A haircut every year 

Thomas Colignatus 
November 18 and December 6, 2011 

Governments in the European Union suffer under high rates of interest. Components in interest are: (1) the risk free rate like Germany has, (2) the liquidity premium that we can determine from the difference between Germany and Holland or Finland, (3) the risk of default that applies to Greece and (4) stigma that consists of irrational factors that become rational since they are rewarded. A new rule helps to reduce (4) and to prevent it developing into (3). Stability is cheaper to achieve than commonly thought. 

The important distinction is between existing debt (solvency) and new debt (liquidity). A government honouring old debt may still meet with fears of default that translate into higher rates of interest on new debt. The crux lies in managing the latter. Buying up old debt is an expensive way to manage the rate on new debt, see also Delbecque (2011), though it may be a cheap way to redeem old debt. The following gives a rule for managing new debt when fear for a default starts to feed on itself.

In October 2011, EU 10 year bonds had widely different rates of interest. Germany paid 2% while Greece paid 18%. The 2% can be regarded as the market risk free rate and the difference 16% is a premium that covers both default risk and some stigma. In the case of Greece there indeed was a haircut, but this was partly triggered because that rate of interest had become so high. Portugal paid 11.7% but a haircut is not in scope yet (see below). Investors receive a premium for a “probable” event that need not happen and that the EU is working hard to prevent. Something is seriously wrong. What markets present as an argument on “probability of default” actually concerns a stigma that confirms itself. At issue is whether we can eliminate that stigma.

The new rule is that the risk premium can play a role indeed when making the loan, but it turns into redemption when the loan is fully served, and when there thus is no default. This means that the debtor pays the high rate and receives a refund when he succeeds in repaying the loan. The new rule essentially means (a) a switch from the so-called bullet bond to an annuity, and (b) the use of a common risk free rate to determine the present value of a loan.

Part of an annuity is redemption. Thus an investor can feel safe that already part of the loan is paid back in the life of the loan. Putting hairs back is of course different from cutting hairs but financially it remains a sound way to deal with the risk of default. Investors can keep portfolios of different dates and thus build up an average level of cash redemption over time as a way to insure themselves.

A longer discussion is in Colignatus (2011c). This mechanism is decidedly cheaper than what the EU has been doing till now, see also Cabral (2011) and Hau (2011). The Redemption Pact by the German Five Experts might not be needed, see Bofinger et al. (2011).

Two schemes 

Let us compare the bullet bond and annuity scheme. Suppose that Greece takes a loan of EUR 10,000 million for 10 years. Markets in October demand 18%. This rate has been calculated by the ECB using the bullet loan format without a default. The standard bullet bond would have annual interest payments and redemption at maturity. 

period  payment     interest        redemption     debt 
1         1800.00     1800.00     0.00             10000.00 
2         1800.00     1800.00     0.00             10000.00 
3         1800.00     1800.00     0.00             10000.00 
4         1800.00     1800.00     0.00             10000.00 
5         1800.00     1800.00     0.00             10000.00 
6         1800.00     1800.00     0.00             10000.00 
7         1800.00     1800.00     0.00             10000.00 
8         1800.00     1800.00     0.00             10000.00 
9         1800.00     1800.00     0.00             10000.00 
10       1800.00     1800.00     0.00             10000.00 

To determine the present value of this bullet loan we discount at the market rate. However, what is the market rate ? For Greece the market rate is said to be 18% so that the present value is 10000m. We can however also use the risk free rate of 2% and the liquidity premium of 0.25%, thus 2.25%. Then the present value is almost 24000m. Greece thus pays a risk premium of 14000m. If Greece works hard to prevent a default, it works hard to give a huge profit to creditors, who then benefit from a premium on a risk that does not materialize. Something is seriously wrong.

This is however how markets work. The risk premium is not a reward for actual loss but for the possibility. Since risk gives expected loss, Greece can only conform to that expectation by defaulting in some part – which governments however are not supposed to do. Thus there is a mismatch between government objectives and how markets work.

The mismatch disappears as follows. In an annuity scheme with 2.25% we set the final debt to zero so that the present value is 9998m. If the loan is served to maturity then it actually is redeemed already in the 6th year. 

period     payment     interest     redemption         debt 
1             1800.00     224.96         1575.04         8423.01 
2             1800.00     189.52         1610.48         6812.53 
3             1800.00     153.28         1646.72         5165.81 
4             1800.00     116.23         1683.77         3482.05 
5             1800.00       78.35         1721.65         1760.39 
6             1800.00       39.61         1760.39             0.00 

Apparently the above bullet bond implies an expected haircut of 50% already after the 3rd year. If Greece indeed would default in the bullet scheme after that 3rd year, the annuity scheme shows that it already had paid back 50%. The investor does not lose value then. A loss of 5000m after the 3rd year in the bullet scheme is the same position of the 5,000m in the annuity scheme. Thus, a haircut on a bullet scheme amounts to using an annuity scheme. See the formula in the Appendix.

The choice of a bullet or annuity format does not matter normally. When there is a fear of default however it does. Another key difference concerns the use of the risk free rate of interest. The rate of interest for a government in distress, the 18% of Greece, is rather a signal for the required annual payment instead of the risk free rate that is used in the formula for the present value. When the risk free rate is given, say 2.25%, the creditor’s fear for default translates into a desire for a higher annuity and thus in a shorter maturity, which is the proper way to deal with default risks. (Credit default swaps are a bank’s way to make even more money when defaults don’t materialize.)

Haircuts of 100%

Another possibility is of course that Greece could default on that annuity scheme. This would be a regime switch compared to what we are discussing here. With the haircuts that have been under discussion now (at most 50% on the bullet) a total default (100%) is not at issue yet. A regulator would no longer support a country that creates this kind of risk.

This argument can perhaps be better understood by looking at Portugal that hasn’t had a haircut yet. If investors really think that there is a risk of a Portuguese haircut of maximum 50% then they can use the annuity scheme, in which there is redemption so that the risk that they run on a bullet scheme disappears into what already has been redeemed. As markets still use 11.7% on the bullet scheme the conclusion is that they implictly use that annuity scheme and hope to profit in excess when Portugal will not have a haircut. 

The alternative suggestion would be that the 11.7% ought to cover a haircut on existing debt: but with existing debt around 100% of GDP the interest rate on a new loan of 10% of GDP then would be rather 500%. This would mean that Portugal would default on 50% of its existing debt and promise those planned proceeds to the new creditor. We are clearly not in this regime. Thus now we see excessive profit taking.


There is also stigma or country aversion, so that a country may fall prey to speculations on such sentiments against it. A stigma can be the only explanation why investors might require a rate of interest for say Portugal that is higher than 2.25% even when the risk of default does not materialize. Stigma is irrational but becomes rational since it is rewarded. A first reward is that investors can extract excess returns. Another ‘reward’ is that it can become self-fulfilling. If there is an actual haircut, then the investor on average only loses the excess return, since implicitly there has been an annuity scheme with the 2.25% risk free rate. 

Much debate in the EU seemed to be about regulating default risk while it actually was about regulating irrational market stigma that becomes rational since it is rewarded.

Countries can do a lot themselves about reducing such stigma but joining a monetary union eliminates their instruments of the printing press and the rate of exchange, and thus there is some responsibility for the union to assist. The ECB operations on the secondary debt market seem to reduce the rate of interest but can also enhance stigma, since they signal that the government is in problems. The issues get complicated when bank capital is affected by the value of old debt, when the ‘bazooka’ is not big enough, and when the ECB is limited to the secondary market (even using a loophole) while the solution lies with new debt. We now understand that the ECB actually wants to cap the risk free rate in the annuity scheme. The solution is to have a new rule that turns the risk premium into redemption when the risk does not materialize, and have a regulator enforce this.

Clearly, the issue is more complex than summarized here, see Colignatus (2011c) for details, including a policy ladder that uses Debt / GDP ranges.


Countries with stigma and (irrational) default risk can switch to annuity loans and cap the rate of interest, such that sentiments translate themselves into maturity. Countries that joined the Eurozone lost their instruments and need a regulator to help them in that capping to protect them against speculators.

The problem is not just Greece or Portugal but also the Treaty of Maastricht that was not built for the current crisis. The identification of the stigma effect and counterproductive market process to the extent that we now see requires reevaluation of the Treaty. 

This can be seen in a wider evaluation, see Colignatus (2011ab) and the interview by Stavrou (2011). Overall it would be better that the ECB becomes a proper central bank without the current issues of legitimacy. 

Thomas Cool is an econometrician and teacher of mathematics in Scheveningen, Holland. He prefers to use the Colignatus name for his scientific work to distinguish that from politics and business.

Formula Appendix

This is the formula for the remaining debt in an annuity scheme with annual payment p, number of paid payments n, principal w and rate of interest r, say for n = 3. The formula can be understood as borrowing a perpetuity value p / r and putting a part p / r - w into an account earning interest.

Consider a bullet loan that after three years is hit by a haircut h on the principal w:

Since these remainders are the same, we can calculate h from the other values, and the haircut on a bullet scheme can be seen as redemption in an annuity scheme.



Bofinger (Peter), Lars P. Feld, Wolfgang Franz, Christoph M. Schmidt, Beatrice Weder di Mauro (2011), “A European Redemption Pact”, http://www.voxeu.org/index.php?q=node/7253

Cabral, Ricardo (2011), “Greece’s 2nd bailout: Debt restructuring with no debt reduction?”, http://www.voxeu.org/index.php?q=node/6818

Colignatus, Thomas (2011a), “High Noon at the EU corral. An economic plan for Europe, September 2011”, http://mpra.ub.uni-muenchen.de/33476 

Colignatus, Thomas (2011b), “An economic plan for Europe”, http://ekathimerini.com/4dcgi/_w_articles_wsite3_1_23/10/2011_411466

Colignatus, Thomas (2011c), “Conditions for turning the ex ante risk premium into an ex post redemption for EU government debt”, http://mpra.ub.uni-muenchen.de/35120/

Delbecque, B. (2011), “Capping interest rates to stop contagion in the Eurozone”, http://www.voxeu.org/index.php?q=node/7106

Hau, Harald (2011), “Europe’s €200 billion reverse wealth tax explained”, http://www.voxeu.org/index.php?q=node/6804

Stavrou, Protesilaos (2011), “Chaos in Europe, the G20 in Cannes and the need for constitutional changes – Interview with Thomas Colignatus”, http://protes-stavrou.blogspot.com/2011/11/chaos-in-europe-g20-in-cannes-and-need.html

 PM The earlier version of November 18.