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4 Membership in a Common Currency Union and Riskiness of Sovereign Debt

Members of the Economic Community of West African States (ECOWAS) have a regional integration agenda that includes creation of a common currency union (CCU). If implemented the new common currency would replace the West African CFA Franc that is currently used by eight countries that are members of the West African Economic and Monetary Union (WAEMU)[1]. The ECOWAS CCU could replace the WAEMU but retain one of its key features, the “Compte d'Ope´rations” (Operations Account). In accordance with this arrangement each member country would surrender its foreign reserves to the CCU authority, presumably the common central bank, and have accounting of its reserves that would be separate from the reserves of other members. The Operation Account would give the country access to its own foreign reserves, among other things, for its sovereign debt service obligations. It would also make available part of other members' foreign reserves, for the country to service its foreign debt. In other words, through this arrangement, the member country would increase its capacity to make payments on its sovereign debt by the portion of other members' reserves that can be accessed as one of the benefits of its membership in the CCU. An additional feature of this arrangement would be subordination of a country's debt from the CCU authority to sovereign external debt.

Figure 1 portrays the change in a country's sovereign debt risk level that results from membership in the CCU. Consider a country with its own national currency that borrows externally and promises to make a given payment, B, at time T. It currently has foreign reserves equal to A0 that have an expected drift, m, with a growth path depicted by the dotted line A0–A0. The distribution of its assets is given by the curved dotted line and the probability of default on its sovereign debt is represented by the area under the horizontal line of promised payments, B, and the curved dotted line. Now if the country is a member of the CCU and has access to a portion of the foreign reserves of the other CCU members, the level of assets that it can use to service its sovereign debt increases from A0 to A1 and the level of its assets available at time T follows the growth path A1–A1. If it makes more productive use of the foreign debt the growth path could be A1–A2.

Considering that the level of promised payments has remained constant, access to additional means of sovereign debt service shifts the distribution to a higher level and results in a new probability of default that is lower than in the case of a country with its own national currency. The new probability of default is depicted by the area under the horizontal line of promised payments and the solid curved line of distribution of asset under the CCU.

Fig. 1 Probability distribution of asset value under CCU and single country currency

Numerical Simulation of Impact of CCU Membership on Sovereign Debt

The following numerical simulation is aimed at shedding light on the gains that can accrue to a country that is a member of an ECOWAS CCU under the arrangement of common foreign reserves specified above. The main feature of relevance for the simulation model is that member countries can use their own reserves and a portion of the reserves of other member countries to service their sovereign debt thus increasing their capacity for promised payment on external debt service. The model is based on the contingent claims analysis presented above. Its five arguments are the level of assets of the country (A), the level of its promised payment (B), the rate of interest on its sovereign debt (r), time until the expected payment, T, and the volatility of the return on its assets (s).

A key feature of the model is that the “actual” probability of default is N(-d2, μ), and (11) states that

For the sake of simplicity, it is assumed that the rate of return on the country's assets, m, is equal to the rate of interest on the loan, r.

Table 4 presents the probability of default on a loan under various combinations

of the expected level of assets and the associated volatility of the return on the assets. The country is assumed to commit to a promised payment, B, equal to $75 to be made in 1 year (T =1). The succession of higher levels of assets indicates the impact of increasingly higher access to CCU reserves for a given level of the country's own assets. By the same token, the succession of decreasing levels of volatility, s, shows the impact of the resulting volatility of the return on the assets to which the country has access under the CCU reserve management arrangement. The main result evidenced by the simulation is that the higher the level of assets, the lower the probability of default. The lower the level of volatility of asset returns, the lower the probability of default. A combination of these two factors accelerates the decrease in the probability of default.

Table 4 Probability of default on sovereign debt under selected levels of assets and volatility (assuming B =$75, T = 1)

Volatility (s)

$100

$125

$150

$175

$200

$225

$250

$300

50 %

33.5 %

19.2 %

10.8 %

6.1 %

3.5 %

2.0 %

1.2 %

0.4 %

40 %

26.0 %

11.5 %

4.9 %

2.1 %

0.9 %

0.4 %

0.2 %

0.0 %

30 %

16.5 %

4.3 %

1.0 %

0.2 %

0.1 %

0.0 %

0.0 %

0.0 %

20 %

5.6 %

0.3 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

10 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

5 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

0.0 %

Source: Author's calculations

To illustrate, if the level of assets increases from $100 to $150, the probability of default is reduced by two thirds (from 33.5 to 10.8 %) under a volatility of 50 %, by 81 % under a volatility of 40 % and by 93.9 % if volatility is 30 %. At a volatility of 20 % the probability is equal to zero if assets reach $150. The reduction in the probability of default is also quite significant as the level of volatility decreases for a given level of assets. Even for a level of assets as low as $100, the probability of default is halved when volatility decreases from 50 to 20 % and is equal to zero for a volatility of 10 %. Very high levels of assets or very low levels of volatility are of insignificant marginal impact because the probability of default reaches zero for the combination of assets equal to $150 and volatility equal to 30 %. It takes more extreme values of assets or volatility to yield a probability equal or close to zero when they are considered individually. The policy implication is that if facing market parameters described above, a borrower country benefits from a 50 % increase in its capacity to service its sovereign debt and through the diversification effect of the pooled CCU reserves to which it has access, faces volatility of these assets equal to 20 %, the resulting probability of default of its external debt is zero and it becomes a risk-free borrower.

Table 5 displays the value of the sovereign loan of the country for a promised payment of $75 and a time to maturity of 1 year for various combinations of asset value and volatility. In other words it indicates the amount of money the country can raise under these parameters. Considering that, as shown in Table 4, the higher the level of asset value or the lower the level of volatility, the lower the probability of default, Table 5 gives the value of the loan assigned to each of the asset levelvolatility combinations. Higher levels of assets command a higher loan value and lower volatility has the same effect. The maximum value of the loan, $71.34, corresponds to a probability of default of zero in Table 4. Table 5 also shows that the highest value of the loan is reached with the combination of assets equal to $150 and volatility equal to 20 %. For a country with an initial combination of assets equal to $100 and volatility equal to 50 %, this represents a gain in loan value of $6.18 or 9.5 %. Significantly higher levels of assets or lower levels of volatility have no marginal impact on the value of the loan, especially when the two parameters are considered individually. In policy terms, the results of Table 5 show that, for a given set of market parameters, as the level of assets to which the borrower country has access increases thanks to the CCU reserve arrangement, it will be able to raise more money from lenders for a given level of promised payment. The same effect is also true if, thanks to the CCU arrangement, the volatility of the assets decreases thanks to the effect of diversification on asset returns that is a possible result of the pooling of reserves.

Table 5 Value of sovereign debt under selected levels of assets and volatility (assuming B = $75, T= 1)

Volatility (s)

$100

$125

$150

$175

$200

$225

$250

$300

50 %

$65.16

$68.30

$69.81

$70.55

$70.92

$71.11

$71.21

$71.30

40 %

$67.63

$69.98

$70.84

$71.15

$71.27

$71.31

$71.33

$71.34

30 %

$69.70

$71.01

$71.28

$71.33

$71.34

$71.34

$71.34

$71.34

20 %

$71.03

$71.33

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

10 %

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

5 %

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

$71.34

Source: Author's calculations

The last question of the study is: how much more can a country borrow as a result of its membership in a CCU. In other words, with respect to the probability of default on the country's debt to what extent can an increase in the level of assets made possible by membership in the CCU counterbalance an increase in the promised payment that would result from a higher level of sovereign debt? Consider a country that benefits from a $25 increase in its level of assets and wishes to increase its debt so that its promised payment also increases by $25. Table 6 displays the resulting probabilities of default for various scenarios of $25 changes for A, from $100 to $125, $125 to $150, $150 to $175, and so on. For the $25 increase in promised payment the following scenarios are considered: $50–$75, $55–$80, $60–$85 and $65–$90. For an initial value of asset of $100, raising B from $65 to $90 would increase the probability of default from15.8 to 42.5 %, a difference of 26.7 %. If on the other hand, for a promised payment of $65 the level of assets is raised from $100 to $125, the probability of default is reduced from 15.8 to 5.9 %, which amounts to a reduction of only 9.9 %.

These results are consistent for all combinations of $25 increases in A and $25 increases in B. However, as the initial risk level of the country diminishes, i.e. for lower initial values of B and higher initial values of A, the changes in A and in B result in lower differences in probabilities of default because intrinsically both initial values are associated with lower probabilities of default in the first place. Another way to illustrate the results obtained above is to compare probabilities of default that are identical although associated with different scenarios. The probability of default of 11.5 % applies to a loan with a promised payment of $60 and a level of assets of $100. It also applies to a promised payment of $90 and a level of assets of $150. So to maintain the same probability of default a country would need to increase its level of assets by $50 (from $100 to $150) to compensate for an increase of $30 (from $60 to $90) in its promised payment. The policy implication for the results of Table 6 are that a country can benefit from membership in a CCU by increasing its sovereign debt capacity but in a limited fashion unless it can access significantly larger levels of assets as the level of debt increases which can, beyond a certain level, be prohibitively costly for the CCU. However moderate increases in a country's indebtedness as a result of CCU membership can provide a reliable economic gain.

Table 6 Probability of default on sovereign debt under selected levels of assets and promised payment (assuming s = 40 %, T = 1)

Prom. Paymt (B)

$100

$125

$150

$175

$200

$225

$250

$300

$60

11.5 %

3.9 %

1.3 %

0.5 %

0.2 %

0.1 %

0.0 %

0.0 %

$65

15.8 %

5.9 %

2.2 %

0.8 %

0.3 %

0.1 %

0.1 %

0.0 %

$70

20.7 %

8.5 %

3.4 %

1.3 %

0.5 %

0.2 %

0.1 %

0.0 %

$75

26.0 %

11.5 %

4.9 %

2.1 %

0.9 %

0.4 %

0.2 %

0.0 %

$80

31.5 %

14.9 %

6.7 %

3.0 %

1.3 %

0.6 %

0.3 %

0.0 %

$85

37.0 %

18.7 %

8.9 %

4.2 %

2.0 %

0.9 %

0.4 %

0.1 %

$90

42.5 %

22.8 %

11.5 %

5.6 %

2.7 %

1.3 %

0.7 %

0.2 %

Source: Author's calculations

  • [1] For the lists of members of ECOWAS and WAEMU see Table 1
 
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