In what galaxy far, far away or alternate dimension do negative interest rates even begin to make sense? Our first reaction when we see something like this is to say to ourselves that this makes no sense at all and will not end well. But as the markets continue to rise and rates go lower and lower we scratch our heads and think that maybe this all makes sense and we’re the ones who are too dim to see it. After all, why would central bankers lead us down the path to destruction? When the central banks say that more stimuli in the form of ever lower rates are on the horizon the pundits cheer and the markets soar. Fundamentals no longer matter as central bankers from the Land of Oz are the wizards behind the curtain. Clearly dad sired an idiot who doesn’t understand that it’s different this time.

The Swiss 50 year sovereign bond currently has a negative 3 bps yield (0.03%). Given the massive amount of interest rate risk (the risk that rates increase) that the buyer would take on who in their right mind would tie up their hard earned cash for 50 years and pay the bond issuer 3 bps per year for the privilege of lending them money? Wouldn’t inflation alone just kill me? What am I missing? What I’m missing is that I have no intention of holding that bond for one year let alone 50 years. If I can find a greater fool somewhere down the line and I am convinced that rates will only go down then I am the alchemist who can truly turn lead into gold. To pump liquidity into the system central banks are buying bonds at a breakneck pace. Their appetite for risk assets is so voracious that the central banks are running out of bonds to purchase. In Japan the BOJ owns a substantial percentage of Japan’s sovereign debt and is even buying stock ETFs because it can’t find enough risk assets to fulfill its mandate. Alas I’ve found my sucker! This quest for risk assets is reminiscent of pre-2008 when you couldn’t find enough high-risk, high-yield subprime mortgage bonds to throw into a CDO so you replicated those bonds using credit default swaps. This way the same soon to be worthless bond can be in multiple CDOs at the same time and investors will line up to purchase the snake oil that you’re peddling. Is history repeating itself?

Duration and convexity are measures of a bond’s sensitivity to a change in market interest rates. Technically speaking duration and convexity are the first and second derivatives, respectively, of bond price with respect to the market interest rate. If D is duration, C is convexity and dr is the change in market interest rates then the equation for the percentage change in bond price is…

Percent change in price = -D dr + ½ C dr^2

As a bond’s yield goes to zero duration goes to bond term and convexity goes to the square of bond term (assuming that coupon rate = yield). The yield on our Swiss bond is negative 3 bps so to make the math easier let’s call that yield zero for now. The duration and convexity of our 50 year Swiss bond at a zero yield is 50 and 50 squared, respectively. If I buy this bond and interest rates decrease by another 10 bps (0.10%) then my percentage return on investment is…

Percent return on investment = -50 x -0.0010 + ½ x 50^2 x -0.0010^2 = 5.13%

This kind of return in a zero return environment is not bad. The problem is what happens if rates rise and rise significantly? If I used leverage (i.e. borrowed funds via the carry trade) to fund my initial purchase of the Swiss bond then I am truly screwed. If market rates increase by say 100 bps (1.00%) and I am using 2:1 leverage then I am completely wiped out. Surely I am hedging my downside risk but who is going to take the other side of that trade? Maybe Deutsche Bank with its $50 trillion derivatives book would be game? What we learned in 2008 is that it’s the off-balance sheet derivatives hiding in the shadows that can take the system down. Can you say AIG?