the government if the lender so desires. The lender will choose to exercise this option if the guaranteed company is unable to service its debt, in which case the market value of the debt is below par. To the lender, the value of a put option thus equals the value of a government guarantee.
A key assumption when applying option-pricing models is the distributional assumption on the development in the underlying assets of the company. As illustrated in Figure 6.1 in Box 1, the distribution of possible negative net asset values is key for assessing the value of the guarantee, because the guarantee will be invoked when net assets are negative.
Increasing volatility of the asset value of the company increases the probability of negative net assets thus increasing the value of the guarantee.
An advantage of applying option models is that they provide analytical solutions. The availability of analytical solutions, however, rests on somewhat restrictive model assumptions, that may not be applicable to specific guarantees. Furthermore, lack of suitable data may in practice impede the use of the option valuation approach. For example, obtaining accurate measures of the volatility of the value of the guaranteed project is often hard, unless the guarantee is given to a company with publicly traded shares.
Simulation models
A third approach is to build a simulation model. This method is fundamentally similar to option pricing. The purpose of a guarantee simulation model is to generate a distribution of losses from the guarantee to
the government. This distribution can be used to calculate the expected cost of the guarantee and to calculate risk measures compiled as the maximum loss that will occur with a given probability.
Building a simulation model applied to guarantees requires a specification of the processes that determine the evolution of the asset value of the guaranteed company. A simulation model can be designed to take many considerations into account compared with the more restrictive assumptions of option models. In this sense the simulation approach is more flexible but also more demanding.
Many debt management offices are well acquainted with simulation methodologies applied to risk analyses of regular debt. These stochastic simulation models are used to generate distributions of future interest costs on the government debt. A main risk factor to be simulated is thus the future course of interest rates.
Correspondingly, an analysis of the distribution of guarantee losses can be carried out by identifying the relevant risk factors underlying the guarantee and simulate their evolution. For example, if the government issues a guarantee on the funding of a bridge construction company, which earns revenues from user fees, future traffic scenarios will be a main risk factor when evaluating the guarantee. If the government guarantees mortgage loans, the future development in real estate prices will be a key risk factor, and so on.
Conclusions
Issuing guarantees for a fee less than its market value amounts to a state subsidy. For certain guarantees the valuation principle applied to fees must therefore be in conformity with any prevailing state aid rules. If state aid is not an issue, the calculation of collected or budget-funded fees need not be based on market values. Applying fees based on the expected cost of the guarantee should on average ensure protection of the government’s net position. This, however, assumes a well-diversified guarantee portfolio, as the uncertainty of government outlays under any single guarantee may be substantial.
Different quantitative methods can be applied to price guarantees. If the operations of the potential recipient of a guarantee are well established or comparable to other companies, readily available market information may exist from which the credit risk can be inferred. If the operations have a unique character, and such information does not exist, it may be necessary to apply a more fundamental analysis, e.g.simulation models. Quantitative approaches, preferably several different ones, can help the decision maker understand the risks and contingencies involved. In practice, however, considering the special nature of many projects guaranteed by the
government, guarantee pricing also has to be influenced by qualitative judgments.
Finally, note that the fact that it may be hard to set appropriate fees is not a valid argument against charging fees for government guarantees. A fee equal to zero would almost certainly be less likely to achieve the objectives of an efficient governance system than a fee derived from a careful analysis of the expected costs and risks involved.