Markets might be misthinking the debt seniority issue when it comes to, for example, IMF/EU bailout programmes.

- The conventional view is that official financing is necessarily detrimental to the value of private investors' claims on a sovereign.

Because the official lenders often refuse to participate in a restructuring: by insisting on seniority, official lenders concentrate credit risk on the remaining private creditors (Gros 2010).

We at Barclay’s think the conventional view is not necessarily correct – at least not all the time.

- Official financing is frequently offered at subsidised, below-market rates, which can free up resources for future debt service to private creditors.
- Official financing can increase the overall size of the pie available to service debt holders, even as seniority reduces the percentage of the pie available to subordinated bondholders.

This column studies when the former can offset the latter, so the sign of seniority’s impact gets reversed. In such situations, private creditors are made better off – not worse off – by new official lending.

# Fair recovery value

It is useful to think of fair recovery values as the ratio of the maximum debt that a country can pay to its stock of debt. The maximum amount of debt that a country can pay could be thought of as the net present value of all its future primary balances. Suppose the maximum politically and economically feasible (and sustainable) primary balance is 2% of GDP. And the discount factor is 4%. Because it is a perpetuity, the net present value of all future primary balances is 50% (2% divided by 4%). Now assume that the current stock of debt is 100%. This implies that in case of default, the recovery value could be 0.5 cents on the euro (50% divided by 100%).

If the concessional rate the official lender charges is low enough, the present values can rise so much that recovery values actually increase after new official lending.

To illustrate this point, imagine an admittedly extreme case where the IMF lends the sovereign an amount equivalent to 20% of GDP at zero rates and rolls over that debt indefinitely. This 20% is utilised to pay back bonded debt as it matures. Total debt continues to be 100% of GDP, but now only 80% of GDP is bonded debt. In this case, recovery values must increase: since there is no debt service earmarked to the IMF (given zero interest rates), the primary balance net of payments to the IMF remains 2%. With an unchanged discount rate of 4%, the maximum stock of debt that the country can sustain (ex-IMF debt) remains unchanged at 50% of GDP. But in the case of restructuring, there is only 80% of GDP of bonded debt. This implies recovery values of 62.5 cents on the euro (50% divided by 80%). This example suggests that if the concessional rate the official lender charges is low enough, recovery values can actually increase post official lending.

# What about Greece and Spain?

We believe the Greek default does not necessarily validate the view of lower recovery values for private investors under official programmes. Investors see the low recovery and the fact that official debt was excluded and conclude that subordination reduced recoveries. However, what they don’t see is the recovery value that would have prevailed without a programme. Greece’s debt dynamics were so poor that recovery values would have been extremely low with or without a programme. Likewise, we believe that the proposed senior financial lending to recapitalise Spanish banks would likely increase potential recovery values for existing bondholders.

Before presenting our framework for analysing recovery values, it is useful to emphasise the scope of our analysis. Markets have been understandably disappointed with the actions taken by Eurozone policymakers in dealing with the crisis. Programmes have invariably been too optimistic: overestimating growth and a country’s ability to adjust and underestimating what it takes to solve the problem. We agree with market scepticism. We have said in the past that there is a moment when markets reach a point of no return and require very decisive policymaking action to move economies away from the vicious circle of lower growth, worsening debt dynamics, and higher yields. As time goes by, the size of action needed increases.

However, the scope of our analysis is much narrower than providing an assessment of the likely outcome of the current peripheral crisis. It should not even be seen as a cost/benefit analysis of entering into a programme or estimating fair spreads following a programme. Our aim instead is to provide a framework for estimating recovery values following official programmes. And our conclusion is that of all the reasons to be pessimistic about the Eurozone crisis outlook, lower recovery values as a result of subordination following IMF/EU financing is not one of them.

Debt buybacks such as the ECB’s Securities Market Programmes (SMP) are different. In its current form, private investors appear to be worse off under the SMP. The reduction in market yields is too marginal to compensate for the resulting subordination of private investors. Either the ECB has to surrender seniority (in which case the SMP will do some good although not much) or it has to make the SMP so large that it effectively ends the sovereign debt problem by reducing significantly the structural vulnerabilities of the current Eurozone set up.

# Revisiting fair spreads

If we define fair spreads as the yield in excess of the risk free rate, the following identity holds:

Fair spread = P * (1 – R) + risk premium (1)

where P is the yearly default probability and R is the recovery value in the event of default. Abstracting from pure risk premium, spreads of bonds issued at par are going to be the result of multiplying the yearly probability of default by the loss given default. In turn, the loss given default will be equal to the notional principal in case the bond is paid in full minus the recovery value in case of default.

For example, without including the risk premium and assuming the probability of default within one year is 5% and that in case of default investors recover 30 cents for each 100 cents of notional, fair spreads for debt with one year maturity would be 350bp (5% times 0.7).^{1}

The conventional view on the effect of official programmes is that even if they can reduce marginally the probability of default (P), the credit risk (spreads) may actually increase as the seniority that those programmes impose reduce the recovery values (R) for existing bondholders.

In the following sections, we demonstrate that the assumption of lower recovery values following subordination needs to be significantly nuanced.

# A framework to analyse recovery values

We can use the debt sustainability framework (kept to barebones) to illustrate the main points. As in every model, it is just a stylised representation of the real world. But it captures in our view the main factors to assess the task at hand.

The primary balance (i.e., government revenues minus non-interest expenditures) required for sustainability is:

PB* = (r – g )/(1+g) D (2)

where D is the stock of debt, r is the average interest on the debt and g is the nominal growth rate. For simplicity, we can assume growth rates (g) equal to zero and hence (2) becomes:

PB* = r D (2a)

The formula is intuitive. If a sovereign needs to stabilise its debt, it will need to generate a primary balance equal to the interest payments on its debt. Put differently, it needs to generate a zero fiscal balance (as the fiscal balance equals the primary surplus minus the interest payments on the debt) to make sure debt remains stable.

Now consider default. Imagine that the maximum politically and economically feasible primary balance that a country can achieve and (critically) sustain is PBMAX.^{2} In theory, if PBMAX > PB*, the country will be generating fiscal surpluses and will see its debt decline over time. However, if PBMAX < PB*, the country is insolvent: it can’t generate a primary balance sufficiently large to pay its debt and would need to eventually default.

Conditional on defaulting, the fair recovery value is equal to the ratio of the maximum debt level that the government can service and the actual stock of debt. This requires estimating the maximum debt that a government can sustain. This is easily obtained from (2a):

DMAX = PBMAX /r (3)

This is the formula we used in the motivation to obtain the 50% maximum payable debt. It is equivalent to thinking of DMAX as the net present value of all future primary balances discounted at the appropriate rate.

The recovery value conditional on default (and hence conditional on PBMAX < PB*) equals the ratio of the maximum serviceable debt level and the current stock of debt.

R0 = DMAX /D = PBMAX /(r D) (4)

Obviously, the lower the primary balance the lower the debt that can be serviced and the lower the recovery value. In principle, if a country cannot realistically achieve a primary surplus the recovery value can be as low as zero.

# Effect of an ‘IMF’ programme on recovery values

We now consider the potential effects of an IMF/EU programme on recovery values. We assume, for simplicity, that the ‘IMF’ lends an amount (D1) at a concessional rate ρ, lower than r . Bondholders of debt with notional value D1 get paid as it matures. Hence, the total debt remains unchanged at D, but the composition is now: D1 of IMF debt and D minus D1 of bonded debt. In exchange for charging a lower rate, the ‘IMF’ gets seniority over bonded debt.

However, countries can default even under an IMF programme if the fiscal adjustment is not sufficient to stabilise debt dynamics. To obtain recovery values for bonds under an IMF programme, we need to estimate the amount of debt that the government can sustain after having paid the IMF.

The primary balance available to service bonded debt results from subtracting the earmarked IMF debt service from the primary balance:

PBMAX – ρ D1 (5)

Using equation (3), the maximum debt that can be serviced once the IMF had been paid would be:

DMAX = (PBMAX – ρ D1 )/r (6)

which can be thought as the net present value (NPV) of all future primary surpluses after payments of debt service to the IMF. To obtain recovery values, we divide it by the amount of outstanding bonded debt. The recovery value post IMF programme (R1) will become:

R1 = (PBMAX – ρ D1 )/(r (D - D1)) (7)

We can then show that the recovery value post IMF is higher than pre IMF (i.e. R1 > R0) if:

ρ D < PBMAX (8)

This is the key condition. Equation (8) suggests that if the concessional rate ρ is low enough, recovery values following an IMF programme are actually higher than without one. This means that the market perception that recovery values post IMF programmes always fall must be revisited.^{3}

# Conclusion

There are two forces affecting recovery values.

- The first is that the amount of money available to pay all debt increases.
- The second is the subordination effect.

This first increases as long as ρ < r. But this does not suffice to increase recovery values. To dominate the negative impact of subordination, the concessional rate ρ needs to be low enough as to make all debt sustainable (i.e., satisfy sustainability condition (2)).

One could argue that the initial IMF/EU programmes for peripheral countries (the Greek and the Irish ones) made the mistake of charging interest rates closer to market levels, despite the fact that by being senior, they carried much lower credit risk. The most recent Portuguese programme and the revisions to the Greek and Irish ones corrected that mistake.

# References

Gros, Daniel (2010), “The seniority conundrum: Bail out countries but bail in private, short-term creditors?”, VoxEU.org, 5 December.

Longstaff, Francis B, Jun Pan, Lasse H Pedersen, and Kenneth J Singleton (2011), “How Sovereign is Sovereign Credit Risk?”, *American Economic Review: Macroeconomics*, April.

1If we assume that the risk premium is one third of the default probability as some authors do, fair yields would increase approximately to 465bp. See Longstaff et al. 2011.

2Strictly speaking one should not think of PBMAX as the absolute maximum that a country can sustain but as the expected value of the plausible fiscal effort given the existence of uncertainty.

3Clearly, we are not incorporating all factors affecting recovery values. For example, an IMF program can generate incentives to increase the politically feasible primary balance. This would increase recovery values. At the same time, the program can go on for too long and allow a much larger debt stock. This would reduce recovery values.