Country Rulers Macrometrics Sovereign Credit Risk Assessment
by Ephraim Clark
Published in GARP Risk Review, September/October, 2002, p. 36

Macrometrics is a model that applies the state-of-the-art tools of modern financial and real option pricing theory to national economies as a means of assessing sovereign credit risk. Besides the exercise price, the expiry date and the risk free rate of interest, option pricing requires knowing the price of the underlying security and the standard deviation of its rate of return. To determine the underlying security in the Macrometrics option framework, it is important to remember that besides the government’s willingness to service its foreign debt - a point I will come back to later - sovereign credit risk and the value of sovereign debt are “derived” from the economy’s ability to generate the net foreign exchange value necessary to service it. Thus, in the Macrometrics option framework, the underlying security is the value of the economy’s capacity to generate the net foreign exchange value necessary to service the economy’s foreign debt. By definition, it must be denominated in a convertible foreign currency, which in our case is the USD. Although this value, which I call the economy’s “international market value”, cannot be observed directly, it can be estimated. Without going into details, the estimation involves defining the economy’s relevant cash flows with respect to the balance of payments and discounting them back to the present at the economy’s required rate of return.

Once a time series for the economy’s international market value has been constructed in this way, it can be used to estimate the economy’s rate of return and its volatility (standard deviation). The first level of sovereign credit risk assessment involves plugging the international market value and the volatility of its rate of return into the Black-Scholes formula along with the riskless rate on US Treasuries, the nominal amount of foreign debt outstanding and the duration of this debt to estimate three important parameters: the theoretical financial risk premium, the maximum amount of foreign debt, and the probability of default. The theoretical financial risk premium is the difference between the required rate of return estimated from the Black-Scholes formula and the riskless rate. It is the overall measure of the economy’s creditworthiness. The maximum debt level indicates the amount of debt that equalises the marginal cost of new borrowing with the economy’s overall rate of return. A balance of payments crisis when the debt level is well below the maximum suggests that the problem is one of liquidity. When the debt level is close to or above the maximum, solvency is the problem. The probability of default is captured in the value of the cumulative normal distribution noted as in the Black-Scholes formula. It measures the probability that default will occur on the debt’s maturity. This maturity is estimated as the duration of total foreign debt outstanding and figures explicitly in the estimate of . Thus, the default probability explicitly incorporates the time profile of the debt service.

According to these criteria, Argentina was an extremely risky proposition as far back as 1998 when its theoretical risk premium was a whopping 12.33%, its maximum debt level was $89 billion, $55 billion less than its actual level of $144 billion, and the probability of default over a 4 year horizon was 60%. The risk premium of 12.33% was over 3% above the economy’s 9% rate of return, which suggests that an eventual default would be the result of insolvency rather than a simple liquidity squeeze. By the end of 2001, the theoretical risk premium and the probability of default had risen to 25% and 82% respectively and the maximum debt level was under $10 billion.

A second level of sovereign credit risk assessment measures the government’s “willingness to pay”, that is, the willingness to continue servicing the debt. This involves using the economy’s international market value and volatility in a real option model of optimal stopping. In this exercise, the option being evaluated is the sovereign’s option to default, which it should do when the nominal amount of foreign debt is high enough to offset the costs of defaulting. The higher the value of the option, the lower is the willingness to pay. Using this methodology, I find that Argentina’s willingness to pay dropped sharply between the end of 1998 and the beginning of 2002.

In the last level of sovereign credit risk assessment, I estimate market perceptions of the country’s underlying riskiness, called “implied volatility”, by substituting secondary market values for foreign debt in the Black-Scholes formula and solving for volatility. I also use cross country correlations in a jump-diffusion loss model to measure “contagion” and capture the effect of sovereign credit risk on portfolios of sovereign debt.

In this paper I outlined the Macrometrics methodology and how it can be used in the assessment of sovereign credit risk. It has shown itself to be a reliable tool with many uses in international risk management. It is also interesting to note that the countryís international market value is a powerful concept with documented results in forecasting sovereign debt reschedulings and defaults as well as in the construction of international portfolios of stocks, long term government bonds and money market instruments that outperform their benchmarks by wide margins.