The bond-stock conundrum

Here's a conundrum. Many commentators have been trying to puzzle out why stocks have been continually hitting new highs at the same time that bond yields have been hitting new lows. See here, here, here, and here. On the surface, equity markets and bond markets seem to be saying two different things about the future. Stronger equities indicate a bright future while rising bond prices (and falling yields) portend a bleak one. Since these two predictions can't both be right, either the bond market or the stock market is terribly wrong. It's the I'm with stupid theory of the bond and equity bull markets.

I hope to show in this post that investor stupidity isn't the only way to explain today's concurrent bull market pattern. Improvements in financial market liquidity and declining expectations surrounding the pace of consumer price inflation can both account for why stocks and equities are moving higher together. More on these two factors later.

1. I'm with stupid

The I'm with stupid view goes something like this...

If investors expect strong real growth for the next few decades, a new bond issue has to provide a competitive coupon in order to attract capital. Soon after the bond is issued, economic growth stagnates and the economy's expected real rate of return falls. The bond's coupon, originally rated for a much healthier economy, has become too good for the new slow-growth environment. The price of the bond has to rise relative to its face value (thus counterbalancing the juicy coupon with a guaranteed capital loss) so that its overall rate of return falls to a level commensurate with the economy's lower real rate of return. That's why rising bond prices are often a sign of a bleaker future.

As for equities, that same decline in the real rate of return will result in a fall in prices. A stock is a claim on whatever profits remain after interest, and lower real growth means a smaller remainder. No wonder then that a number of investment commentators believe that the modern rise of stock and bond prices requires one set of investors to be acting irrationally; after all, things can't be simultaneously better and worse off in the future. Either that or arbitrage between the two markets is simply impossible, say because large actors like the Fed are rigging the market. Whatever the case, concurrent bull markets implies a giant market inefficiency, as Diego Espinosa has described it.

Massive inefficiency isn't a very satisfying theory for the twin rises in bond and stock markets. Thankfully, we don't need to resort to changes in real growth rates to explain securities price changes. Let's explore two other factors that could be driving the concurrent bull market pattern:

2. Falling inflationary expectations and concurrent bull markets

Assume that the real growth rate is constant over time but inflation expectations decline. The real value of all flows of coupon payments from existing bonds are suddenly more valuable, causing a one-time jump in bond prices. If inflation expectations consistently fall over time, then a bull trend in bond prices will emerge. This is standard stuff.

And stocks? What many people don't realize is that those same declining inflation expectations will set off a bull market in equities as well. The general view is that a firm's bottom line waxes or wanes at the same pace as inflation, the result being that real stock returns are invariant to inflation. Corporate shares are supposed to be hedges against inflation.

This is (almost always) wrong, a point I've made before (here and here). Let me take another stab at it. In short, thanks to the interaction between historical cost accounting and the way taxes are collected, rising inflation expectations will boost a firm's real future tax burden, reducing real cash flows and therefore stock prices. Falling expectations about inflation act like a tax cut, increasing real cash flows and stock prices.

For folks who want to work through the logic, what follows is a numerical example. Take a very simple firm which incorporates itself, buys inventory and a machine with the cash raised, operates for four years, and dissolves itself. At the end of each year it pays out all the cash it has earned to its shareholders. At the outset, the company buys 40 unfinished widgets for $60 each. Over the course of its life, it expects to process 10 widgets a year and sell the finished product at a real price of $100. In order to process the unfinished widgets, it buys a widget upgrader for $500. The upgrader is used up, or depreciated, at a rate of $125 year so that it will be useless after year four. Since the company will have also depleted its inventory of unfinished widgets by that time, it has nothing left over after the fourth year.

The first table shows the anticipated cash flows that will be paid to shareholders after taxes have been rendered to the tax authority, assuming 0% inflation over the course of four years. The cash amounts to an even $876.25 a year.

Let's boost the expected inflation rate to 1% (see table below). The real value of cash flows starts out at $876.25 in year one but steadily declines, hitting $866.66 by year four. Shareholder get less real cash flows than they did in a stable inflation environment.

On the other hand, if we ratchet down expected inflation to -1%, the real value of cash flows starts out at $876.50 in the first year but climbs to $886.24 by the end of year four. Shareholders enjoy a larger real flow cash payments than they did in either the stable or the rising expected inflation environments. If cash dividends are immediately spent on consumption, this means that shareholders enjoy the greatest flow of consumption when inflation expectations are falling.

A reduction in expected inflation will cause a one-time jump in our company's share price. If these reductions in expected inflation occur consistently over time, we get a series of jumps in the company's share price, or a bull market.

The core intuition behind this result is that under historical cost accounting, a company's cost of goods sold and its depreciation expenses are both fixed in time. Cost of goods sold is valued on a first-in-first out basis, which means the price of the oldest good is used to value unit costs (in our case, $60), while depreciation is calculated as a fixed percentage of a machine's original purchase price. When inflation is stable, this is unimportant. But once expected inflation rises, the firm's costs grow stale and can no longer keep up with its anticipated revenues, the result being artificially higher pre-tax accounting profits and a larger tax bill. These bloated future tax bills drain cash from the firm, resulting in lower expected cash payouts to shareholders over the life of the firm.

When expected inflation falls, the firm's anticipated revenues shrink relative to its costs, the result being lower future pre-tax profits and a lighter tax bill. Less cash filters out of the firm, leaving more cash in the kitty for shareholders to enjoy at the end of each year.

The table below shows how our firm's real tax bill varies across each of these scenarios:

So a reduction in expected inflation is (almost always) good for equity prices as it amounts to a tax cut. Why have I inserted a caveat? When a company is indebted, lower-than-expected inflation will increase the real burden of that debt. If its debt load is heavy, the debt effect may outweigh the combined effects of cost of goods sold and depreciation. One reason why falling inflation expectations in Japan during the 1990s and 2000s didn't result in an equity boom is that Japanese companies tend to be far more indebted than companies in the rest of the world. (This may also explain why Japanese stocks outperformed U.S. stocks during the inflationary 1970s.) For most of the world's markets a reduction in expectations surrounding the rate of inflation is an ideal situation for equities.*

What do we know about the actual shape of inflation expectations? In general people have been marking their expectations downwards since the early 1980s, a trend that has been amplified since the credit crisis as central banks around the developed world have consistently undershot their inflation targets. We thus have the underpinnings for a concurrent bull market in stocks and bonds, driven by falling inflation expectations.

3. Liquidity and the concurrent bull market pattern

Let's move on to our second factor. Assuming that the real growth rate and expected inflation both stay constant, we can also generate concurrent bull markets in stocks and bonds by simultaneously improving their liquidity. Innovations in market infrastructure over the years have made it easier to buy and sell financial assets. Investors can increasingly use financial assets as media of exchange, swapping them directly for other financial assets rather than having to go through deposits as an intervening medium. Think buzz words like re-hypothecation and collateral chains.

As financial assets become more liquid, a larger portion of their overall return comes in the form of a non-pecuniary liquidity yield. All things staying the same, investors must cough up a larger premium in order to enjoy this liquidity-augmented return, resulting in a one time jump in asset prices. Consistent improvements to liquidity will result in a step-wise asset bull market.

I've written here about the ongoing liquidity enhancements in equity markets, and speculated here that thirty-year bull market is bonds is (partly) a function of improved bond liquidity. In the same vein, Frances Coppola once penned an article noting that when everything becomes highly liquid, the yield curve is flat, reducing returns across all classes of financial assets (a flattening of the yield curve implies a jump in the price of long term bonds).

While I think that liquidity-improving innovations in market technology and declining inflation expectations can explain a good chunk of the stock bull market, I don't think they can't quite explain as much of the secular rise in bond prices. After all, market interest rates haven't just plunged. In many cases both nominal and real bond interest rates have gone negative.

We can salvage this problem by resorting to another liquidity-based explanation for why bond investors are willing to accept negative returns. Government bonds provide a unique range of liquidity services in their role as a financial media of exchange, a role that cannot be replicated by central bank reserves or any other medium of exchange. Reserves, after all, can only be held by banks, and corporate bonds aren't safe enough to serve as universally-accepted collateral. However, governments have gone into austerity mode, reducing the flow rate of bonds coming onto the market. At the same time, central banks are buying up and removing government bonds from circulation. As a result, the supply of unique liquidity services provided by bonds is growing increasingly scarce, forcing investors to bid up the price of these services. Liquidity premia are high. So a negative real return on bonds may be a reflection of the the hidden fee that bond investors are willing to pay to own a government bond's flow of liquidity returns. I've written about this here.

In sum, the I'm with stupid theory, with its implication of massive inefficiencies, shouldn't be our only theory for concurrent bull markets. Asset prices move for many reasons, not just changes in expected real growth. Bond and equity investors may be reacting non-stupidly to shifting liquidity patterns and declining inflation expectations, the result being a steady bidding up of the prices of both assets.

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*If you are interested in the difference between Japan and the rest of the world, here are some papers worth investigating: 

The Taxation of Income from Capital in Japan, Kikutani and Tachibanaki (pdf)
The Cost of Capital in the U.S. and Japan: A Comparison, Ando and Auerbach (pdf)
Are Japanes Stock Prices to High. French and Poterba (pdf)

Transporting the macroblogosphere back to 1809: Usury Laws and the 5% upper bound

The zero-lower bound is the well-known 0% floor that a note-issuing bank hits whenever it attempts to reduce the interest rate it offers on deposits into negative territory. Should the bank drop rates below zero, every single negative yielding deposit issued by the bank will be converted into 0% yielding notes. When this happens, the bank will have lost any ability it once had to vary its lending rate.

The ZLB is an artificial construct. It arises from the way the banking system structures the liabilities that it issues, namely cash and deposits. We can modify this structure to either remove the ZLB or find alternative ways to get around it. Much of the discussion over the econblogosphere over the last few years has been oriented around various ways to get below zero.

There is another artificial bound, this one to the upside—let's call it the 5% upper bound, or FUB. The FUB is an archaic bound. Up until 1854, the Usury Laws prevented the Bank of England from increasing rates above 5%. This constraint meant that for almost two centuries, the Bank of England's discount rate was bounded within a narrow channel that had as its upper limit the 5% mark as stipulated by the Usury Laws and a lower limit of 0% due to the existence of 0% yielding banknotes (see chart above).

Imagine that we had a time machine and transported the econblogosphere, still hot over the ZLB debate, back to 1809. What sorts of discussions would we be having if we had risen up against the FUB? Given that the conventional route of increasing rates was constrained by the usury prohibitions, what sort of unconventional monetary policies would bloggers be providing to the Directors of the Bank of England to deal with inflationary booms? Would this advice be symmetrical to the policies they have been advocating for escaping the ZLB?

1809 is a significant date because the convertibility of the pound into gold had been suspended for over a decade. Although convertibility would be resumed in 1821, England would be on a 'fiat' standard very similar to our own for another decade. In the years since suspension, the pound had gradually depreciated against gold and other European currencies. A healthy debate began to flourish over whether the Bank of England was responsible for the pound's depreciation (ie. inflation) or if external events such as crop failures were to blame. It was in that context that banker/economist Henry Thornton published his famous Enquiry into the Nature and Effects of the Paper Credit of Great Britain. Although Thornton was circumspect on the precise causes of the deprecation of the pound, he drew attention to the difficulties that the Usury Laws caused in controlling the volume of credit. Here is Thornton:

In order to ascertain how far the desire of obtaining loans at the bank may be expected at any time to be carried, we must enquire into the subject of the quantum of profit likely to be derived from borrowing there under the existing circumstances. This is to be judged of by considering two points: the amount, first, of interest to be paid on the sum borrowed and, secondly, of the mercantile or other gain to be obtained by the employment of the borrowed capital...

The borrowers, in consequence of that artificial state of things which is produced by the law against usury, obtain their loans too cheap. That which they obtain too cheap they demand in too great quantity.

Thornton pointed out that if there was a large deficit between the price at which a businessman could borrow from the Bank of England and the mercantile rate of profit—the rate at which the same businessman could invest the borrowed money—then the demand for and granting of credit would become excessive. While nudging the discount rate higher would normally be sufficient to reduce this excess, the laws against usury might prevent these increases from taking place.

If we were to drop Nick Rowe into the 1809 economic debate, he would complement Thornton quite well by making good use of the same pole-on-a-palm analogy he has so aptly used to explain the ZLB. Running an inflation targeting central bank is sort of like balancing a long pole upright in the palm of one's hand, says Nick. The bottom of the pole is the interest rate and the top is the inflation rate. As the pole starts to lean (ie. the price level begins to change), the holder needs to quickly move their palm far enough in the same direction (ie. interest rates must be changed) so as to stop the pole from falling over. A wall to the either the north or south impedes the holder's palm from moving sufficiently far and will cause the pole to tumble over.

Applying this analogy to monetary policy, the Directors of the Bank of England might be required to stop excess inflation by moving rates north of 5%. With the Usury Laws in place, the Director's efforts would be impeded. Nick's illustration is Thornton all over again.

Scott Sumner, Lars Christensen, David Beckworth, and other monetarist-types have been strong advocates of quantitative easing as a way to get below the ZLB. Whisk them back to 1809 and would they advocate getting above the FUB by quantity dis-easing, or QD — mass repurchases of Bank of England notes through the liquidation of the Bank of England portfolio of assets?

Assuming that the threat of QD is able to increase the expected purchasing power of the pound (just as the threat of QE is supposed to reduce the same), then the Directors could initiate a QD program to improve the real return on pound notes and deposits. As soon as the real return on notes and deposits exceeds real returns on capital, the inflationary boom will come to a halt. Conveniently for the Directors, the nominal 5% rate will have remained in place — only real rates will have increased — thereby allowing the Directors to abide by the Usury Laws.

What about New Keynesians like Paul Krugman? Promising to hold off on future interest rate increases after a recovery has begun is the sort of advice New Keynesians have given to the Fed as a way to bridge the ZLB. This is called providing forward guidance. As Krugman says, a central bank needs to "credibly promise to be irresponsible".

Parachute Krugman into 1809 and he would be counseling the Directors to do the opposite: hold off on reducing rates from 5% after a contraction had already set in. In other words, the Directors need to "credibly promise to be hard-asses." As long as this promise is taken seriously by the market, the promise of future monetary tightening translates into lower inflation in the present, and the real interest rate rises. This should reign in the inflationary boom. Much like Sumner and Christensen, Krugman's advice would allow the Director's to hold steady at the 5% nominal rate dictated by the Usury Laws, letting real rates do the job of reeling in prices and slowing down the economy.

What about Miles Kimball? Transport Miles back to 1809 and he'll probably be the most aggressive in the outright removal of the Usury Laws. Just as he is currently campaigning for the ability of central banks to set negative rates on deposits, I'm sure he'd by picketing outside of Parliament for the right of the Director's to bypass the Usury Laws and set 6-7% nominal rates.

Incidentally, what did the Directors of the Bank of England actually do? According to Jacob Viner, there is evidence that

bankers found means of evading the restrictions of the usury laws. In 1818, the Committee on the usury laws stated in its Report that there had been “of late years ... [a] constant excess of the market rate of interest above the rate limited by law.” Thornton notes that borrowers from private banks had to maintain running cash with them, and borrowers in the money market had to pay a commission in addition to formal interest, and that by these means the effective market rate was often raised above the 5 per cent level. Another writer relates that long credits were customary in London and a greater discount was granted for prompt payment than the legal interest for the time would amount to.

More convincing evidence that the 5 per cent rate was not of itself always an effective barrier to indefinite expansion of loans by the banks is to be found in the fact that the directors of the Bank of England, although they professed that they discounted freely at the rate of 5 per cent all bills falling within the admissible categories for discount, in reply to questioning admitted that they had customary maxima of accommodation for each individual customer and occasionally applied other limitations to the amount discounted.

In Paper Credit we find Henry Thornton verifying Viner's claim, noting the "determination, adopted some time since by the bank directors, to limit the total weekly amount of loans furnished by them to the merchants."

So the Director's preferred route for getting out from under the thumb of the Usury Laws was to maintain the 5% discount rate, but ration the quantity of loans issued at these rates, thereby limiting the quantity of credit in circulation. While this policy might not have been sufficient to prevent an inflationary boom, it may have prevented a hyperinflation from breaking out.

Before I sign off, I want to reverse something I said at the outset. I wrote that the 5% upper bound was archaic, but that's not entirely true. Sure, high interest rates are no longer illegal. But high nominal interest rates have never been politically palatable. Central bankers are not independent of politics, and therefore probably still operate with something akin to a 5% upper bound. Let's call it an "upper-ish" bound, or the point at which a central banker starts to get dirty looks from those who have the power to reappoint him. Central bankers may need to resort to unconventional techniques to free themselves of the upperish-bound. The Fed's motivations for adopting quantity targets in 1979, for instance, may have been such a technique. An overt jacking-up of interest rates to 15-20% would have been political suicide, goes the theory, so the FOMC chose to engage in a bunch of hand-waving about hitting money supply targets, thereby distracting would-be critics with a new set of monetary verbiage. This left Paul Volcker free to implement what would be at its peak a tremendously onerous 22%+ fed funds rate.

We're of course not anywhere near the upper bound these days, at least not in the developed world, but it's still an interesting puzzle to work through in order to help understand the current situation. Our investigation also offers a history lesson. In choosing to remove it over century ago, the FUB was revealed to be neither a law of nature nor a design of God. The FUB was a choice. Hopefully we'll eventually realize that the same applies to the ZLB.

Beyond bond bubbles: Liquidity-adjusted bond valuation

Real t-bill and bond yields have been falling for decades and are incredibly low right now, even negative (see chart below). With an eye to historical real returns of 2%, folks like Martin Feldstein think that bonds are currently mis-priced and warn that a bond bubble is ready to burst.

Investors need to be careful about comparing real interest rates over different time periods. Today's bond is a sleek electronic entry that trades at lightning speed. Your grandfather's bond was a clunky piece of paper transferred by foot. It's very possible that a modern bond doesn't need to provide investors with the same 2% real coupon that it provided in times past because it provides a compensating return in the form of a higher liquidity yield.

[By now, faithful readers of this blog will know that I'm just repeating the same argument I made about equity yields.]

Here's a way to think about a bond's liquidity yield. Bonds are not merely impassive stores-of-value, they also yield a stream of useful services that investors can "consume" over time. In finance, these consumption streams are referred to as an asset's convenience yield. (HT Mike Sproul)

For instance, the convenience yield of a house is made up of the shelter that the house owner can expect to consume. A Porsche's convenience yield amounts to travel services. What about a bond's convenience yield? I'd argue that a large part of a bond's convenience yield is comprised of the liquidity services that investors can expect to consume over the life time of the bond. Let's call this a monetary convenience yield.

In an uncertain world, it pays to hold a portfolio of goods and financial assets that can be reliably mobilized come some unforeseen event. A fire alarm, a cache of canned beans, and a bible all come to mind. Liquid financial instruments, say cash or marketable bonds, are also useful since they can be sold off quickly in order to procure more appropriate items. This ability to easily liquidate bonds and cash is a meaure of their monetary convenience.

Even if the unforeseen event for which someone has stockpiled canned beans or bonds never materializes, their holder nevertheless will enjoy the convenience of knowing that in all scenarios they will be secure. The stream of uncertainty-shielding services provided by both a bond and a can of beans are "consumed" by their holder as they pass through time.

This monetary convenience yield is an important part of pricing bonds. Prior to purchasing a bond, investors will appraise not only the real return the bond provides (the nominal interest rate minus expected inflation) but will also tally up the stream of future consumption claims that they expect the bond to provide, discounting these claims into the present. The more liquid a bond, the greater the stream of consumption claims it will yield, and the higher its monetary convenience yield. The greater the stream of consumption claims, the smaller the real-return the bond need provide to tempt an investor into buying. (HT once again to Mike Sproul on consumption claims)

Which brings us back to the initial hypothesis. If the liquidity of government debt has increased since the early 1980s, then we need to consider the possibility that bonds are providing an ever larger proportion of their return in the form of a monetary convenience yield, or streams of future consumption claims. If so, the observed fall in real rates isn't a bond bubble. Rather, negative real rates on treasuries may reflect technological advances in market microstructure and improvements in bond market governance that together facilitate the increased moneyness of bonds. Put differently, investors aren't buying bonds at negative real interest rates because they're stupid. It's possible that investors are willing to accept negative real interest rates because they are being sufficiently compensated by improving monetary convenience yields on bonds.

I find this story interesting because we usually think that in the long term, real interest rates are determined primarily by nonmonetary factors, including the expected return to capital investments and the time preferences of consumers. The story here is a bit different. In the long term, real interest rates on bonds are determined (in part) by monetary forces. The higher a bond's monetary convenience yield, the lower its real interest rate. Oddly, bonds may be bought not by consumers who are willing to delay gratification, but by impatient consumers who want to immediately begin consuming a bond's convenience yield (ie. using up future consumption claims). The line between consumption and saving is blurred and fuzzy.

In my previous post on equities, I gave some numbers as evidence for the increased liquidity of stocks. Bonds aren't my shtick, so I won't try to prove my hypothesis. All I'll say is that the rise of repo markets would have contributed dramatically to bond market liquidity since repo increases the ability to use immobilized bonds as transactions media. Give Scott Skyrm a read, for instance.

There is a case of missing markets here. If we could properly prices a bond's monetary convenience yield, then we could get a better understanding of the various components driving bond market prices over time.

Imagine a market that allowed bond investors to auction off their bond's monetary convenience yield while keeping the real interest component. Thus a bond investor could buy a bond in the market, sell (or lease) the entire chain of consumption claims related to a bond's liquidity, invest the proceeds, and be left holding an illiquid bond whose sole function is to pay real interest. By stripping out and pricing whatever portion of a bond's value is related to its monetary nature, investors might now precisely appraise the real price of a bond relative to its real interest payments. Excessively high real prices relative to real interest would indicate overvaluation and a bubble, the opposite would indicate undervaluation and a buying opportunity.

But until we have these sorts of markets, we simply can't say if bond prices are in a bubble. Sure, real rates could be unjustly low because bonds prices have been irrationally bid up. But they could also be justly low if bonds are simply providing alternative returns in the form of monetary convenience. Without a moneyness market, or a convenience yield market, we simply lack the requisite information to be sure.

More on own-rates

The discussion on own-rates, the natural rate, and Sraffa cropped again.

Andrew Lainton blogged here, followed by Nick Rowe here, Daniel Kuehn here, and David Glasner here.

It seems to me that Nick and David are more or less on the same side of the aisle. I commented on Nick's post here, and Nick provided a helpful response. I commented on Glasner here, and he gave me some good feedback.

Tipsy TIPS spreads

David Glasner noticed a very interesting anomaly yesterday. In short, 5-year TIPS rates seem to be rising while 10-year TIPS have been falling. He encouraged his readers to do some investigating to find out why. See my findings below.

Inflation swaps and TIPS

Econbrowser has a post on inflation expectations as measured via TIPS spreads. This links back to an earlier comment I made on Glasner's blog, in which inflation swaps are posited as an alternative to TIPS spreads. Here is the comment from Econbrowser:

"One might worry about characteristics in the TIPS market distorting the estimates of the real yields."

 and

 "The real yield curve starts at five years, so one can’t be sure what the real yield curve suggests for the horizon less than five years. "

 Why not use zero coupon inflation swap prices? They (supposedly) don't suffer from some of the same distortions as TIPS (liquidity premia), and you can get shorter terms.

 For instance, here is the 2 year inflation swap.

 http://www.bloomberg.com/apps/quote?ticker=USSWIT2:IND

Just subtract the 2 year swap rate from the nominal 2 year rate and you have the 2 year real rate. 

See the Cleveland Fed's explanation of their methodology for measuring inflation expectations, which includes the use of  inflation swaps