The issuance on August 21, 2019 of a thirty-one year zero coupon bond at a negative yield was for me like finding the Higgs boson (aka the “God Particle”) was for a particle physicist in 2012. While theory predicted its existence a few decades ago, the actual discovery was nonetheless stunning. Just as the discovery of the Higgs boson validated the standard model of physics, and invalidated other theories of the universe, the issuance and trading of a negatively yielding zero coupon bond has validated, in my view, the theory that investment today is mostly about psychology, scarcity, need for safety, and overwhelmingly politics; and much less about clean, economic arbitrage-free mathematical relationships, time-value of money, and “no-free lunch” by which most finance professionals are trained.

There are indeed other zero coupon bonds trading at negative yields in Germany, over a half dozen of them. For example, there is the two year maturity BKO of 6/11/21 that trades at a negative yield of -0.86% and a price of 101.50. Then there is the DBR 0 of 4/5/24 maturity that is a little less than five years to maturity and trades at a price of 104.18 today and a yield of -0.88%. The seven year maturity zero trades at -0.82% and a price of 105.91. The ten year maturity zero has a price of 106.66 and yield of -0.65%. And of course finally and most importantly we have the thirty year zero issued a couple days ago that closed at 104 today and a yield of -0.127%. Just by looking at the term structure of yields, one can roughly estimate the term structure of the price of insurance (for return *of* capital instead of return *on* capital) by subtracting the price of the bond above 100 from 100. (*All data in this paper is taken from the Bloomberg terminal* August 22 and 23, 2019.)

The big deal is that bond investors assume that “anomalies” like negative yields are fleeting, and the term structure of yields should reflect this. Depending on who you speak with, roughly the five- to ten-year point is considered long enough for fundamental distortions in yields to be smoothed out. But thirty years is a very long period, and until recently, beyond the reach of policy makers and governments; but quantitative easing has changed all that. Our hero for this note is the thirty one year maturity German government zero coupon Bund issued on 8/21/2019, with a maturity date of 8/15/2050, and no call or put option provisions. It does not pay any interest until the maturity date, but this “non-interest” compounds annually, with a day-count convention of ACT/ACT. This, folks, is as simple and atomic as a bond ever got. This bond is basically equivalent to the “discount factor”, and there is no need to engage in complex coupon stripping and discounting math. We can just read the discount factor from the price. The reason that I call this the “god-particle” is because this bond is the most fundamental building block of finance theory, because the risk-free discount factor is the fundamental building block of all financial math. Never in the history of bond trading has a thirty year zero coupon bond been issued at negative yields or above par in price. And until recently it was considered, at least in academic finance, to be an impossibility.

The price at issue was 103.61, and the redemption price will be exactly 100 [*Source: Bloomberg, August 21, 2019]*. Since the yield to maturity is so close to zero, there is no present value computation to speak of, and all the bond math follows from one long division using pen and paper. Both in character and purity, this bund is breathtakingly “pure” in its valuation. The consequences of the simplicity, however are astounding. Just as a peek into the true nature of atomic physics shows the breathtaking simplicity and beauty of nature, a peak into the second grade math of a zero coupon bond exposes where we appear to have come to in the world of finance. Since there is only one cash-flow, the price of the bund is par (100) discounted back to today. We can simply say that the buyer of this bond is willing to pay 3.61 percent upfront, or roughly 12 basis points per year for insuring that the nominal, i.e. not inflation adjusted principal is returned. This bond has essentially no credit risk, since Germany is widely noted to be one of the most responsible fiscal managers in the world. So we can assume that the yield has negligible impurity from any other factor.

Things start to get more interesting when we look at the risks of this security.

The duration of a zero coupon bond by definition is equal to the maturity of the bond. Now remembering our first bond math course, there are two important definitions and interpretations of duration. The Macaulay duration is the weighted average maturity of cash-flows from a bond. Since there is only one cash flow at maturity, the Macaulay duration at issuance of this bund is 31 years. The intuition behind Macaulay duration is that it’s the “fulcrum” that balances the weight of the intermediate cash-flows against the principal’s return. So in this case the fulcrum is at the maturity, i.e. both intuitively and mathematically, this bond’s cash-flows are akin to a very long lever, with the one and only pivot point at maturity. As Archimedes told us many years ago “give me a lever long enough and a fulcrum on which to place it, and I shall move the world”, here the owner of the bond is building an incredible amount of potential return for a very small change in yield. This long term zero at a price above par is very much like an Archimedian lever and there aren’t too many of them around, unless one uses derivatives or synthetic leverage. In other words, if you are an unlevered investor who can only buy fully paid cash bonds, there is no other choice than to buy this bond in order to obtain the price and yield tradeoff you desire.

The modified duration is the other important concept, and is the sensitivity of the bond to yield changes, i.e. the percentage price change for a small change in yield. For this bund, the modified duration is about 31 years; i.e. a 1% change in yields can change the price by approximately 31% of its value.

The convexity of this bond, or the rate of change of the duration, is about 10; i.e. for a large fall in yields, the bond’s price will increase by a factor of convexity times the square of the yield change, and for a large rise in yields, the bond’s price will be cushioned by the convexity, leading to a significant amount of asymmetry. For a zero coupon bond, the convexity is super high anyway, increasing as the square of the maturity. For example, a cousin of this bond is the German bund maturing on August 15, 2029 which has a ten year maturity. The ten year zero has a convexity of “only” a tenth of the thirty year bond.

Combining the discussion of the prior two paragraphs, this bond then provides a turbo-charged call option on falling yields. Not unlike Armageddon equity put options, a long term zero coupon bond is very much like an option on bond prices, and hence the perceived demand from hedgers who need the convexity to hedge their long term liabilities. Since bond math does not care (investors do) between negative and positive yields, pushing yields further negative exponentially increases the price of this bond. If an investor is buying this bond based on simply the price, which has no theoretical limit (yes, these trees can theoretically grow to the sky!), then the more the need to diversify against equity market risk, the higher the price of this bond, and the more rapid the rise in the price for the same decline in yield.

What about the perspective of the issuer of these bonds? Since there are no other unlevered instruments in the market that can match the convexity of a zero coupon bond, it is optimal for the issuer to issue while supply of convexity is scarce, and demand from risk management needs is massive. This is akin to the cycles in natural catastrophe re-insurance. The best time to sell insurance is when demand for insurance is high and supply is low. Of the almost two billion Euros offered, less than 900 million Euros was bought by buyers in the auction, and according to my Bloomberg, the rest (almost Euro 1.2 billion), was “retained for market intervention”, which presumably means that the Bund will be fed out to the market if the demand increases in the future. In other words, the public, at least publicly refused to pay money for the privilege of lending money, so the buyer of last resort, the issuer or its affiliates, held back the rest on its own books in reserve, maintaining the price.

Since the “time-decay” of this option is so low per year, the cost of holding the Bunds is negligible in the short run. Eventually, however, the bunds and the guaranteed loss on them will very likely be borne by European tax-payers. The most likely outcome is that indexed funds will be forced by their rules to buy these negatively yielding Bunds. 2019 has been a year of record inflows into indexed bond funds, and as discussed in my previous post, many of these indexed bond funds are passive buyers of negative yielding global bonds. The flows are simply overwhelming the supply available, and if the issuer can keep the scarcity premium high enough, there will be willing buyers, as long as there is not a big reversal in bond market investment flows.

Hence why fixed income is still the domain of active managers, who presumably can find better investments for their funds.

So what might this all mean for investors, other than the sheer beauty of demand and supply mismatch exhibited in all its glory? Is this time really different? Are we permanently in a world where bonds are going to trade at negative yields, i.e. as “insurance” products, rather than as investment products with positive expected returns?

Most important, it is probably apparent to most investors, but perhaps not to central bankers, that this is all a collateral effect of the massive liquidity creation of the last decade. As discussed by many astute market observers, asset prices have risen much faster than economic variables such as GDP. Since the monetary stimulus has largely been a failure — at least in Europe and Japan — to generate goods and price inflation, the next step might be wealth transfer from savers to the common public via “helicopter money”. Certainly the price of borrowing would justify this. See a recent paper by none other than Stan Fischer, advisor of both Mario Draghi and Ben Bernanke about the possibility of Central Banks “Going Direct”.

I have to think that giving unlimited amounts of money to spend to the public would be inflationary for good and services, and probably not so good for asset prices, which are technically stores of money. So while central bankers never want to address asset price inflation outside of the closet, it appears that we are setting up for asset price deflation and real-asset inflation. Land, gold, commodities are all tangible “things” that should do well if global central banks change their mode of operation from supporting banks to going direct to the public. The opportunistic issuance of long term zeros should be a warning to investors that governments who have benefited from the ever lower and falling yields are now getting ready to satisfy the demand for yield and be paid handsomely for it. In other words, monetary policy will start to overlap with fiscal policy.

All else being equal, this will likely result in temptation to issue more for longer and spend the money on fiscal and social spending. While this possibility might seem remote today, history supports the return of fiscal loosening, especially when borrowing is more than free. And while this might not be legally or politically feasible, what stops the US government from issuing debt in Euros at a lower yield and using the Euros generated for larger geopolitical expansion for example? The power of low long term yields in creating non-financial, indeed global geopolitical change, is enormous.

We also have to grant that if the fundamental discount factor that drives all financial calculus is above par for the next thirty years, all asset prices which use the same discounting calculus are today probably much higher than they would be in the absence of low yields. The risk of any sharp rise in rates or yields is that diversification will be less beneficial for portfolio risk mitigation. If all asset prices fall simultaneously due to a fall in the price of zero coupon bonds aka the discount factor, where will one hide? This argues, yet again, for market participants to consider building portfolio defense using explicit hedging instruments.

Finally, Alan Greenspan recently commented essentially that there is nothing fundamental about the zero bound in interest rates, or “zero is just a number”. Most investors would probably differ and say “Really?” To accept that zero in long term yields is just a number is akin to saying that there is no difference between being a borrower or a lender. Like the perpetual motion machines of yesteryear, we all know that you cannot, forever, get something from nothing. And while the long term zero coupon bond in Germany seems like this hypothesis is wrong, only time will tell whether this time is indeed different. We might indeed look back at today in a few years’ time, and not unlike the aftermath of the crisis, ask ourselves: “What Were We Thinking?”