Sample

We have performed historical simulations over the period 1984-2000 for schemes of the form
outlined above using a set of ten severely and moderately indebted African countries: Benin,
Burkina Faso, Burundi, Cameroon, Ghana, Kenya , Madagascar, Malawi, Rwanda and
Tanzania. This group of countries was selected from the set of all countries classified by the
World Bank as severely or moderately indebted and which in addition satisfied the following
three criteria

· Service on concessional debt is a sufficiently large proportion of total debt service to
allow the scheme to have a significant impact on overall debt service.

· The country has at least one export commodity making up 10% of total exports or one
import commodity accounting for 10% of total imports.

· The country publishes statistics on total imports and exports, with at most a few gaps,
which allow calculation of the required hedge ratios.

Application of these three criteria reduced an original candidate list of many more countries to
the ten listed above^15.

In section 3, we set out a range of alternative designs. We need to choose a more limited
number of schemes for simulation. In what follows, we will report on two schemes:

A. A commodity swap scheme, as defined by equation (6), with price deviations
measured relative to a four year moving average of past prices lagged one year (i.e. the
moving average of prices four, three, two and one years previously)¹⁶.

B. A swaption scheme, as defined by equation (7) and relating to the same moving
average with a ± ? % band (strike prices ? % above and below the moving average price
trend). We set ? = 15%.

We consider these schemes as implemented as constrained by concessional debt service and
as unconstrained.

The Hedge Ratio

For simplicity, we focus on a country with a single major export, with export share a and
price P, and for which oil imports have price Q and notional “share” ? in total exports¹⁷. We
also focus on a straightforward commodity swap structure, as defined by equation (6), with
nominal value $A¹⁸.The scheme defined in equation (6) relies on the choice of hedge
parameters ? and µ for the export and import commodities respectively.

The most simple starting point for the analysis is the share-based hedge which sets the export
commodity swap parameter ? equal to the export share a and the oil import swap parameter µ equal to the “share” ? of oil imports in total exports. Hedging using the export and oil import
shares effectively adopts a unit (dollar for dollar) hedge ratio. Basic hedging theory teaches
that hedge ratios will normally differ from unity – see, for example, Hull (1997, pp.35-7). The
variance minimizing hedge ratios will depend on the correlation between changes in the
revenue stream to be hedged and changes in the price used to hedge this stream, and on the
relative volatilities of the revenue stream and the hedge price. Furthermore, hedging using
export shares considers the export and import side hedges independently. This is only valid if
changes in the export and import commodity prices are mutually uncorrelated, if the changes
in the export price are uncorrelated with changes in import expenditures and if changes in the
import price are uncorrelated with changes in export revenues. These are strong requirements.
Where these conditions do not hold, a portfolio approach is required which takes into account
the covariance structure of the prices, export revenues and import expenditures.

Although it is possible to derive analytic formulas for the variance-minimizing hedge under
these more general conditions, it is simpler to derive the hedge ratios empirically by multiple
regression of the quantity whose variance one wishes to minimize on the relevant prices.
Write the country’s commodity export revenues as X, its oil import expenditures as O and (as
previously) its scheduled concessional debt service as S. Then X – O – S is residual forex
availability. The optimal hedge ratios are found by regression of this quantity on the
commodity export price P and the oil price Q.

Typically, for the countries we consider, export revenues and oil import expenditures have
both trended up in nominal and real terms. This suggests scaling by the trend in export
revenues so that effectively we are considering the debt service to export ratio, in line with the
debt sustainability literature. The precise regression takes as dependent variable

where a tilde indicates a centred five year moving average. This is regressed on the similarly defined export price deviation

and the oil price deviation

where, however, the price moving averages are four year moving averages defined over the period t-4 to t-1¹⁹.

Regression-based weights should generate a superior hedge to the share-based weights in the
presence of correlations between commodity prices and oil prices and if these prices influence
other expenditure and receipt items. The practical problem is whether it is possible to rely on
these weights being constant over time. There will always be a worry that particular hedge
ratios estimated over short samples of often poor quality data can generate hedges that may be
less good than those obtained by use of simple export and import shares. The apparent
superiority of the regression-based weights may therefore be illusory. We therefore report
results based on both share and regression-weights. The former may be thought of as
providing a lower bound and the latter an upper bound on attainable performance.

 

15 Source for debt data: World Bank. Sources for export revenue and import expenditure data: aggregate exports
and imports, IMF (International Financial Statistics); agricultural commodities: FAO. Gold export values and
petroleum imports and export values were estimated by multiplying volume statistics (see footnote 5) by the
appropriate world prices scaled down by 5% in the case of petroleum exports.

16 Source for price data: World Bank.

17 In most HIPCs, total imports considerably exceed total exports with the difference covered by grants,
remittances and capital inflows. Expressing oil imports as a share of exports rather than imports implies
equivalence between an extra dollar spent on oil and a dollar lost from a lower value of commodity exports. It is
straightforward to extend the hedge ratio discussion to cases in which there is more than a single export or
import commodity.

18 We do not attempt to estimate variance minimizing hedge weights for the swaption scheme (7). The associated
nonlinearities imply that optimization would need to be within a Monte Carlo simulation framework. We do not
pursue that direction in this paper but simply apply the swap hedge ratios to the swaptions scheme.

19 Backdating of the moving averages is required to ensure that the modified debt service is known at the start of
each year. This precludes use of a moving average incorporating either current of future prices. Regressions were
performed over the period 1985-2000 (1999 for Cameroon because of lack of data).

By Prof. Christopher L. Gilbert, Prof. Alexandra Tabova

Next: Welfare Analysis

Summary: Index