Saturday, March 7, 2015

Paul Krugman contemplates the lower bound

Paul Krugman has two posts discussing the effective lower bound to interest rates. The first I agree with, albeit with a caveat, and the other I don't.

In his first post Krugman takes Evan Soltas to task for including not only storage costs in his calculation of the effective lower bound, but also the extra convenience yield provided by deposits. Krugman's point is that once people are "saturated" with liquidity, as they seem to be now, then forgoing the liquidity of a short term marketable debt instrument (like a deposit) costs them nothing. If so, then the lower bound to nominal interest rates is solely a function of storage costs.

I agree with Krugman on this count. Take the 2 1/8% Nestle bond maturing May 29, which may be one of the first corporate bonds in history to trade at negative rates:

If it costs 0.50%/year to store and handle Swiss paper currency, then the rate on a Nestle bond can't fall below -0.50%. If it trades at -0.55%, an arbitrageur will contract to borrow the bond until it matures on May 29, sell it now, and convert the proceeds into 0% yielding SFr 1000 banknotes (these notes eventually being used to repay the bond lender). Our arbitrageur will incur 0.50%/year in storage costs while getting 0.55%/year from the bond lender, earning a risk-free return of 0.05%. Competition among arbitrageurs to harvest these gains will prevent Nestle's bond yield from falling much below storage costs.

However, here's the caveat. Krugman is assuming that liquidity is a homogeneous good. It could very well be that "different goods are differently liquid," as Steve Roth once eloquently said. The idea here is that the sort of conveniences provided by central bank reserves are different from the those provided by other liquid fixed income products like deposits, notes, and Nestle bonds. If so, then investors can be saturated with the sort of liquidity services provided by reserves (as they are now), but not saturated by the particular liquidity services provided by Nestle bonds and other fixed income products.

Assuming that  Nestle bonds are differently liquid than central bank francs, say because they play a special roll as collateral , then Soltas isn't out of line. Once investors have reached the saturation point in terms of central bank deposits, the effective lower bound to the Nestle bond isn't just a function of the cost of storing Swiss paper money, but also its unique conveniences.

This changes the arbitrage calculus. Our arbitrageur will now have to pay a fee to the lender of the Nestle bonds in order to compensate them for services forgone. Let's say the cost of borrowing the bond is 0.25%/year. Shorting the bond once it hits -0.55%, paying the borrowing cost of 0.25%, and storing the proceeds at a cost of 0.50% a year results in a loss of 0.20%. With the arbitrage being unprofitable, the Nestle bond can theoretically fall further than in our previous example before it hits the effective lower bound (specifically, its lower bound is now -0.75%).

How realistic is it that different goods are differently liquid? Since everybody seems to turn to Michael Woodford as the ultimate moderator of all questions monetary, here he is in his famous Jackson Hole paper [pdf] talking about the potential for different assets to have different types of convenience yields: might suppose that Treasuries supply a convenience yield of a different sort than is provided by bank reserves, so that the fact that the liquidity premium for bank reserves has fallen to zero would not necessarily imply that there could not still be a positive safety premium for Treasuries.
Unfortunately, it's almost impossible to know for sure whether the liquidity services of a Nestle bond, or any other bond for that matter, are valued on the margin when people are already saturated in reserves. This is because there is no market for liquidity. If there was, then we could back out the specific price that investors are currently placing on a given bond's liquidity services, say by asking them to put a value on how much they need to be compensated if they are to forgo those services for a period of time. I've mentioned liquidity markets in many different posts. But I digress.

Krugman ends his first post saying that "I am pinching myself at the realization that this seemingly whimsical and arcane discussion is turning out to have real policy significance." But in his second post he backtracks, saying that a "minus x lower bound" isn't all that special in term of policy, implying that x (i.e. storage cost) is low and likely to diminish thanks to financial innovation. Here I disagree. Once a central bank has reduced rates to the point at which it is facing a run into paper storage, it can turn to a new tool to buy itself even more room to the downside for rate cuts: the manipulation of x, or the storage costs of cash.

To conclude, we've all found out by now that there isn't a zero lower bound. Instead it's a minus x lower bound. The next step is to realize that x isn't set in stone, it can itself be made into a tool of monetary policy.


  1. There is still the question of how effective this would be. If owners see negative rates as previews of coming economic attractions, they may conclude negative rates will be better than any alternative.

  2. When Treasury borrows directly from the Central Bank, will the bond carry a negative interest rate?

    Or will negative interest rates only apply to sales of bonds to the private sector?

  3. You use the example of a Nestle 2 1/2% which trades with negative interest rates. I think you could look at this bond as if it were a call option with an unknown strike price.

    Here is my line of reasoning. It is possible to buy a call option on Nestle. The call option will give the owner the option of purchasing a share of Nestle stock at a strike price anytime during the effective time span of the option. It is easy to place a market value on such an option based on the trading price of the stock.

    A property secured bond has a similar characteristic in that the bond holder could at some point (in case of failure of the bond issuer) could become an owner of shares in a restructured company. A potential Nestle buyer would decide whether an investment in Nestle paper could be better done by buying shares (with immediate ownership benefits) or buying bonds (with potential benefits). The two choices have very different daily-available maneuvering options.

    I do not see government bonds of any issue in the same way as private debt. There would never be the possibility of a private investor of holding a share of ownership in government. It seems to me (using a private sector perspective) that government bonds are only useful as a vehicle of money storage for long periods of time. I would only use them if I wanted to save (as if I believed the advertisements on TV that urge individual savings). despite the perils of inflation and potential loss of capital.

  4. Hi JP,
    Firstly, great blog! Almost certainly my favourite.

    Before proceeding with my question, I should probably disclaim any real understanding of markets and monetary issues.

    That said, I was curious about why sovereign yields can fall below zero, but want to take it from a bond supply/issuance perspective. If there is no burning need for deficit reduction, as is usually the case in countries that can borrow in their own currency, issuing any sovereign debt implies a "real" profit for the government in charge. Why don't countries that can issue under these favourable terms milk it for all its worth i.e. keep issuing to finance public investment until they see yields move up and 0 profit. Especially since negative real yields usually suggest low growth/inflation expectations.

    Is it because the economics is contentious? Or because the political process can be cumbersome? Or am I missing something big altogether?


    1. I'd imagine that sovereigns may from time-to-time avoid new debt issuance, even at highly advantageous rates, because as you say, the political process is cumbersome. A corporation won't hesitate to issue new debt if it results in a profit, say by using the proceeds to buy back stock. The corporate decision-making process is much more straight forward than the political one.