By Florent Gbongué, PhD *
WAEMU countries have drawn up ambitious national development programs with a view to achieving emergence within a given horizon . Note that the implementation of these programs requires the mobilization of significant resources, which are internal (tax revenues) or external (debts). In this article, we are interested in the optimal mobilization of external resources through the determination of the optimal cost of borrowing on the WAEMU regional financial market.
The analysis of coupon rates on government securities of the countries of the union reveals the existence of implicit rate spreads (STIs) or implicit risk premiums, given the zero coupon structure proposed in Gbongué’s work and Planchet [2015f], Gbongué et al. , Gbongué [2018a], Gbongué [2018b] and Gbongué . It should be noted that mid-market companies constitute, in financial theory, an essential measure of investors’ perception of the implicit sovereign risk in local currency. In practice, they comprise two components, which are attributable to default and liquidity implicit in government securities (see Stander ).
The term structure of mid-cap companies can be defined as the function that, at a given date, for each maturity, indicates the implicit risk premium that the sovereign issuer would have to pay. Therefore, it participates in the real determination of the cost of financing countries when they mobilize resources in the local financial market (see Gbongué ). In the literature, the existence of a risk premium on government bonds is justified by the work of Merrick , Duffie et al. , Vrugt , Bernardo and Caio , Berardi et al. , etc., with regard to the default of certain countries at the international level.
Indeed, Merrick  proposes a model capable of simultaneously determining the recovery rate RV and the term structure of the probabilities of default in neutral risk universe for Russia and Argentina. This model is applied to dollar Eurobonds during Russia’s default crisis in 1998. Thus, credit spreads can be deduced from the relationship of Duffie and Singleton . In the Brazilian context, Bernardo and Caio  analyze investors’ sovereign risk perception by proposing a parametric dynamic model (in the absence of arbitrage opportunity) to determine the RV recovery rate and the term structure. probability of default based on the work of Duffie and Singleton . With an error rate of less than 0.08%, they conclude that the model is suitable for pricing new emissions.
In the light of the foregoing, we show, in an original way, the existence of an implicit sovereign risk premium in the WAEMU zone, thanks to a methodology capable of quantifying mid-cap companies according to two approaches (direct and indirect), from sovereign issues observed as at 31/12/2017. In practice, we present the results of the models proposed in Gbongué . In addition, we advise the indirect approach to determine the implicit risk premium required by investors as it allows to break it down and distinguish the share attributable to implicit credit and liquidity premiums.
Depending on the approach used, estimating mid-caps requires upstream calibration of a construction model of a zero coupon yield curve (ZC), which is a crucial step. Downstream, we assume that the price of the bond is risky, which requires a special valuation of this price. The latter brings out a risk factor, whose evaluation by Nelson Siegel’s model , makes it possible to obtain mid-caps.
However, the indirect approach is a bit complex because it requires several steps. The first concerns the calibration of a construction model of a ZC rate curve. The second assumes the existence of a credit default risk. In this context, the valuation of the bond price is based on the Merrick model  and credit premiums are obtained using the Gumbel model.
Finally, we propose a new valuation of the price of the bond in the last step because we assume the simultaneous presence of credit and liquidity premiums. Having determined zero coupon rates and credit premiums in the first two stages, we calibrate Weibull’s model to obtain liquidity premiums. Section 3 presents the evolution of the term structure of ZC rates, as well as credit and liquidity spreads.
- Digital illustration
Applying the models described above on the BRVM data in circulation at 31/12/2017, we first obtain the zero coupon structure, illustrated in Figure 1 below:
This ZC rate curve is increasing, with a positive slope, which is in keeping with the current economic context of the union. This result is important because it provides credit and liquidity premiums, which reflect the economic reality of WAEMU. They are naturally increasing on observable maturities (0 to 12 years). Figure 2 illustrates this assertion:
In order to legitimize the quantification of credit and liquidity premiums by the indirect method, it is compared to the direct method. The comparative analysis finds that the two methods show almost similar results, as illustrated in Figure 3 below:
In this contribution, we have seen that its originality comes first and foremost in its ability to demonstrate the existence of an implicit sovereign risk premium. Secondly, it presents two different approaches (direct and indirect) to quantify these implicit risk premiums, which lead to similar results. Finally, it makes observable the credit and liquidity premiums in the context of the WAEMU zone, which will better structure and manage the public debt. If we have proposed the benchmark MIE curve, on the other hand, it is possible to obtain the yield curve for each country of the union, by applying a shock coefficient to the curve of the mid-cap, showing the intrinsic risk. of these countries.
 For example, Côte d’Ivoire wants to reach emergence in 2020.
* Florent Gbongué, PhD in Actuarial Science at the University of Lyon. A specialist in economics and finance, he is the author of several scientific and professional articles and acts as a reviewer at the journal Africaine de Développement. Contact: +225 47 28 20 72 / email@example.com