(Bloomberg) — Pricing a bond that never matures is one of the more straightforward tasks in all of finance. Divide the annual interest rate by its prevailing yield and — voilà — price.
But if negative interest rates are really here to stay, well then, things could get crazy real quick. That, at least, is the conclusion of former Long-Term Capital Management co-founder Victor Haghani.
In a report published by his current firm, ElmPartners, Haghani and his colleague James White considered what would happen to the theoretical value of various long-term bonds if negative rates became a long-term economic feature rather than a short-term phenomenon.
For starters, take $100 worth of bonds that pay 1% in annual interest over a span of 100 years. If rates fell to -1%, the present value would soar to $200. A substantial gain for sure, but nothing the mind can’t comprehend.
OK, now stretch that maturity to 1,000 years. Instead of $200, your bonds are now worth a staggering $2.3 million.
And for bonds with no maturity date? The value suddenly races to infinity.
Of course, the authors concede no rational investor in the real world would ever pay the infinite sums that the cold, hard numbers dictate. And if predicting the course of interest rates in the next decade is a fool’s errand, trying to divine the path over millennia would seem preposterous. But if you think there’s even a remote chance sub-zero rates could persist for long periods of time, then paying what might seem like ludicrously high prices for long-term bonds, they argue, isn’t wholly without merit.
“We are not claiming that most people hold these beliefs … but if you do (and we don’t think it’s unreasonable to do so), then you’ve got a paradox on your hands,” they wrote.
Haghani and White dubbed their thought experiment the “Perpetuity Paradox,” in a nod to the St. Petersburg Paradox, a conundrum related to probability and decision theory in economics. (For an explainer, click here.) Yet real-life parallels do exist, particularly in a world where the insatiable demand for safe assets has pushed yields on over $12 trillion of bonds below zero.
Take for example, the 3% bond issued in 1896 by the Netherlands, one of the few remaining perpetual government bonds.
That bond last traded at 330 Dutch guilders (yes, it continues to be priced in its original currency) — nearly spot-on with the value you’d get in a simple online bond-pricing calculator if you input 1,000 years left to maturity and a market rate equal to the bond’s yield of 0.909%.
But what if you assume sub-zero rates have the power to stick around for a thousand years? Then that same Dutch bond now has a present value of over 100,000 Dutch guilders (or about $50,000).
Perhaps more realistically, consider Austria’s 100-year bond, one of the closest approximations to a modern-day sovereign perpetual bond out there.
The same bond-pricing calculator produces a price of 173 euros when you use its current yield of 0.95% as the discount rate, an indication the market expects interest rates to average about 1% over the remaining 98 or so years of the bond’s life. But assume the discount rate falls to -0.5% and then stays there, then the bond’s expected price shoots past 400 euros.
“It seems difficult to dismiss negative rates as just a fleeting phenomenon,” Haghani and White wrote. “That means it’s worth seriously thinking through the issues involved in valuing and investing in long-lived cash-flow streams, whether arising from government bonds, real estate or equities, near and below the zero interest rate frontier.”