Cost-Risk modeling

A risk-based approach to public debt sustainability assessment originates from an idea that risk management tools, widely used in managing business and financial risks of the business entities, can be applied on the level of national economy in managing government debt to ensure fiscal solvency and macroeconomic stability. In the most generic sense, the risk management is considered as a process of identifying, assessing and controlling threats to an entity’s activities. A risk as the term refers to a corollary of uncertainty that consists of two components:

 the risk likelihood that specific outcome will occur;

 the risk exposure of the specific activity to the impact of this outcome.

In order to control risk associated with some activity, it needs to be properly measured. According to the Holton (2009), in the context of risk management there is distinction

74 between a risk metrics - the attribute of risk being measured, and a risk measure being the operation that quantifies the risk attribute. For example, risk metrics may be volatility of portfolio debt servicing costs, and standard deviation is a measure of volatility. The risk measures can be separated to those quantifying only risk likelihood, only risk exposure or those combining both likelihood and exposure (Holton, 2009). Volatility, e.g. is a measure of likelihood that some outcome will occur, while Value-at-Risk is a measure that combines volatility with risk exposure, counting the maximum possible loss for given probability.

According to Wheeler (2004), risk management lies at the heart of public debt management and makes crucial link between the formulation and implementation of debt management strategies. Risk management is important to both sides of public debt management process, for the formulation of the debt management strategy but also for the strategy implementation on the operational level. On the strategic side of debt management and fiscal policy, policy planners and external auditors typically apply complex macroeconomic models and risk management methodologies to measure mid- to long-term risks associated to public debt attributes. While particular choices of underlying model’ specification differs across countries and institutions, methodology of public debt risk assessment basically combines some form of forward-looking risk management tools and theoretical concept that describes evolution of the debt cost/level in order to transform macroeconomic inputs to risk measures output. The architecture of public debt cost-risk modeling is illustrated in Figure 3.2.

Figure 3.2: Cost-risk modeling architecture

Source: author

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 Estimation of cost/level of debt for the specified period when model inputs are the most expected outcomes of macroeconomic variables (baseline scenario). It gives the path of the cost or share of debt in GDP, assuming that no external shocks or shifts in macroeconomic environment will occur in the observed period;

 Estimation of cost/level of debt under the different assumptions on key variables changes (risky scenarios). Risky scenarios allow estimation of path of cost/debt assuming either different macroeconomic polices/financing strategies or external shocks occurrences;

 Estimation of debt cost/level risk exposure throughout a comparison between baseline and alternative outcomes, or/and estimation of likelihood of alternative outcomes.

Therefore, cost-risk analysis represents basic framework for estimation of change in debt servicing cost associated with change of main risk factors driving its level. Debt sensitivity analysis can be thought of as a special case of cost-risk analysis. As discussed in the previous chapter, debt sensitivity analysis estimate debt dynamics under some alternative and/or risky scenario. If some risk estimation procedure is included in analysis to depict risky scenario occurrence, than the output of debt sensitivity analysis will consist of both forecasted debt servicing costs and associated risk measurement, as illustrated in the Figure 3.3.

Figure 3.3: Cost-risk framework of scenario analysis

Source: Velandia-Rubiano (2002)

This cost-risk analysis is generally derived from risk management practice of institutional investors dealing with large portfolios of securities. It is closely related to the Markowitz

76 theory of portfolio optimization and Value-at-Risk (VaR) evaluation, two concepts that exploits trade-off between risk and return (or cost) for the purpose of risk management. Although these two concepts are primarily developed for the purpose of investment management, they can be easily modified for the benefit of securities’ issuer. Basically, portfolio optimization is a procedure that aim to minimize risk of portfolio return (objective function) subjected to given targeted value of portfolio expected return as a constraint, or the other way around – by maximizing expected return for chosen level of riskiness. Optimization is achieved throughout proper choice of portfolio weights across individual securities. Similar approach can be applied to government portfolio of debt instruments, with expected debt servicing cost as a constraint and minimization of its riskiness as an objective function.

Basic idea of VaR is to estimate level of loss in portfolio value that will not be exceeded at a given level of confidence and for a given time span. From the standpoint of debt instrument issuer, VaR can be mirrored to Cost-at-Risk (CaR) modeling, where CaR represents debt servicing cost that will not be exceeded at a given confidence level and time span. Optimal weights of portfolio and CaR value can be obtained either by analytical closed-form or numerical solution, depending on how debt servicing costs and risk are modeled in particular cases.

While portfolio optimization has some theoretical advantages over Cost-at-Risk modeling, CaR approach is by far quite more present in the risk management practice of debt management offices, due to its lower computing requirements and easiness of implementation. Cost-at-Risk may be defined in absolute or in relative terms. Absolute value of CaR counts change in value of debt servicing cost for the given time period, relative to the initial value at the beginning of the period. Relative CaR counts change in value of debt servicing costs under some risky scenario, relative to expected debt servicing cost under the baseline scenario of expected dynamic of risk factors. In that context, cost- risk framework in Figure 3.3 may be interpreted as an illustration of a relative CaR.