Saturday, March 28, 2015

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.

*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)


  1. It's easy to see why bond yields fall with inflation or GDP. It is less obvious why also equities.

    It has to do with the fact that a company is a portfolio of projects and options on new projects.

    Low GDP is just saying that new projects are few and the yields are low. But coming into such a situation means that previous projects were made at higher rates and yields. Depending on the duration of these legacy projects, their values should rise. It so happens that our largest companies often own near-permanent monopoly projects that have relatively small investment opportunities. These projects surge in value in a low-growth low rate world, since they are essentially high yield low risk bonds. The lack of opportunities cause those yields to accumulate, as we all notice.

    It would be more interesting to ask why risky and insubstantial equities are also rising. It's not hard to understand why quality has done well.

    1. "Depending on the duration of these legacy projects, their values should rise. It so happens that our largest companies often own near-permanent monopoly projects that have relatively small investment opportunities. These projects surge in value in a low-growth low rate world, since they are essentially high yield low risk bonds."

      So where were all the blue chip companies who's share price surged in fall 2008 and early 2009 when GDP growth was lowest + declining the fastest?

      "It would be more interesting to ask why risky and insubstantial equities are also rising."

      Part 2 of my post on inflation expectation's role in stock price formation can be used to explain the rise in both quality and no-so quality equities along w/ bond prices.

    2. Okay, fine. See ya later...

  2. JP:

    "today's concurrent bull market pattern"

    I suppose it depends on what you mean by "today". Since 2010, stocks have boomed while yields have remained at historically low levels. Inflation expectations have remained range bound. Most of the liquidity improvements you cited in your earlier post occurred long before the current period. I challenge you to find an asset manager that believes market liquidity has actually improved in the past few years. Therefore, neither liquidity nor falling inflation expectations can explain the concurrence of low nominal and real bond yields along with a historically strong risk asset rally.

    Also, in your inflation discussion you state the assumption of a constant real growth rate expectation. This is inconsistent with the "pessimism" explanation for low yields.

    Unfortunately, I'm still left with either a massive market inefficiency (nowhere in evidence) or distortions caused by monetary policy.

    1. "Also, in your inflation discussion you state the assumption of a constant real growth rate expectation. This is inconsistent with the "pessimism" explanation for low yields."

      That's the whole point. I'm generating twin bull markets w/o having to rely on growing pessimism (or optimism) over real growth.

      "Inflation expectations have remained range bound."

      In the US 10-year expected inflation has come down from over 2% to 1.7%. I'm sure its fallen more in Europe.

  3. I see your point on the "pessimism" argument. Your post is a work-around. The first problem with the work-around is, in the bigger picture, the net movement in inflation expectations over the four years leading up to the oil price collapse was minor. Hard to point to this as a driver of a massive bull market.

    The second problem with the work-around is the level of real bond yields: they are around 200bp (or more during the four year period) lower than they were throughout Japan's "lost decade", and they are at historical lows barring other periods of Fed intervention in bond markets, or high-inflation periods. The "pessimism" argument is, first and foremost, an attempt to explain this anomaly. My response is this thesis must, by necessity, ignore asset price movements, or it would have to argue (illogically) for a massive market inefficiency to exist. Unfortunately, your post does not address how booming asset prices can correspond with real yields that are normally associated with a lack of positive NPV investment projects in the economy. For this, one has to turn to the distortive effects of monetary policy (although, I remain open to other explanations!).

    1. The use of a work-around is mainly a device to provide a way to think of all the other gears that are operating behind the curtains. But we can bring real growth expectations back in.

      Falling inflation expectations can explain some of the stock bull market. A slight improvement in real growth expectations since 2010 could explain the other. This would otherwise cause a fall in bond prices, but the same decline in inflation expectations that helped drive the stock bull market could offset this effect. Improved liquidity in markets gets us closer to twin bull markets.

      (You may not be fond of this last effect, but keep in mind that an asset's liquidity return is an expected return, much like expected inflation or earnings, involving the discounted flows of liquidity returns far into the future, and is unfortunately not observable. We can only depend on anecdote so much.)

      Lastly, to get the large drop in bond rates that you describe, you need something like a supply shock to bond liquidity services, ie. austerity and QE. (ie. my second last paragraph). This may finally bring us into agreement, although you refer to this "distortive" monetary policy in your comment whereas I see it as just a secondary effect of monetary policy.

    2. JP,
      I think we're dealing with mathematics here. Stock prices doubled in the four years between mid-2010 and mid-2014. Small changes in inflation expectations cannot account for that mathematically; and, in fact, the 5yr b/e was 1.8% at the beginning and end of the period. Similarly, liquidity premia are not likely to be high enough such that their (unobserved) expected decline would drive a doubling of stock prices.

      I would say focus on the big picture: stocks doubled, bond yields are abnormally low. Cash storage costs, inflation expectations and liquidity expectations can theoretically account for movements in stocks and bonds; they cannot account for the movements observed.

    3. Diego, the problem here is most of the questions we are debating require data that cannot be observed. You mention break evens, but TIPS are a fairly lousy indicator of inflation expectations since the signals they generate suffer from the very same liquidity disturbances I am using to generate concurrent bull markets. That being said, I don't think a lack of data means we must assume an I'm with stupid approach, or some sort of mass inefficiency. It seems to me that at best we'll have to both stay silent on the concurrent bull market phenomena until we get more data.

    4. Perhaps, then, we could at least agree that the "pessimism" approach is intellectually inconsistent in the absence of market inefficiencies.

      It seems the vast majority of economists, including Janet Yellen, toss around the "pessimism" argument without, apparently, giving much thought to the contradictory behavior of risk asset prices. So far I've only seen your attempt to provide a consistent explanation. I really appreciated it despite my objections.

    5. "Perhaps, then, we could at least agree that the "pessimism" approach is intellectually inconsistent in the absence of market inefficiencies."


      I think your observation is a good one, that's why I wrote the post.

  4. Let's pretend that I work for the Federal Government and have some money to invest after paying all my obligations.

    I consider investing in either the bond market or the stock market. As a small investor, I am most likely to buy either a bond or stock that is being sold by someone else. I am bidding up the price of either the bond or stock sufficient to meet the sellers expectations.

    Because I am bidding up the price of both investment vehicles, I am driving down the yield of both instruments.

    I also reflect that to pay me the wage I receive, Government is borrowing and running a deficit year-after-year. This action year-after-year must result in more bonds and more money floating around in the entire macro-economy. Clearly, alternate investments such as real property and equity in stocks does not increase in supply as quickly as the potentially possible increase in supply of money and bonds. The discriminating investor might therefore consider that a potential inflation factor could be applied to real property and equity in stocks, but not to bonds or money. Bonds or money are the drivers for inflation, not the candidate for revaluation.

    Returning to the post premise that bond prices and stock market prices are a prediction of future economic growth, I think the premise is incorrect. In my example, I am simply saving part of my wages in a vehicle that I hope will return more future money than zero (from saving but not investing in a vehicle). My action says nothing about future economic growth.