The simulation design set out in the two preceding sections generates 23 = 8 separate simulations: the choices being a swap (A) or swaptions (B) scheme, constrained or unconstrained by the initial debt service obligations, and using share or regression weights.
We need a criterion by which to judge the relative success of different schemes. We propose to ask what reduction in debt service would leave countries indifferent between the reduced but otherwise unmodified debt service payments and debt payments under the proposed schemes but without any overall reduction. This provides a common debt reduction metric in which alternative schemes can be evaluated both within and across countries.
We show in an appendix that, to a first order approximation, the percentage reduction d in debt service which would leave the debtor country indifferent between the current and the proposed arrangements is given by
where ? is the reduction in the variance of free foreign exchange, as defined in section 2.1 but measured relative to the export trend, i.e.
the ratio of average debt service to average commodity exports, and ? is the coefficient of partial risk aversion, defined in the same way as relative risk aversion but relative to commodity export revenues instead of income.
The proposed measure d is a simple transformation of the variance reduction ? and the ranking of schemes for any given country is therefore the same whether one uses the variance reduction metric ? or the equivalent debt reduction metric d. The advantage of the latter measure is only that it gives an order of magnitude measure of what the variance reduction is worth, at least under simple and broadly standard assumptions.
The disadvantage of this measure is that it necessarily depends on an assumed risk aversion coefficient. If countries are highly risk averse, they will be willing to pay a lot for even a small degree of risk reduction, while if they have low risk aversion they would prefer even a small reduction in overall debt service to a large reduction in uncertainty. In what follows, we use a conservative value of unity for the partial risk aversion coefficient. Use of a higher value for risk aversion, perhaps 2.5, would increase the valuation of the risk reduction benefit proportionately.
By Prof. Christopher L. Gilbert, Prof. Alexandra Tabova
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Summary: Index