Friday, October 10, 2014

a game theory example

Recording here as much as anything for my further reference an example by Viossat (2008), who credits it to Eilon Solan, who adapted it from Flesch et al (1997):

W
LR
T1,1,10,1,1
B1,1,01,0,1
E
LR
T1,0,1-x1,1,0
B0,1,10,0,0


I have not verified this for myself, but allegedly (for x≥0)
  • If x=0, TLW is the only Nash equilibrium; it is not quasi-strict.
  • Any strategy profile in which players 2 and 3 play L and W and and player 1 plays T with probability of at least 1/(1+x) is a Nash equilibrium.
For x=0, aside from action profile TLW, player 1 gets payoff 0 for matching player 3 and 1 otherwise; similarly 2 wants not to match 1 and 3 wants not to match 2.

Wednesday, October 8, 2014

dispersed information, intermediation, and communication

Intermediation is crucial to a modern economy, but it also creates a lot of principal-agent problems. Some of these are well modeled and studied, but some that, to my knowledge, are not are related to the ease with which some kinds of information can be conveyed relative to other kinds of information; where relevant information is predominantly quantifiable, at least some of the problems that are created and/or solved by intermediation are comparatively minor, whereas when relevant information is effectively tacit, it will often become a large friction in making things work.

To be more concrete, there is a recent story about Ben Bernanke's being unable to refinance his mortgage, and the LA Times says he probably could if went to a lender who meant to keep the loan, as opposed to a lender who wanted to pass it along to other investors in a security.  If you're trying to make a lot of loans on a small capital base, you have to keep selling off old loans in order to get the money to lend to new borrowers, but the people buying the loans may not fully trust your underwriting; on the other hand, the purpose of the intermediation is that the people with the money don't have to go to all of the expense associated with doing a full underwriting themselves.  What's left is to look at a set of easily communicated information about the loan, preferably something that can be turned into a small set of meaningful statistics about a pool of loans.  This means that, even more than in a market where all underwriters were holding their loans until maturity, your ability to get a loan will depend on the information that can be easily gathered and communicated, and less on qualitative and less concrete information.

In an economy in which some agents are good at doing underwriting and other agents have capital to invest, it seems like a good equilibrium would be one in which the underwriters can develop and maintain a reputation such that "This security was underwritten by Jens Corp, which gives it a rating of BB+" or some such; the rating provided by the underwriter incorporates the unquantifiable information and makes it (in some sense) quantitative.*  Note here that I'm asking the issuing agent itself to provide a rating; if an outside credit agency is to provide a rating accounting for all of the information that was put into underwriting the loans, that agency would have to either do all of the underwriting work over again, rely on the issuer's reputation in the same way I'm proposing investors could, or rely again on quantitative metrics.  Ten years ago credit agencies had chosen the last of these three options, and issuers gradually figured out to sell off loans with bad qualitative characteristics and good metrics that fit the credit agencies' bills.  This ultimately is the bias I'm trying to avoid.

There might be some value to having a rating agency that knows the reputation of a number of small shops and can, in some manner, pass that along to investors, but that, too, will depend on an equilibrium in which the issuing financial company is issuing a credible indicator of the quality of the loans.  Even if a financial company could get to that equilibrium, somehow developing this reputation through a history of responsible issuing and pronouncements, maintaining the reputation may depend on outside observers' believing that the company's management and culture and future interests promote its maintaining that reputation, i.e. that the company and its agents will at every stage find it less valuable to sell a set of bad loans for a high price than to maintain its ability in the future to sell a set of good but hard-to-verify loans for a high price; this requires that a disciplined underwriter would expect to maintain a certain amount of business by being able to find a sufficient stream of people who are hard-to-identify good credit risks.  I like to think this could happen, but I'm not sure it's the case.

* It may well be that the most plausible world in which this could come about would be one in which the information conveyed would be effectively multi-dimensional; rather than just "these loans have approximately this likelihood of default", you might convey "the loans have approximately this likelihood of default under each of the following macroeconomic scenarios:", etc. In an age of computers, it might even be acceptable to have something that seems, to humans, fairly complex, as long as it can be readily processed by computers in the right ways; it is worth noting, though, that higher complexity may make it harder to verify, even after the fact, which might hurt reputation building. If I sell off 100 loans and say that each has a 5% chance of default, and maybe 3–7 of them default, that seems about right, and I manage to do it several more times, and it can be noted that my assertions seem to be borne out by experience, but if I say 10 of them are in this bucket, and another 10 are in a different bucket, and so on, then, while overall levels of default can still be verified, it becomes harder to verify that each separate bucket is right, and I think that the opportunity to lie about one tenth of my portfolio, while still (perhaps?) keeping my reputation fairly intact on certain kinds of loans, give me more incentives to attempt to liquidate parts of my reputation and make it more likely for an equilibrium to collapse. The extent to which this is a concern is going to come down to how credible "I guess I'm just not good at underwriting X kind of loan anymore, but we're still doing great at everything else!" is, and how many times I can do it before nobody takes me seriously anymore.

Monday, September 29, 2014

interactions and evolution

I've been thinking for a while that it might be possible for a gene that never has a (narrowly construed) positive effect on evolutionary fitness might be (in the long run) beneficial if it imposed a larger evolutionary load on phenotypes that were, in the long-run, kind of in trouble anyway, by hastening to get them out of the way. I still haven't actually put together a solid model that would make this compelling, but I've just discovered Wynne-Edwards, who at least suggested that individual organisms might sacrifice their own survival to benefit a group, especially a kin group; he was building off of work by a guy named Kalela who wrote about voles or shrews suppressing their own fertility when the group was running against the local ecosystem's carrying capacity. At least as I understand it from a second-hand telling by E.O. Wilson.

Tuesday, September 2, 2014

liquidity

I've asked here before, "What is liquidity?", if not literally then sort of metaphorically or something. Or maybe I haven't; who knows? Anyway, I think one of the problems is that, like "infinity", the term "liquidity" is used to refer to a few different related but quite distinct things. When we refer to a corporate (especially bank) balance sheet, though, we're referring to the exposure of a bank to sudden, unexpected obligations and its ability to handle them. In particular, suppose our bank has, by any reasonable estimation, an ability in the long run to meet all of its liabilities, but has maybe $50 in cash on hand, and you have a few hundred dollars in an account and the contractual right to go up and try to withdraw $100. This bank's liquidity would be characterized as "Not good."  On some level, a company that has a $100 loan maturing today and expects to be able to roll it over (i.e. borrow the $100 from someone else to pay the old loan) is in the same position; perhaps in a well-functioning financial market they should be able to do that, and are thus in the long-run "solvent", but if something goes awry they find themselves in breach of some obligation.

So let's compare Matt Levine's description of Lending Club; it appears that Lending Club, with (by the relevant accounting rules) a very high leverage ratio, has little if any liquidity exposure; its contracts are written in such a way that it only owes a creditor money as long as a debtor pays it that money.  While this may, as he says in footnote 6, leave them with a business risk, it leaves them without a risk that they will suddenly have to meet the sort of legal contractual obligation that a bank intermediating lending would have.

Five to ten years ago — and maybe today, but I'm less well-connected now — a lot of hedge funds were making money on liquidity premiums, deliberately buying things like wind farms that were somewhat likely to be profitable but couldn't be sold as quickly as (say) IBM stock if a sudden need for cash arose.  Wind farms are actually a specific example I remember being presented to me of an illiquid asset that was owned by a financial company; if that company had a contractual obligation (possibly requiring a creditor to trigger it, e.g. by showing up at a teller window) to provide dollars on a moment's notice, the wind-farm may be a good asset for the long-run but it won't provide liquidity protection from that event.  If the company had a contractual obligation to provide, say, good title to a wind farm at a moment's notice, all of a sudden this looks like a great asset from a liquidity standpoint; better (at least from the standpoint of that (weird) risk) than cash.

That isn't meant to be entirely* fatuous; certainly traders of derivatives for physical delivery (e.g. oil futures) occasionally find themselves in analogous positions. If the world foreign exchange market were in turmoil, a dollar balance might be useless to fund an obligation in rubles, even if there were some objective sense in which, at any reasonable exchange rate, it would be high enough to cover the debt. What it does mean is that "funding liquidity", which is more or less what we're discussing, is about matching assets and liabilities in a way that is much more general than maturity matching in general, and that to the extent that it is, in practice, something that can be captured usefully in a low-dimensional way, that fact is phenomenological and not theoretically fundamental.


* Only mostly.

Saturday, August 2, 2014

productivity and labor compensation

This post will be much more practically oriented than most of this blog, and a premium is placed on brevity.

It is occasionally noted (though often obscuring important details) that
  • cash income
  • per household
  • deflated with consumer prices (especially if badly chained)
has, in my lifetime, lagged badly behind
  • economic production
  • per hour worked
  • deflated with the GDP deflator
in the United States.  Especially through 2008, almost all of this is because of
  • an increasing portion of labor compensation becoming "in-kind", in part for tax reasons,
  • decreasing household size, and
  • chaining effects and increasing prices of imports relative to exports.
Our worsening terms of trade are certainly interesting, and a reasonable target for policy attention, but most sources that compare the first series to the second series try to imply that the difference means something very different from what it does.

Now, in the last five years labor compensation has lagged behind production in common units of account; this is frequently true early in the business cycle, and the "beginning" of this business cycle has been frustratingly longer than usual, but it's premature to diagnose a secular shift.

Monday, July 7, 2014

the value of markets

One of my favorite financial writers writes:
The job of equity markets is to provide liquidity and price discovery. An efficient market will provide liquidity at a very low cost, and will adjust prices very quickly to respond to changes in demand.
He goes on to mostly ignore the tension between the two.

Suppose you own a large block of stock and decide to sell it to build a deck on the back of your house.  What should a well-functioning market do?  I think most people in the field would say that a perfect market — in particular, a very liquid one — will allow you to sell it all quickly for very close to its current price.  The purpose of the market, after all, is to allow you to buy and sell stocks when you want to, ideally in a cheap and efficient manner.

Now suppose you own a large block of stock and decide to sell it because you've found out that the CEO is laundering money for a drug cartel and most of the reported "profits" of the company are fraudulent.  What should a well-functioning market do?  I think most people in the field would say that a perfect market — in particular, one that is doing its price-discovery job well — should drop precipitously, incorporating the information that your trade conveys about the value of the stock into its price even before you finish trading — such that the last few shares you sell will be at a substantial discount to the earlier, less informed price.

Finally, suppose you own a large block of stock and decide to sell it.  What should a well-functioning market do?  Well, ideally it would know why you're selling.  In practice the best you might expect is that some of the market participants to eventually get a sense of whether certain kinds of trades (placed at certain times of day, in certain size, perhaps in sequences of orders that seem connected to each other) are more likely to indicate that the price is too high than other kinds of trades, which mostly just mean that somebody lacks a back deck and wants one.  If it gets pretty good at this, you might even hear the guy who got the scoop on the CEO's corruption complain about the "lack of liquidity" in the market; he might even badly abuse the term "front running".  For more on that, go read Levine's column.

There is one more important wrinkle to add here, which is time-horizon.  Suppose we're talking about a small cap stock that trades 50,000 shares a day, and you're trying to sell 100,000 shares (for deck-like reasons).  You decide to break it up into smaller orders to sell over the course of two weeks.  After you sell 10,000 shares the first day and 10,000 shares the next day, traders in the stock (such as there are) figure out that there's probably a bunch more sell orders coming over the next several days.  Is that information about the value of the stock or isn't it?

Well, ideally again, perhaps someone would step in and do a block trade with you at (close to) the initial price.  Insofar as the market isn't likely to be perfectly liquid, though, your trade can be expected to lower the price at least a bit, at least for a while. A trader with a time-horizon of months will regard this as a temporary "liquidation" that doesn't really concern the long-term (even months-long) value of the stock, but to a trader with a time-horizon of a day or two, "something's going to push the price down over the next day or two" is as informative as information comes.

So at this point the approximately ideal market with some first-order approximation of reality layered onto it probably drops a little bit for now, with the common expectation that it will bounce back in the next month or two, with the drop at such a size that some extra buyers are willing to come in and in some aggregate sense spread the sale out over the next few months, making a bit of extra profit on the deal, but small enough (and with a small enough expected attendant rebound) that you're willing to forego that "bit of extra profit" in order to get your hands on the cash now.  On some level, perhaps you might as well call up Goldman Sachs and pay them the fee for doing a block trade with you.

Tuesday, June 17, 2014

instruments of Fed policy

If the fed raised the reserve requirement (not now; under the sort of circumstances that we persist in calling "normal" more than five years since they were last seen), that should steepen the yield curve as long-term credit becomes scarcer relative to the supply of demand deposits and other short-term highly liquid investment. In periods historically where the yield curve becomes inverted I imagine some benefit might have been derived from somewhat tighter constraints, and where it's steepest perhaps somewhat looser; perhaps it would make sense to change reserve requirements in tandem with a target for the steepness of the yield curve.

The tl;dr version of the previous post is that, in the short term — on the order of an eighth of a year — the FOMC is likely to continue to ask the New York Fed to aim at something that is readily monitored in something like real-time, and it seems like the difference between long-term rates and short-term rates is a better target over that kind of period than short-term rates alone; in particular, if long-term rates go up over the weeks after an FOMC meeting, presumably that means the market has come to believe that inflation and/or returns to sunk capital will be higher than was believed at the last meeting and a somewhat high short-term rate is appropriate.

So I'm now suggesting that the FOMC set a target for the steepness of the yield curve, and, just as it customarily used to change the deposit rate in lockstep with the FOMC federal funds target, the board of governors would then customarily change the required deposit ratio in lockstep with the target for the steepness of the yield curve. There are clearer reasons for deviating from this from time to time than was the case with the deposit rate, and I'm not denying the board of governors the ability to do that, but rather than "leave them unchanged" as the default, I would suggest something slightly procyclical as the default instead.