Why so down?

If you've been reading Bill Gross's last few letters, you'll know that he's been a bit grumpy of late. It's that dang new trend that has hit bond markets, negative interest rates. Gross has been using words like incredible, surreal, and inconceivable to describe their arrival.Negative nominal bond rates certainly seem odd. Just look at the chart below, which illustrates what could very well be the two lowest-yielding bonds in the world, maybe all of history: the 3.75% Swiss government maturing in July 10, 2015 and the 4% Danish government bond maturing November 15, 2015. But is the idea of a negative rates really so strange?

Gross blames negative rates on central bankers who "continue to go too far in their misguided efforts to support future economic growth," in doing so "distorting" capitalism's rules. He's not alone; plenty of people claim that without autocratic price fixers like the SNB's Tommy Jordan and the Danmarks Nationalbank's Lars Rohde, rates would rapidly to rise to a more natural level like 1% or 2%.

Not necessarily. Even an economy without meddling central banks could be characterized by negative nominal rates from time to time, or, stealing from Tony Yates; "a negative rate doesn't distort capitalism, it IS capitalism."

Let's exorcise central bankers entirely from the economy. Imagine that we live in a world where things are priced in grams of gold. People walk around with pockets full of gold dust and a set of scales to measure the appropriate pinch necessary to pay for stuff. In this world, we all have a choice between two states: 1) we can hold gold dust in our pockets or 2) we can lend the dust to someone else for a period of time in return for an IOU. (Let's assume that the borrower is risk free.)

Each state has its own advantages and disadvantages. If we hold the gold dust in our pockets, we'll have instant access to a highly-liquid medium of exchange. Unlike illiquid media of exchange, liquid media provide us with the means to rapidly re-orient ourselves come unexpected events. With gold dust on hand we can purchase the necessities that allow us to cope with sudden problems or to take advantage of lucky breaks. At the end of the day, we may never actually use our gold to purchase things, preferring to keep it horded under our mattress. Even so, it hasn't sat their idly, but has provided us with a stream of consumption over time. The discounted stream of comfort that liquidity provides represents the total expected return on gold dust-held.

If we choose the second state and lend out our gold dust, we lose access to this liquidity and thus forfeit the expected stream of comfort that gold dust provides. Because we need to be compensated for this loss, a borrower will typically pay the lender a fee, or interest. But gold dust is burdensome. It is heavy and must be arduously weighed out and stored overnight in expensive vaults. IOUs, on the other hand, are a breeze to store. By offering to take our gold dust off our hands for a year or two, a borrower agrees to unburden us of storage expenses while providing us with a feather-light IOU in return.

So on the margin, when choosing between gold dust and an IOU, we are comparing the low storage costs of the illiquid IOU against the extra liquidity of cumbersome gold dust.

What might make rates turn negative in our central bankless gold dust world? Here are two ways:

1. Rising storage costs

Say that the costs of storing and handling gold dust grow substantially. At some much higher carrying cost, rather than requiring a fee from a borrower (i.e. positive interest) a lender will willingly pay the borrower a fee (i.e. will accept a negative interest rate) for the benefit of being temporarily unburdened of their gold dust. The loss of liquidity that the loan of gold dust imposes on the lender is entirely overwhelmed by the benefits of being freed from onerous storage costs. We get a sub-zero interest rate.

2. A narrowing liquidity gap

The second way to arrive at sub-zero interest rates is to narrow the vast gap between the respective liquidity returns on gold dust and IOUs. There are a few ways to go about this. Imagine that retailers who had previously only accepted gold dust as payment begin accepting IOUs too. Simultaneously, borrowers innovate by printing their paper IOUs in round numbers, making them far easier to count than grams of dust. All of this narrows the liquidity gap by improving the liquidity of IOUs. If the liquidity of IOUs improves so much that it exceeds the liquidity of the gold dust, an IOU effectively provides a greater stream of relief-providing services than gold. When this happens, lenders will clamour to pay a fee in order to lend their gold dust, since the superior optionality that an IOU provides is valuable to them. This fee represents a sub-zero interest rate.

Another way to narrow the vast liquidity gap between gold dust and IOUs is to create so much liquidity that, on the margin, liquidity becomes like air; it has no value. Neither gold dust nor IOUs can offer a superior liquidity return if society no longer puts any price on liquidity. In this situation, the interest rate on IOUs is purely a function of storage costs. Since an IOU will typically be less costly to store than the dust, the borrower of gold will typically receive a fee from the lender, a negative interest rate, in order to cover storage costs. Paul Krugman takes this tack here to explain negative rates.

So in the end, we can get negative nominal interest rates without central bankers. How far below zero can interest rates fall in a gold dust world? At least as low as the cost of storing gold dust and the degree to which the marginal value of an IOUs liquidity exceeds that of gold dust. Obviously we don't actually use gold dust in the real world, but the same principles apply to a cash-using economy. The theory behind negative rates isn't so surreal after all, Mr. Gross.

Some links to read:

Beyond bond bubbles: Liquidity-adjusted bond valuation by JP Koning [link]
What's the Actual Lower Bound? by Evan Soltas [link]
How Negative Can Rates Go? by Paul Krugman [link]
It turns out that the US was never at the zero bound by Scott Sumner [link]
What gold's negative lease rate teaches us about the zero-lower bound by JP Koning [link]