Tuesday, April 23, 2013

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.


  1. The only question is how big the liquidity premium is empirically.

    A few years back, I stumbled on an interesting bit of evidence. There are "on the run" and "off the run" bonds. The two are identical in terms of coupons, time to maturity, and default risk. But on the run bonds are traded more frequently and trade at a lower yield. They are more liquid because they have a thicker market, and they have a thicker market because they are more liquid. Pure Menger snowball.

    In normal times, the yield differential is very small. But in a crisis it gets much bigger.

    Ah! I now see you had already commented(?) on my old post. http://worthwhile.typepad.com/worthwhile_canadian_initi/2008/12/trading-volume-and-financial-crises.html

    Anyway, somehow I think it might be possible to get an estimate of the liquidity premium from data on turnover plus data on the yield differential between on the run and off the run bonds??

    1. Nick, that was me back before I started commenting with my full name. Wow, I've been reading you for 5 years.

      Comparing on-the-run to off-the-run bonds is a great way to get an idea of relative liquidity, or the margin by which one issue's liquidity exceeds that of another. But it doesn't give us a measure of absolute liquidity.

      I used the on-the-run premium technique to figure out relative liquidity in the stock market. Reitmans has two classes of stock that are entirely similar except that one is non-voting. The non-voting are far more active than the voting. The voting shares *should* trade at a premium to the non-voting because of the attached voting right, but they often don't. I infer the premium of non-voting to voting to be a liquidity premium.

      But we get the same problem as with treasury spreads. Reitman's offers a rare liquidity premia natural experiment: same issuer, same term, say dividend, same everything. So we can manually back out the relative liquidity premium of non-voting over voting. But we don't just want the degree to which the non-voting is more liquid than the voting. We want a measure of outright or absolute liquidity. That way we can compare across issuers and asset classes.

    2. JP: suppose you draw a graph. Frequency of trade (velocity?) on the horizontal axis, and liquidity premium on the vertical. You want to plot the curve. You get data of the difference between velocity of on-the-run and off-the-run bonds. That difference, divided into the difference in yields, gives you an estimate of the slope of that curve. Extrapolate that slope out to where velocity is zero (and so liquidity premium should be zero too), and you get an estimate of the whole curve.

    3. In other words, if you know relative liquidity premium, and difference in velocity, and you assume that a zero velocity bond would have zero liquidity premium, you can estimate the absolute liquidity premium.

    4. I get it. Interesting idea.

      It's difficult to know what data should go on the horizontal axis. Frequency of trade, size of trades, bid ask spreads, some combination? Whatever data we choose could give us a different slope and therefore different estimations of the absolute liquidity premium.

      Which reminds me of this old post on L-data.

    5. I think I would put "velocity of circulation" on the horizontal axis. And calculate it by: V=(daily volume traded/total stock of bonds). Which is equivalent to: V=(daily value of trades/market cap).

      As we move along the spectrum of assets, from least liquid to most liquid, V should rise, along with the liquidity premium.

    6. Another thought. The on-the-run premium is a measure of *expected* liquidity in US 10-year note markets.

      Future expectations concerning 10-year bond liquidity are to some degree specific to that market. Data from 10-year markets may be too unique to use in estimating the expected liquidity of other terms and assets.

      Another thing. V, or "velocity of circulation," captures current conditions, but doesn't necessarily capture expected future velocity or liquidity of a given asset. It's a bit like using current inflation as a measure of expected inflation.

    7. "V, or "velocity of circulation," captures current conditions, but doesn't necessarily capture expected future velocity or liquidity of a given asset."

      Also raises the question: velocity over what look-back period?

  2. JP,
    Does this statement make sense?

    "Because 5yr Treasuries are incrementally more liquid, holders are willing to lose 1.5% p.a. of real wealth on the security vs. earning a historical 2%."

    I say incrementally because I don't really know if liquidity has improved in the Treasury market. By far the biggest spikes in the on/off the run premium, after all, occurred in 2008 and 1998, not in 1990 or 1980. Further, I believe the repo market was deep and liquid prior to 1998.

    1. Diego,

      Your use of the word incrementally implies that bond monetary convenience yields haven't increased at all, or barely. But we don't have data for this.

      Which underlines the whole problem. To make intertemporal comparisons of real returns we need to see market-priced monetary convenience yields over time, but we don't have this data.

      My old post on improving equity liquidity makes sense, but it's mere speculation since I haven't presented a market-priced convenience yield as evidence.

      Without legitimate data on convenience yields, I think we should lean towards agnosticism about real overvaluation/undervaluation.

  3. JP,
    I think the data on off/on the run bond premiums would be instructive. I'll try to find it. Meanwhile, I do think its worthwhile putting yourself in the place of a typical fiduciary bond holder. Of course you will pay some premium to be able to dispose of term Treasuries quickly -- the convenience yield. How many of these fiduciaries would accept a guaranteed 1.33% p.a. loss for five years in exchange for that "convenience"? Truly, such a preference would have to stem from extreme concern over price volatility. The problem is that nowhere else is such an extreme level of concern evident. All risk asset markets -- with the exception of private label mortgages -- seem to be functioning quite normally, if not exhuberantly.

    1. Here's a link to some charts on the off the run premium:


    2. As I said to Nick, the on-the-run premium is a good indicator of relative monetary convenience. But I want an absolute indicator, not a relative indicator. Knowing that Bob is 2 inches taller than Jim doesn't tell me how tall Bob is.

      "How many of these fiduciaries would accept a guaranteed 1.33% p.a. loss for five years in exchange for that "convenience"?"

      It's possible that investors put a high enough value on monetary convenience, say 2% a year, that they bear a -1.3% real return for five years in order to enjoy a net +0.7% return. It's also possible they they only put a 0.5% per annum value on monetary convenience, in which case the total return is -0.8% or so. In which case the bubble argument makes sense. Without a market for monetary convenience, who knows? We can speculate about it, but we need a market to verify.

  4. I think the point you are trying to make is that bonds as money substitutes are better/more liquid than ever. This notion i actually disagree with. I think it's just a base money issue at this point, exploding global base money will have an impact on interest rates globally, that is the crux of what we are witnessing. Liquidity, I would argue is far worse than say.. 04/05/06 period. Certainly the repo market was far far deeper during that time period, one interesting side effect of zero rates is that balance sheets become costly for the dealers when there is 0.0bps of mark up in your repo transactions at the same time as regulatory costs associated with your balance sheet going up. As for the on-the-run / off-the-run story, that all goes back to balance sheet and the cost of liquidity, which again i would say is certainly worse than 05/06.

    1. Not *are*, but *could be* more liquid than ever. What I'm trying to point out that it is impossible to definitely compare the state of bond market liquidity over time without having evidence in the form of market prices. We can always find anecdotal evidence, but liquidity price data clinches the argument.

  5. JP,

    Check these products out


    They aren't exactly what you have in mind I don't think, but they are a start.

    1. John, good find. Now that you mention it, we have these products in Canada too... market-linked GICs. They sort of mimic the idea of a fixed term deposit of shares. In theory, anyone holding this instrument should get a better return than the index since they're forfeiting the liquidity of shares for a fixed term.

    2. On an average day, I carry $100 of currency in my wallet. What with inflation and foregone interest, my $100 cash holdings cost me $8 per year. But the total convenience yield of my $100 cash holdings is about $1500 per year, when you consider the trouble it saves me when buying snacks, paying for gas and parking, etc. (Note to econ. students: The marginal convenience yield of the 100th dollar held is equal to the marginal cost of that dollar.)

      Now look at things from the point of view of the currency issuer. A dollar bill costs 6 cents to print and lasts 2 years. So printing costs 3% per year, and a lot less for higher denominations. There are also handling costs, so let’s say a dollar bill costs 4% per year to keep in circulation.

      When a bank issues 100 paper dollars, it gets a $100 bond yielding 5%. After subtracting the 4% costs, the bank has a profit of 1%. This 1% profit would attract rival currency issuers, until some rival offers dollars that pay 1% interest, thus yielding zero profit to the issuer. That’s a nice deal for the customer, to get $1500 of convenience yield while the issuer gets zero profit. But note that in spite of the enormous convenience yield, the dollar has no liquidity premium. It is priced just like a bond.

      Play with the numbers a little. If the costs were 5%, then the dollar would bear zero interest, or more accurately, the interest on the dollar would be exactly burned up by printing and handling costs. There is still no liquidity premium. Or what if costs were 7%? Then the dollar would lose 2% of its value every year, and still no liquidity premium. What if costs fell to zero? Then competition would assure that the dollar bore 5% interest, but still no premium.

      Conclusion: The value of the dollar is determined by the interest rate and printing and handling costs, but not by convenience yield.

    3. If the convenience yield on cash is really that high, then the $100 bond should yield far more than 5%. Being deprived of cash for a fixed period of time (ie. being a bond buyer) is incredibly costly in your scenario, so a bond buyer needs a much higher rate before they'll bite. Holding cash for a fixed period of time is incredibly convenient, so bond issuers should be willing to pay a much higher rate than 5% to coax in buyers.

    4. The governing factor here is arbitrage by money issuers, not high liquidity demand by money users. The fact that someone out there is willing to pay $1500 for an apple doesn't mean that farmers will be able to charge more for an apple than their own cost of production.

      If there are $100,000 worth of bonds out there, and the people out there require $100 currency to conduct their business conveniently, then the issuance of $100 of currency (in exchange for bonds) will not affect bond yields or prices.

    5. "The value of the dollar is determined by the interest rate and printing and handling costs, but not by convenience yield."

      I'm getting confused. Let's simplify this and talk in terms of assets. The price of any asset in the market place will be determined (in part) by its convenience yield. All things staying the same, an asset (say a 30-year bond, gold, a house, common stock) that suddenly provides more convenience will rise in price. That seems non controversial to me. My post focused on bonds specifically.

      It gets more complicated with deposits. That's where you want to take the conversation. But you agree with the previous paragraph, right?

    6. This is a case of dollars having a horizontal supply curve (with dollars on the horizontal axis and oz./$ on the vertical), while the liquidity demand for those dollars slopes down. Printing and handling costs act like a tax on dollars, and with a horizontal supply curve, the entire tax is borne by the customer. Thus if the market interest rate is 5%, a dollar with P&H costs of 3% will yield just 2% to its holder. The holder is willing to bear the 3% costs because convenience yield is (say) 20%. But that doesn't mean that the dollar issuer can start charging people 15%/year to use his dollars. The issuer will find that as soon as the yield he pays on his dollars falls below 2%, rival issuers will take all his customers by offering dollars that yield 2%.

    7. But what about a 30-year treasury bond?

      Convenience yield rises, that'll drive it's price up, right?

    8. If the convenience yield is something like a coupon payment, then yes. That's because a coupon payment is both a gain to the bond holder and an expense to the bond issuer. But if the convenience yield comes from the fact that some of the bond holders can use them as money, or they like the pretty color of the ink on the bond, then the bond price can be unaffected.

      BTW: Convenience yield is usually explained as being the advantage that people get from holding heating oil rather than heating oil futures. The convenience yield of money is complicated by the fact that it might be just as easy to buy stuff with the futures contract on money as with the money itself.

    9. "...can be unaffected."

      or, alternatively, can be affected?

      The US government doesn't spend anything on ensuring the superior liquidity of the run 10-year note, yet it trades at a premium over off the run equivalents.

  6. JPK

    Under-valuation/over-valuation are slightly ill-defined terms. For example, if I say there's a bubble in bond prices, I could mean:

    1)I expect bond prices to fall down from here. This could be due to 'endogenous reason or because I'm making a comment on central bank policies or whatever. But there's no notion of equilibrium or history here.

    2) I consider the sudden rise in monetary convenience yield to be a disequilibrium phenomenon.

    3) I consider the sudden rise in the monetary convenience yield to be an equilibrium phenomenon in the sense that the system has little tendency to move, but the ex-ante savings and investment plans of economic agents have not relaised so that the equilibrium is sub-optimal.

    In some theories, a spike in the monetary convenience yield of nominally safe bonds - a bubble - is isomorphic to a shortage of aggregate demand. You seem to suggest that we shouldn't be quick to write it away as a disequilibrium phenomenon, and I agree, but equilibrium itself has more than one interpretation.

    1. Ritwik,

      Just to make sure I got that, you're attributing to me the suggestion that observed bond prices could reflect an optimal equilibrium rather than a disequilibrium or a sub-optimal equilibrium?

      "...of economic agents have not relaised..."

      Do you mean to say "...have not been realized.."?

    2. I may be mis-reading you, but I do see this post as an attempt to question the disequilibrium narrative and to forward an 'equilibrium' explanation. Of course, I don't think you imply an optimal equilibrium, so you could be comfortable with both the optimal or the sub-optimal equilibrium explanations.

      Yes, I did mean 'realized'.

    3. Thanks. It's always valuable to hear one's point restated in different language since it provides a different frame of reference, just wanted to double check that I understood you.

      I don't have a great intuitive grasp of disequilibrium vs equilibrium, but given what I do know I think your restatement makes sense.

  7. re: convenience.

    Might it be useful to think of it rather/also in terms of insurance? Steve Randy Waldman has written very nicely about this.

    In my words: the utility people derive from holding financial assets is the insurance against future real risk (not having enough to eat, etc.)

    In short, financial holdings provide protection against the unavoidable existential risk: uncertainty, the inability to predict the future.

    I suppose you could say that convenience and insurance are flip sides of the same coin (can't resist: so to speak), but still they seem to provide importantly different ways of understanding this. FWIW...

    1. The analogy to insurance is a fair one. I'm less interested in how financial assets as a class insure against uncertainty... am more interested in how the "moneyness" quality of any good or asset insures against uncertainty.

    2. Just to confirm: when you say "liquidity" or "moneyness" here (synonymous?), I think it means "can be easily, quickly, and reliably exchanged for bank deposits or physical currency." Right?

      Before replying more, not sure if you've caught my reply to you over at my place: http://www.asymptosis.com/currency-is-equity-equity-is-currency.html/comment-page-1#comment-10133

      Great ideas and discussion here...