Yesterday Reuters published an article entitled "Restive bond markets may complicate ECB's exit plans".

This was a piece speculating about how and when the ECB can taper off and finish its Asset Purchase Programme ("APP"), its version of Quantitative Easing. The piece stated that "Currency strength and a doubling of benchmark borrowing costs over just two months may be tightening euro zone financial conditions faster than the ECB would like, potentially jeopardizing its timeline to exit stimulus".

This seems to us to be a ridiculous understatement of the ECB's actual predicament.

The reality of the position is contained in our paper of October 2017 entitled "The European Central Bank is bound upon a wheel of fire: it cannot raise interest rates or reduce its Asset Purchase Programmes without a risk of bankrupting itself" and it is available from the Research Papers section of our company website. The circumstances posited in the paper seem to have exactly come to pass.

The Reuters article goes on to state that "Long-term borrowing costs in powerhouse economy Germany have roughly doubled in the past two months. At 0.74 percent, they are close to a 2-1/2 year high". If this is true, several points derive from it:

1. Long-term would be 7-10 years or more;
2. Rates for Germany have increased by over 30 basis points in those maturities;
3. Germany has the best credit rating among the Eurozone countries: if rates for Germany have gone up by 30 basis points, rates for Spain and Italy and others can be assumed to have gone up by more;
4. The ECB's APP has been pursued throughout the last 2 1/2 years, so that the portfolio will have been bought when rates were falling up to mid-2015, and when rates were lower but steady from 2015 until now.

This last point is vital because it is opaque whether the portfolio contains latent profits on purchases made up to mid-2015 where the bonds still have some life to run. If the bonds have already matured and been repaid, there is clearly no latent profit in the portfolio. For bonds bought since mid-2015, there will be no latent profit because they were bought when yields were zero or negative, and there could even already be latent losses.

The opacity of APP derives from the structure of the Eurosystem, in which the ECB ordains the APP operations, but they are executed by the Eurozone National Central Banks ("NCBs"). Profits and losses are attributed - but only when realised by an NCB via a sale of an APP holding prior to maturity - by the transacting NCB to the ECB, and then it is attributed back out to all the NCBs (including the transacting one) in line with their capital keys in the ECB. The ECB has been in the habit of distributing its profits annually, rather than building up a Reserve of Profit.

The APP portfolio is about €2 trillion and the current mark-to-market value of it is opaque:

• because it is held at the NCBs;
• because the NCBs do not produce mark-to-market reports on their individual holdings;
• because neither the ECB nor the Eurosystem produce any consolidated figures for the APP operations transacted by NCBs at the risk of the ECB;
• because the ECB's annual report does not shadow, against its capital or its P&L account, the latent profits or losses attributable to it from the APP operations.

Thus we are left to speculate, but at least we know that the ECB has paid a price at the high end for these bonds (for reasons laid out in the October 2017 paper), and has acquired most of the portfolio when interest rates were zero or even negative.

We suspect - and it was reported yesterday in the Daily Telegraph that the ECB is the biggest buyer of Italian government bonds - that the average credit quality of the APP portfolio is some way below that of German governments (AAA in the Standard&Poors system), but we know that it is all of "investment grade" quality, meaning rated BBB+ or better (Italy is rated BBB+).

We do not know the average remaining life but we can posit that it is spread over 3-10 years, and so we can model that the APP portfolio comprises:

• €500 billion with 10 years' remaining life
• €500 billion with 7 years' remaining life
• €500 billion with 5 years' remaining life
• €500 billion with 3 years' remaining life

It is a simple matter to calculate the reduction in value on bonds with these remaining lives in the case that:

• The investor has a holding of €1 million of a bond with an annual coupon of 1%
• Interest rates were 0.40% to the same maturity as the bond
• Interest rates have now risen by 10 basis points (0.10%) to 0.50% to the same maturity as the bond

The price reduction on a holding of €1 million nominal at each maturity for a 10 basis point increase in interest rates is:

• 10 years: €10,049
• 7 years: €7,026
• 5 years: €5,014
• 3 years: €3,006

Such a price reduction either reduces the investor's latent profit - if they bought the bond when interest rates were higher than 0.50% - or creates a latent loss - if they bought the bond when the interest rate was 0.40%. If they bought the bond when the interest rate was lower than 0.40%, this rise in rates to 0.50% increases a latent loss that the investor was already sitting with.

Assuming that the ECB APP portfolio of €2 trillion is spread evenly across the maturity spectrum with €500 billion held in each tenor, its value reduction for each 10 basis point increase in rates is:

• On the 10 year holdings: €5,024,394,590
• On the 7 year holdings: €3,512,806,942
• On the 5 year holdings: €2,507,000,836
• On the 3 years holding: €1,502,856,791
• On the entire portfolio: €12,547,059, 159

This is just for a 10 basis point increase, and the Reuters story states a 30+ basis point rise in German long-term costs. We must therefore consider, given the average credit quality of APP, that the rates may have gone up by anything between 20 and 40 basis points when averaged across all maturities and credit qualities in the APP portolio.

The value reductions deriving from these possibilities applied across our model portfolio would be:

• 20 basis points: €25,094,118,319
• 30 basis points: €37,641,177,478
• 40 basis points: €50,188,236,638

To cushion itself against these kinds of losses the ECB can set the following resources:

• €7.6 billion subscribed-and-paid in capital (Eurozone shareholders have fully paid in their subscriptions)
• €1.1 billion estimated profit for 2017, if it is in line with the 2016 profit and has not yet been distributed
• €28.6 billion Revaluation Reserves as per the chart in the 2016 accounts that is quoted below
• €3.1 billion subscribed-but-not-paid in capital of the non-Eurozone shareholders, such as the Bank of England
• Total €40.4 billion, assuming the Reserves have not been eroded and that the non-Eurozone shareholders are willing to pay in for this purpose

€28.6 billion Revaluation Reserves consisted of:

• Gold - €13.9 billion
• Foreign Currency - €14.1 billion
• Securities - €0.8 billion
• Post-employment benefits – (€0.2 billion)

The 30 basis point rise in yields on the APP portfolio would cause a sufficient loss to wipe out almost all of the ECB's resources, unless the recent rise in yields has had the effect simply of reducing the latent profit on the portfolio because it was purchased when rates were higher than they are now.

This seems unlikely as the ECB's programme of purchasing bonds in to the APP has continued and in size all the way through the period of very low rates, its aim being to release large amounts of cash into the Eurozone economy.

In addition Reuters story is that rates have already gone up by 30 basis points, and for the best credit. If that is the case they will have gone up by more for the worst credit.

These circumstances we take as prima facie proof of our paper in October 2017 and our statement now: the ECB is bankrupt on a mark-to-market basis. However this fact is disguised by the accounting practices of the Eurosystem taken together with the NCBs being the owners of the APP bonds but at the ECB's risk.

If we are correct, then the ECB's only way out of this is not to allow the NCBs to sell off any of the APP, but rather to have the NCBs hold all the bonds until maturity, wherever interest rates go to in the meantime, and let the portfolio run off naturally over the next 10 years or so.

Whether the NCBs, particularly the ones already lending heavily into TARGET2, will be happy to do that will make for an interesting discussion within the ECB Governing Council.