As with many of my articles, this one starts with a personal story from my insurance business career (skip down four paragraphs to the end of the story if you want):

25 years ago, when it was still uncommon, I wanted?to go to an executive course at the Wharton School for actuaries that wanted to better understand investment math and markets. ?I went to my boss at AIG (a notably tight-fisted firm on expenses) and asked if the company would pay for me to go… it was an exclusive course, and very expensive compared to any other conference that I would ever go to again in my life. ?I tried not to get my hopes up.

Lo, and behold! ?AIG went for it!

A month later, I was with a bunch of bright actuaries at the Wharton School. ?The first thing I noticed was aside from the compound interest math, and maybe some bond knowledge, the actuaries were rather light on investment knowledge, and I would bet that all of them had passed the Society of Actuaries investment course. ?The second thing I noticed were some of the odd investments described in the syllabus: it was probably my first taste of derivative instruments. ?At the ripe old age of 29, I was learning a lot, and possibly more than the rest of my classmates, because I had spent a lot of time studying investments already, both on an academic and practical basis.

I had already studied the pricing of stock options in school, so I was familiar with Black-Scholes. ?(Trivia note: an actuary developed the same formula for valuing optionally terminable reinsurance treaties six years ahead of Black, Scholes and Merton. ?That doesn’t even take into account Bachelier, who derived it 73 years earlier, but no one knew about it, because it was written in French.) ?At this point, the professor left, and a grad student came in to teach us about the pricing of bond options. ?At the end of his lesson, it was time for the class to have a break. ?I went down to make a comment, and it went like this:

Me: You said that we have to adjust for the fact that interest rates can’t go negative.

Grad student: Of course.

Me: But interest rates could go negative.

GS: That’s ridiculous! ?Why would you ever lend money and accept back less than you gave them, and lose the time value of money?!

Me: Almost of the time, you wouldn’t. ?But imagine a scenario where the demand for loanable funds leaves interest rates near zero, but the times are insecure and violent, leaving you uncertain that if you stored your cash privately, you would run too large of a risk of having it stolen. ?You need your cash in the future for a given project. ?In this case, you would pay the bank to store your money.

GS: That’s an absurd scenario! ?That could never happen!

Me: It’s unlikely, I admit, but I wouldn’t say that you can never have negative interest rates.

GS: I will say it again: You can NEVER have negative interest rates.

Me: Thanks, I guess.

Well, so much for the distant past. ?Here is why I am writing this: yesterday, a friend of mine wrote me the following note:

Good evening.? I trust you had a blessed Lord’s Day in the new building.?

Talking bonds today with my Econ class.? Here’s our question. Other than playing a currency angle why would anyone buy European debt with a negative yield?? The Swiss and at least one other county sold 10 year notes with a negative yield.? Can you explain that?? No interest and less principle [sic] at the end.

Now, I didn’t quite get it perfectly right with the grad student at Wharton, but most of it comes down to:

• Low demand for loanable funds,?with low measured inflation, and
• Security and illiquidity of the funds invested

The first one everyone gets — inflation is low, and few want to borrow, so interest rates are very low. ?But that doesn’t explain how it can go negative.

Things are different for middle class individuals and large financial institutions. ?Someone in the middle class facing negative interest rates from a checking or savings account could say: “Forget it. ?I’m taking most of my money out of the bank, and storing it at home.” ?Leaving aside the inconvenience of currency transaction reports if the amount is over $10,000, and worries over theft, he could take his money home and store it. ?Note that he does have to run a risk of theft, though, so bringing the money home is not costless.

The bank has the same problem, but far larger. ?If you don’t invest the money, where would you store it? ?Could you even get enough currency delivered to do it? ?if you had a vault large enough to store it, could you trust the guards? ?Why make yourself a target? ?If you don’t have a vault large enough to store it, you’re in the same set of problems that exist for those that warehouse precious metals, but with a far more liquid commodity.

Thus in a weak economic environment like this, with low inflation, banks and other financial institutions that want certainty of payment in the future are willing to pay interest to get their money back later.

Part of the problem here is that the fiat currencies of the world exist only to be?units of account, and not stores of value. ?Thus in this unusual environment, they behave like any other commodity, where the prices for futures are often higher than the current spot price, which is known as backwardation. ?(Corrected from initial posting — i.e. it costs more to receive a given cash flow in the future than today, thus backwardation, not contango.) ?The rates can’t get too negative, though, or some institutions will bite the bullet and store as much cash as they can, just as other commodities get stored.

To use another analogy, a while ago, some market observers couldn’t get why anyone would accept a negative yield on Treasury Inflation Protected Securities [TIPS]. ?They did so because they had few other choices for transferring money to the future while still having inflation protection. ?Some people argued that they were locking in a loss. ?My comment at the time was, “They’re trying to avoid a larger loss.”

Thus the difficulty of managing cash outside of the bond/loan markets in a depressed economy leads to negative interest rates. ?The financial institutions may lose money in the process, but they are losing less money than if they tried to store and protect the money, if that could even be done.