Martin C. W. Walker
3 min readFeb 21, 2019


Impossible Finance — The Zero Coupon Perpetual Bond

Bonds for the uninitiated are simply a form of loan. The issuer of the bond borrows money from the purchaser. Generally, bonds have a maturity date when the issuer repays the owners of a bond the face value. Issuers also periodically pay holders of bonds coupons (or interest). A bond’s value is based on calculating the net present value of those cash flows, adjusted for the risk of default.

One special type of bond is the “Zero coupon bond” which does not pay interest but is issued at a discount to the face value. It is the face value that is paid by the issuer when the bond matures. Another variation is the “Perpetual Bond”. This bond never matures and in theory, the issuer (assuming their continued solvency) will pay coupons forever.

Now what happens if you combine features of these two types of unusual bond and create a zero coupon perpetual bond? The formula for calculating the value of a perpetual bond is shown below.

D = Coupon per period

r = discount rate

n = number of periods i.e. infinity

This is a very simple calculation for a Zero Coupon Perpetual bond. The answer is zero because D = 0. Zero divided by anything is zero. Summing up an infinite stream of zeros, strangely enough is also zero.

Now who would ever be crooked enough to ever sell a bond that does not pay interest or repay the capital? Who would be stupid enough to buy a security like this? Could it even exist in this world? Sadly, in recent years, thousands of what are effectively Zero Coupon Perpetual bonds have been issued and billions of dollars have been spent buying them. Except, they are called cryptocurrencies (though some people insist on calling them “Digital Assets”).

The otherwise closest investment, in economic terms, to Zero Coupon Perpetual Bonds, are pyramid schemes. Pyramid schemes are a slightly better bet through because if you are an early investor, the organiser of the scheme may pay you some money. Pyramid schemes are however illegal in most countries. The real-world manifestation of the Zero Coupon Perpetual Bond, the cryptocurrency is completely legal. In most countries there are no restrictions on buying cryptocurrencies. In both the UK and US it is legal to invest in derivatives linked to cryptocurrencies (where leverage increases the rate at which the investor can lose money). In some countries you can even invest your pension into cryptocurrencies.

The value of cryptocurrencies, in spite of a collapse in value, is stopped from falling to their natural value, i.e. zero, by a combination of market manipulation, investor ignorance and a tsunami of lies on social media from those paid to promote these worthless frauds. Why do regulators not act more firmly? Fear of seeming to crush “innovation”, confusion over how to apply the law and in some cases the relentless lobbying of the cryptocurrency industry.