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4.3.2 Lending

The main link between development institutions and emerging markets, of course, takes place through lending. Being that loans are private financial instruments (as opposed to bonds, which are publicly traded), it is difficult or impossible to access the proprietary information needed to create a table similar to the one for bonds shown in Figure 4.2. It would not necessarily be more varied (as we have mentioned before, the majority of loans are in USD), but it would probably cover nearly as many currencies.

In Section 4.4 we shall look at some sample projects that should mimic the type of project a development institution carries out in a typical emerging market. In particular, we shall see how a loan instrument is structured around a project. In the rest of this section we shall look at some peculiar, technical issues that characterize development lending.

In Section 3.3.1 we have seen how to fair value a loan in the presence of credit risk. We shall repeat now a fairly important concept that we have introduced when dealing with the prepayment option of a loan. When it comes to loans extended by development institutions to sovereign borrowers (of which the great majority are developing countries), there is a fairly important detail concerning the assumption of the recovery rate. Although the probability of default is calibrated using the same assumptions used by the market (this is important in order to use CDS spreads[1]), when the fair value of the loan is calculated, a different, higher recovery rate is used.

Development institutions, we have already mentioned, can be seen as credit cooperatives: its members contribute funds (some more than others, of course) and then the institutions lend these funds back. This cooperative approach combined with the fact that development institutions are lenders of last resort makes default of payment to a development institution very unlikely. This entails an assumption of a recovery that is much larger than the, say, 25% assumed by the market.

When it comes to development lending, a fairly common instrument is the guarantee. A guarantee is not a loan but a promise made by a development institution that a loan, or part of it, taken on by a sovereign entity will continue to meet its obligations even in the case of default of the sovereign entity. From its description it seems conceptually similar to a CDS written by the development institution to sell protection to the sovereign entity. Conceptually, it is similar, but the main differences consist of the fact that a guarantee is not a swap (hence it is not regulated by ISDA); it deals with an underlying, which is usually amortizing (as opposed to a CDS which protects a non-amortizing instrument such as a bond); and most of the time there are issues of nonacceleration, which we have mentioned in Section 3.3.1.

These types of differences are central to the way development institutions hedge loans, and are useful to describe the risk involved in mixing different types of instruments. As an example, let us consider the case in which we have issued a nonaccelerating, floating-rate loan of the type


Now let us consider the case where we have issued a nonaccelerating, fixed-rate loan


with a coupon C and at the same time a swap (which we have written on one side of the equal to stress that we receive floating) such that the following is true


If we enter into the swap with the borrower, assume that the swap amortizes in the same way as the loan and we do not ask for collateral postings from the counterpart, we could be tempted to think that the floating-rate loan or the combination of a fixed-rate loan plus a swap, such as the one shown above, are identical. In both situations we end up receiving LIBOR plus spread. This is tempting but incorrect because it does not take into account the fact that the typical development loan does not accelerate, whereas a derivative regulated by an ISDA agreement does.

To illustrate this, let us rewrite the swap more precisely taking into account the amortizing principal and also the credit risk of our counterpart (because in this particular type of swap no collateral is exchanged irrespective of the credit rating of either party). To simplify the notation we make the assumption, far from implausible, that, given we are an institution with an excellent rating and the borrower is a developing country, our credit risk is negligible compared to our counterpart and therefore we are going to ignore first-to-default considerations and the equation will only feature Si, the survival probability of the borrower.[2] Doing so we have


where in the recovery term, MTMj means the mark-to-market of the swap only when it is positive (since we are seeing the issue from our perspective). From this we can see that, in case of default, the recovery of the swap is on the value of the MTM at time Tj; in the case of the loan the recovery is on the present value of the principal at time Tj. We can ask ourselves the question, is the floating-rate loan given by Equation 4.1 equivalent to the combination of the fixed-rate loan given by Equation 4.2 and the swap given by Equation 4.4? The answer is no: although the second term in Equation 4.4 cancels with the first in Equation 4.2, Equation 4.4 is still different from Equation 4.1 because of the recovery amount.

The substitution of a combination of accelerating and nonaccelerating instruments instead of a nonaccelerating one, although in terms of cash flow makes sense, it creates a discrepancy in case of default, which is easy to see when we calculate the fair value of both situations.

  • [1] One could be led to think that the obvious solution would be to use Equation 3.17 with the spread as quoted by the CDS contract and a different recovery rate. Although we have said that the recovery rate is not a traded quantity, it is still closely linked to that particular CDS rate. To be more specific: should one go to a market maker asking for a quote on a CDS with a specifically stated recovery rate, the quote received would differ from the standard one, which in turn would lead to a different implied survival probability.
  • [2] The way we are going to rewrite it is not necessarily more precise, it is only a way that is more suited to our argument. The discrepancy between the way we usually write swaps and loans as in Equations 4.2 and 4.3 is given by the fact that, in general, swaps are collateralized and therefore, as opposed to loans, do not need to feature survival probabilities in the cash flows. In our example, we assume that our swap is not collateralized and consider the counterparty risk through an explicit survival probability factor and not in other ways (such as, for example, through a CVA). Another way would have been, of course, not to fair value the loan in this example, but then we would have had two external terms, a CVA-like number for the swap and a loan loss provision for the loan, which would have rendered things even less clear. We have preferred to write the swap as given in Equation 4.4, which, although slightly odd, is a least consistent with our argument.
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