Tuesday, June 14, 2016

market liquidity and price discovery

Two consequences associated by convention with market liquidity are a liquidity premium (the asset's price is higher than it would be if it didn't have a liquid market) and market efficiency (in many ways, but I have in mind at the moment price discovery — the price is more indicative of the correct "fundamental" price if the market is liquid than if it's not.  I've spent much of my life in the last couple of years formalizing the idea that the liquidity premium can be negative — if something is consumed regularly and can be stored, people may be willing to pay less if they trust their ability to buy it as they need it than if they worry that the market is unreliable — but it's worth noting a way in which market liquidity can also impede price discovery.

In [1], Camerer and Fehr note that a situation with strategic complementarity is more susceptible to irrational behavior than a situation with strategic substitutes; that is, if our action spaces can be ordered such that each of our best responses is higher the higher are others' actions, then I am likely to worry more about other people's actions than if it is lower the higher are others' actions.  For concreteness, consider a symmetric game in which actions are real numbers and my payoff is -(a-λ<a>)2, where <a> denotes the average of everyone's action and λ is some real number; for λ=1, any outcome in which everyone picks the same action is an equilibrium, and I care deeply what other people are doing, while for λ=0 my best response is 0 independent of what others are doing. For λ=0.9, the only equilibrium is one in which everyone chooses 0, but if I think there's a general bias toward positive numbers, I may be better off choosing a positive number — and thereby contributing to that bias. If λ<0, then if I expect a general bias, I'm better off counteracting that bias; even a relatively small number of agents who are somewhat perceptive to the biases of themselves and others will tend to move the group average close to its equilibrium value.

Now consider an asset with a secondary market; in general the value of an asset to a buyer is the value of holding it for the amout of time the buyer plans to hold it, plus the value of being able to sell it at the time and price at which the buyer expects to sell it.  In a highly liquid financial market, especially one in which a lot of the traders expect to hold their asset for a short period of time, an agent deciding whether or not to buy will base the willingness to pay very sensitively on the price at which the asset is expected to be sold some time later.  If the market becomes less liquid, it makes less sense to buy with the intention of holding for a very short period of time; the value of owning the asset is a larger fraction of the total value of buying it.  λ is still positive, but is much less close to 1; I still care what other people will pay for it when I sell, but at least as a relative matter the value it has to me as I hold it is rather more important.  More to the point, though, I expect the seller to whom I sell it to make a similar calculation; the price at which I am able to sell it will be more dependent on what I expect it to be worth to the next owner to own it, and less on what I think the next seller thinks the seller after that will pay for it.  The cycle in which we care more about 15th order beliefs than direct beliefs in fundamentals is more attenuated the harder the asset is to sell.

It's worth noting that James Tobin suggested a tax in the market for foreign exchange for reasons related to this.

Addendum: Scheinkman and Xiong (2003): "Overconfidence and Speculative Bubbles," Journal of Political Economy, 111(6): 1183--1219 seems to be relevant, too.

[1] Camerer and Fehr (2006): "When does ``Economic Man'' Dominate Social Behavior?," Science, 311: 47 – 52

Monday, June 6, 2016

money illusion and dipping into capital

I think that I use the term "money illusion" somewhat differently from how many writers use it, though I think my use is slightly more appropriate to the ordinary use of those words separately and is a more useful and coherent phenomenon.  In either case, the essential point is that a dollar five years from now is different from a dollar now, and that mistakes can be made by decision-makers who assume otherwise.  One of the ways in which this manifests itself is in a maxim against "dipping into capital", which holds that retirees, endowed non-profits, and those people from Jane Austen novels who "had" an income of so-many-pounds per year unconnected from any employment, should only spend the "income" derived from retirement savings / endowment / whereever that money came from, and never sell down the asset.  There are surely circumstances in which that's a good rule of thumb for boundedly rational agents to avoid worse mistakes, but it seems in part to suppose that one thereby has "the same amount" of capital later as one has initially.  In solving a Ramsey problem with a perfectly liquid instrument of savings, however, there is no distinction between "principal" and "interest", and if a risk-free asset pays an interest rate that varies with time, the optimal solution will typically involve selling some of the asset to increase consumption at certain times and buying more of it at other times to save for later; the exact result will depend on other details, but even if the dollar amount of savings tends to return to some constant dollar amount over long period of time, it is rarely optimal to keep it exactly constant all the time.

A related phenomenon is "reaching for yield": when investors, especially bond investors and often in denial, view the interest rates available on safe investments as insufficient, they may become more inclined to buy the bonds of riskier companies, which tend naturally to pay higher rates of interest, until, of course, they don't.[1]  While this is often done by investors who just seemingly can't really believe that interest rates are as low as they are, and feel entitled to the interest rates that prevailed in the Carter administration, sometimes the people who do this are people drawing a line between "capital" and "income", and looking to turn a higher portion of the expected return into a form that their rules of thumb will allow them to spend.  They would often, perhaps generally, be better off buying a bond with a 3% yield and selling off 1% of their holdings each quarter[2] than buying a bond with a 7% yield so that they don't have to sell it.

This post is loosely triggered by a badly flawed column at wsj.com yesterday; a somewhat more coherent version of its argument, though, is that an environment of low interest rates encourages income investors to buy stocks with higher dividend yields[3] and thereby reduces investment as companies use cash to raise their dividends instead of spending it on research and development.[4]  One of my favored models of a liquidity shock, especially when thinking about things intuitively, is as a suddenly high private discount rate on cash; I suddenly need dollars very urgently, such that putting them off until next month or even perhaps next week is very costly to me in some sense, so that I'll take $1000 now instead of $1100 next week or $1300 next month; in particular, if I have an asset that I think is, in some longer-run sense, worth more than $1100, I might find liquidating it in a hurry at $1000 to be better than whatever consequences would befall me if I spend time trying to find a better price.  More generally, I've treated the ability to sell an asset as giving it some "just in case" value; it's more attractive than an otherwise similar illiquid asset because I don't know whether there will be a liquidity shock.  The ability to sell all at once if necessary, though, and the ability to sell a bit at a time according to a previously anticipated schedule, are likely at least to be closely related, if not, in presence of systemic events, to be exactly the same.

Let's incorporate the "don't dip into capital" mentality by supposing that, even if assets could be sold easily for cash, that the owner won't sell them; they are, if you will, practically illiquid because of the owner's behavioral biases, even though the market exists.  With the realistic incomplete markets, the marginal discount rate of a serviceable amount of cash for most people most of the time is likely to track general interest rates reasonably well; somewhere between what you get from relatively safe savings and the rate at which you could borrow if you needed to.[5]  If it weren't in that range, you'd presumably borrow or save more or less than you do.  If you're intent on putting most of your money into assets that you refuse to sell, though, the private discount rate and the general market rates have considerable room to diverge, and the conditional optimization problem requires that you discount future cash flows at your own, private discount rate — which, if the cash flows tend to be very long term, is likely to be somewhat high.[6]  If dividend yields are low, presumably because the markets think the values of stocks lie more in their payouts in the distant future than their payouts in the next year or two, then if most of your income is from stocks that you refuse to sell, your private valuation of a stock that you're considering buying (and, we suppose, holding forever) should be driven by expected dividends discounted at that private rate — thus valuing higher dividend yields at a higher fraction of their market value than low dividend yields.  The same would apply to bonds; this, then, may be a serviceable "reaching for yield" kind of model to use where we think we have agents of that sort we want to incorporate into our financial/economic model.

[1] Until 30 years ago, the extra interest rates that risky companies paid on their bonds actually did more than make up for the risk of default by a sizeable margin, and a diversified portfolio of such bonds that could absorb losses on a few bonds would more than make up for it in the extra income payments.  That gap generally tightened in the 1980s, and, while it has still been generally positive in the last 25 years, it's more of a strategy that generally gets a reasonable premium for a risk, not a reliable way to secure a high return.  That said, of course some high-yield bonds will in fact make all of their scheduled payments without default, but it shouldn't be forgotten that there's a reason they're trading with a higher yield to maturity than the safer portions of the bond market.

[2] I mean, this is false, and in an important way; corporate bonds are much more expensive to buy and sell than large-cap stocks, for example, and I'll note later in passing how illiquidity might justify the behavior to some degree.  The right approach is probably to buy the 3% bond, but not with all of your money; keep some of your money in shorter-term instruments that mature as you'll need the cash.

[3] Note that here the caveat in the previous footnote has much less force; you can sell down stock holdings somewhat gradually with relatively little in the way of transaction costs.

[4] A bit off topic, but a quick list of problems with the column: 1) it notes that companies are buying back their shares, which runs exactly counter to the idea that they're turning long-run share value into income; holders have to sell their shares to receive the payouts; 2) the corporate sector as a whole is holding a lot of cash on balance sheets right now, even after giving some of it to shareholders; a failure to engage in R&D is not plausibly due to a shortage of cash caused by shareholder payouts; 3) those low interest rates also enable most companies to borrow money cheaply, financing either payouts to shareholders or R&D or both that way, and it isn't reasonable to imagine that higher payouts to confused shareholders are anywhere near the scale needed to cancel out that effect.

[5] This range may be big compared to some things, especially in the short term, but on the scale of years will be at least reasonably well defined.

[6] E.g. if you "have an income" that is safe and expected to grow for decades, you might be motivated to smooth your consumption in time, spending more now and less later, rather than living on beans now and in luxury later, even if you had to pay a somewhat high interest rate in order to borrow to move that consumption sooner.

Thursday, June 2, 2016

prices and appraisals

I'm fond of commenting that assets don't have prices; transactions have prices, and offers to transact have prices, but the best one can hope for in assigning a "price" to an asset is to expect that one can reasonably predict approximately what it will trade for, or would trade for, under some almost true counterfactual.[1]

A judge in Delaware has declared that Dell shareholders whose shares were taken in a leveraged buyout a few years ago were underpaid, and it would be in the spirit of Levine's commentary, though he doesn't quite do so himself, to note that their voting against the buyout at $13.75 per share is prima facie evidence that they valued the shares at a price above that, though possibly for strategic rather than fundamental reasons.[2]  The judge apparently argued that the $13.75 was based on a correct determination of long-run prospects, but that the bidder's cost of equity is higher than the sellers', and he thus calculated a "value" for the shares based on the bidder's assessment of future value and an imputed cost of equity for the sellers.

Let's repeat again that nobody was bidding a higher price than $13.75.  The value of the shares to an individual will depend on that individual's risk-preferences, cost of equity (related to risk-preferences), and assessment of the prospects for the shares;[3] insofar as an effective market mechanism gets the shares to their highest-valued owner, the market price would be the highest value that any owner, given those criteria, places on the shares.  As Levine notes,
This buyout didn't create value by changing Dell's business model; it created value by changing Dell's ownership -- by moving the shares from people who mostly didn't value them that highly (public markets) to people who did (private-equity buyers).
Some potential buyers may have a lower cost of equity (and thus would put a higher value on it), but a lower assessment of the prospects, or a lower ability to handle some idiosyncratic risks associated with them; others might have higher assessments or better risk-profiles to take on the risks but a higher cost of equity.  The judge seems to have hypothesized a non-existent bidder with the combined attributes that would maximize the value, without regard for the fact that the bidder is, in fact, non-existent.

I'm not sure that some kind of judicial overruling of a take-over price is never warranted, but it seems to me that procedural protections are on much firmer philosophical ground; the fact that there were a couple of apparently independent bids, and that the winning bidder here seems to have been assiduously fair in the process of securing the votes of the majority of shareholders, should in this case have been dispositive.  Especially insofar as the buyer's control affects its prospects,[4] "you have to pay what someone who doesn't exist would pay to buy a company you control" just doesn't make any sense.

[1] In particular, there's a legal dictum that "a fair price is what a willing buyer would pay a willing seller", which is sensible insofar as it has content, but that's not very insofar; the dictum is typically applied where there isn't both a willing buyer and a willing seller, at least not at the same price, and the price at which a hypothetical willing buyer and willing seller would trade depends entirely on why they are willing to buy and sell. The dictum might, therefore, be occasionally useful in framing analysis, but it never really contributes very much toward determining what a "fair price" ought to be.

[2] This is the classic hold-up problem, which eminent domain and buy-out procedures are supposed to mitigate; it's worth noting, perhaps here, that this judicial appraisal procedure itself is among the counter-protections in the buy-out process.

[3] It perhaps gets too confusing to note here that the "prospects for the shares" in fact consisted of their being bought by Dell at a price that would be overruled three years later by a Delaware judge.

[4] Though this appears in at least some sense not to have been a big part of this deal, the arguments about short-termism and R&D belie that at least somewhat.

Wednesday, June 1, 2016

financing illiquid assets

I remember, many many years ago, being surprised to learn that the credit rating of a mortgage borrower was as important to underwriters as it was;[1] the loan, after all, is secured by an asset worth 25% more than the loan,[2] and it seemed to me that the focus would be on verifying the value of the asset, conditional on which it wouldn't really matter all that much if the borrower defaulted.  The problem is, even in what I'm going to date myself by calling "normal times", seizing collateral and selling it is a real nuisance, and is not what banks specialize in; they welcome the backstop, sure, but not least because it strengthens the borrower's interest in repaying the loan.  The bank really just wants a borrower who's going to repay the debt.

Matt Levine recently commented that the very essence of collateralized lending is lending against illiquid assets — viz. assets that would be annoying to repossess and sell; for liquid assets, the owner can raise funds by selling the asset.  This comment is more surprising to me than it is wrong, which is not to say that it isn't at least frequently somewhat wrong, starting with the housing market, where the whole point of your garden-variety mortgage is that you want to own the asset, and not that you have some other need for funds for which you might prefer to temporarily liquidate it.  What he had in mind is the banking industry; both banks with abstract assets and other large companies with physical capital frequently use somewhat illiquid assets as collateral where, in an idealized world of perfect markets and divisible assets they might sell off a third of a factory and buy it back when they no longer needed the cash.[3]  Some of the models I've played with emphasize the extent to which an asset's value increases because it can be sold — because of its market liquidity — but notwithstanding some literature on the extent to which assets gain value because they can be used as collateral,[4] I maybe haven't appreciated enough the extent to which the ability to sell an object and the ability to use it as collateral can substitute for each other.

[1] This is before it wasn't, before it now is again.

[2] Again, back when people put down 20%, at least for the mortgage loans under discussion here.

[3] In fact, the most frequent use of "collateralized borrowing" in finance actually tends to use very liquid collateral, but are not in fact legally "collateralized borrowing" at all; they are the sale of an asset and simultaneous agreement to buy it back shortly thereafter.

[4] The clear example is Kiyotaki and Moore (1997): "Credit Cycles," Journal of Political Economy, 105(2): 211--48, though Geanakoplos has a whole oeuvre that hovers closely around this, and Gary Gorton is probably worth mentioning, too.