Facebook's stablecoin and interest

Per Matt Levine, Facebook is setting up a cryptocurrency backed by a variety of low-risk assets, but they're not stabilizing it the way I would.

Users of Libra do not receive a return from the reserve. The reserve will be invested in low-risk assets that will yield interest over time. The revenue from this interest will first go to support the operating expenses of the association — to fund investments in the growth and development of the ecosystem, grants to nonprofit and multilateral organizations, engineering research, etc. Once that is covered, part of the remaining returns will go to pay dividends to early investors in the Libra Investment Token for their initial contributions.

If one were to use Libra as a unit of account, and ask what the "risk-free" interest rate in Libra would be, the answer should be more or less equal to the average return on the assets being used to back it.  I would propose that instead they retain all returns in the reserve, take out a fixed fee (say 2% per year) to manage the ecosystem and pay out returns to investors, and allow the value of the coin to follow the pro-rata share of the reserve.  This fixes the "risk-free" interest rate for Libra at 2% — if it takes off and becomes a significant unit of account for long-term transactions, this will increase its suitability for that purpose by eliminating interest rate risk.  In particular, even if some of the currencies in the basket start to hyperinflate badly, and their interest rates go way up, the coin remains stable in a more absolute sense, and the rate at which it depreciates compared to risk-free investments is relatively unaffected.

Note 1:  I would like to see a fixed interest rate; I use 2% in the example, but another number might be better.  It should be high enough that the costs are covered, which might be a tricky number to come up with if those costs don't scale linearly with the size of the pool; probably you should pick a conservative size and expect that the early backers may have to subsidize it while it's small.  Conditional on its being "large enough", though, I'd rather it be as small as possible, though of course my money's not on the line here.

Note 2:  If the interest rate is close to 0, and you're in a society in which "interest" is repugnant, then denominating transactions in this currency allows you to avoid the problems this creates for positive interest currencies.  This note highlights that "interest" isn't some absolute economic phenomenon; it's a property of the unit of account, and in particular of its failure over time to capture the true market rate at which value at different points of time are being traded.

urbanization and land value

Suppose land has two uses, urban and farming, and that some land is more suitable than other land for cultivation, but the only thing that determines suitability for urban use is proximity to other urban land.  Suppose there's a single city in the middle of our universe that is growing at some exogenous rate; farming land right next to urban land is presumably worth more than similar land farther away, but I would strongly guess that fertile land next to the city is worth at least as much as infertile land next to the city.  If your land is 10 miles away, though, your land is going to be worth more if the land in between your land and the city is infertile than if it's fertile.  With some kind of spatial correlation in fertility, there's probably some distance away from the city where land value correlates negatively with fertility.

national debt

In the past couple of years, politics seems largely to have given up on the idea that the federal deficit is of any importance; some people go so far as to actively say that it doesn't matter.  There is some truth to the statement that the budget constraint is a bit different for a government than for an individual, but I do believe that it represents some kind of (fuzzy) constraint, with some kind of attendant (hard-to-price) cost associated with incurring more debt.  Right now, though, I want to think about it from a different angle than the idea that, at some point, we would be unable to borrow more money or buy goods with the money we can print.

For a closed economy, total savings equals investment; investment in new capital is one of the important factors in the long-run increase in real wages.  With an open economy, people from other countries can invest in US capital as well, so we get an accounting identity

federal deficit + investment = private savings + trade deficit

If the federal deficit were to come down, investment would go up, or private savings would go down, or the trade deficit would go down.  What I'm wondering is how much of each would be likely to happen?

Presumably it depends on the details -- at the coarsest level, a tax hike would probably have a different effect than a spending cut, and it seems likely to matter which tax you hike or which spending you cut.  It seems like we ought to be able to say something useful about a general tendency, though, perhaps with caveats.  Twentieth century macroeconomics would suppose that this is intermediated through interest rates, and would probably expect all three to absorb some of the change, with the portion depending on how sensitive investment, private consumption/savings decisions, and foreign trade partners (including foreign exchange markets) were to interest rates.  The identity holds regardless of mechanism, though, and interest rates don't seem to have been obviously responsive to government deficits; perhaps more importantly, I don't think the people who deny any meaning to the deficit could be persuaded by this mechanism.  The identity itself, however, is pure arithmetic.  Something must give.

So what happens when the government gives a bunch of money to a group of people, whether in exchange for goods or services or not?  In the latter case, those goods or services and/or the scarce resources that went into their production are no longer available; a Keynesian might believe that some nonscarce resource is being newly employed, in which case that's not a factor.  If you're removing a consumer good from the market and prices aren't changing, it seems that you're forcing private savings or the trade deficit to change; if you're removing more of a capital good, perhaps you expect investment or the trade deficit to change.  If you hand out the cash and it doesn't go anywhere, private savings is what automatically absorbs it at the first instance, but it seems likely that a lot of it would quickly go to investment or trade deficit.

While correlation is, of course, not causation, if I really wanted to pursue this a first thing to do would probably be to look at data on these four variables and see both which linear combinations change the most and what the time behavior looks like over the course of a year or two.  I would think that the federal deficit is the most exogenous of the four, and that interpreting the correlations as exhibiting the causal effect of federal deficits would be a good first pass, but I would hope more generally that some regularity would suggest a next step in the investigation.

batch auctions with liquidity sale type

One of the less celebrated problems with this blog is that it doesn't know what its audience is; sometimes I assume very little background knowledge, and sometimes I assume quite a bit, and sometimes I assume knowledge of some arcane or advanced concepts and yet explain basic ones in the same post. This post could be written in a number of different ways; I'm going to assume I can talk about "convexity" in high-dimensional Euclidean spaces, but will define "Minkowski sum", but will only allude, and only in this very sentence, to the large expanse of follow-on ideas that can be pursued by those who know what support functions are.

There has been talk for many years about replacing the continuous double auction of the stock market with frequent batch auctions; orders to buy or sell would be accumulated over the course of five minutes, a price set to clear the market, the executable trades at that price executing against each other. The New York Stock Exchange does this twice a day — at the beginning and end of the trading day — and I have in the recesses of my head the notion that there was an ECN 15–20 years ago that in fact did frequent auctions of the sort I'm going to build to, and maybe they used some of the math I've redeveloped to do it. Perhaps they did so without glossing over a problem I'm going to gloss over: I'm going to assume that shares and money are arbitrarily divisible, so that if you ask to buy 100 shares for no more than $5,000, I'm allowed to have you buy 33.2 shares for $1,565.1934 (because that's less than $50 per share times 33.2 shares).

So here's a mathematical way of representing the problem: let x be the number of shares of the stock I want to sell, and y the number of dollars I want for those shares; if I'm trying to buy, these numbers are negative. I'm going to represent the order as a (straight) line segment connecting the origin to this point (x,y). If I take all of the orders, I can construct the Minkowski sum of the corresponding line segments, which is the set of points in the x-y plane that can be achieved by taking one point on each line segment and adding them together. (For example, if I have two line segments that are not parallel, the result will be a parallelogram.) For any point in the Minkowski sum, then, I have an x-coordinate and a y-coordinate, and they correspond to some[1] set of executions[2] of the various trades, with the x-coordinate corresponding to the total (net) number of shares sold, and the y-coordinate to the minimum number of dollars demanded in exchange for that number of shares. In particular, points in the Minkowski sum of the orders — we'll call this set M — for which the x-coordinate is 0 represent combinations of executions that clear the market — the same number of shares are bought as sold — and points in M for which x is 0 and y is negative represent such combinations that clear the market and allow at least some of the market participants to get a better price than they had insisted on.[3] We are especially interested in the point in M with x=0 and the smallest possible value of y; we are also interested in the slope of the boundary of M there.[4] It turns out that this slope is the "correct" price to use; anyone who wants to buy at a higher price or sell at a lower price can trade the full amount of their order at that price, while those orders with that exact per-share price may be filled, not filled, or partially filled in order to make sure that the net number of shares traded is 0.

Now, the slightly more interesting thing I might want to do — and, again, I think there was an ECN doing this at the turn of the millennium — is say "I'd like to buy 100 shares of ABC minus 50 shares of XYZ for up to $2,000, but am only willing to trade insofar as I get them in that 2:-1 ratio."[5] Now we have two kinds of shares, and we have line segments in a three-dimensional space: one dimension for each kind of stock (x₁ and x₂, say), and one for money (still y). Minkowski sums can be constructed as well in three dimensions as in two, and now we're looking for the smallest y such that x₁=x₂=0 and the "slope" there is now two slopes,[6] and we thus get prices for both stocks, but with orders of this sort in the mix, they aren't independent of each other; they have to be calculated jointly.[7]

Well, here's an idea I've had that I don't think was in that ECN, possibly for good reason. One problem with infrequent batch auctions would be how brokers and shareholders would handle margin calls; if the value of my portfolio drops enough in an auction to trigger a margin call, such that I'm compelled to sell stock, which stock I sell may depend on the stocks' price. To the extent that the previous auction's results are likely to be similar to the next one's, there may be a clear choice, but it struck me as interesting and perhaps possible to allow trades of the form, "sell whichever of (list of five baskets of stocks) has the highest price"; in fact, I can include a limit price, such that I don't sell any of them if the price is below a certain level.[8] The order is no longer a line segment; it is now a simplex[9] with six vertices, one at the origin and one at (basket,limit price) for each basket. The rest, perhaps surprisingly, goes through as before; the slope of the boundary of the Minkowski sum at the point at which the markets clear most profitably will set the prices of the stocks and (therefore) of the baskets.[10]

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[1] not necessarily unique

[2] Or partial executions, or non-executions; some fraction between 0 and 1 of the trade has executed.

[3] Note that the origin is in each line segment, and thus is also in the Minkowski sum; we can always choose not to execute any orders, and thus no shares will be bought and no shares sold.

[4] It will always be possible to draw a line that intersects M at this point in such a way that no point in M lies below the line. If M has a vertex at that point, then there may be several such lines, in which case you're welcome, as far as I currently care, to pick any of them, and suppose that the slope to which I refer is the slope of that line.

[5] A possibly interesting special case would have a limit price of 0; "I'll swap my 50 shares of XYZ for 100 shares of ABC (but am unwilling to put in dollars to do it)."

[6] With, perhaps, a whole suite of planes such that M dips below none of them, but intersect all of them at (0,0,y); again, there is at least one such plane, and if there are more, any is suitable, and has a slope in the x₁ direction as well as in the x₂ direction.

[7] For example, if the price of ABC is low enough that my order fully executes, then I'm selling XYZ shares, perhaps pushing down their price; on the other hand, if a bunch of orders to buy ABC come in and push the price high enough that my order doesn't execute, that may then require a higher price for XYZ in order for that market to clear.

[8] This "limit" order may be less motivated by the notion of a margin call than other kinds of liquidity shocks; perhaps I have some valuable use for $5000, and would like to get it from whichever of these combinations of stocks allows it, but if the prices of the stocks are sufficiently low I'd rather just hang onto them.

[9] For what I'm writing here, I suppose that the five baskets are "linearly independent"; I can't think of a reason this limitation would chafe anyone.

[10] If the highest-value basket has a value exactly equal to the limit price, you might get a partial fill, and if two or more of the proffered baskets have the same value (higher than the others and the limit price), then you may end up executing a convex combination of those baskets.

costly signalling

Thinking about basics again, and it seems like a framework for the basics of costly signalling that is slightly more general than the average textbook version might be of some value.

The basics that an agent has some piece of information that it would like to credibly communicate, and has available a set of possible actions, some of which would directly lead to a lower payoff, but especially if the piece of information were false; as long as my gain from being believed exceeds the cost if my message is true, but is less than the cost if my message is false, then I can credibly and profitably use those actions to communicate my information so that other agents will behave in a way that helps me recoup my signaling cost.[1]

There are a variety of things I might like to incorporate into this, and what I'm particularly contemplating right now is something mechanism designish: if a designer can change the set of actions available and/or their costs, which such changes will improve welfare?  I think that the most interesting thing to note that requires a moment's thought but not a deep analysis is that, while reducing the costs of signalling seems like a good idea, everything falls apart if it becomes cheap to signal the information when it's false — unless the reduction in cost fully compensates you for being unable to communicate credibly, at least.  The clearest beneficial case, then, would be one in which you can make signalling cheaper when it's true, but without reducing the cost of sending a false signal.

I might want the information to be continuous, or at least richer than binary.  In that case, you're likely to get "partially pooling equilibria", such that if the agent wants it to be believed that a parameter is large, the agent behaves with some randomness, with some overlap in behavior between situations in which the parameter is small and when it's in-between, ultimately leading observers to make a higher guess for the value of the parameter when they see a "higher value" sort of signal, but not putting full confidence in it.  The mechanism designer then is likely to face a choice in which a lower cost of signalling in general makes the signals less informative, resulting in some knock-on inefficiency that has to be weighed against the direct cost.

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[1] You could also have the cost of signalling be the same, regardless of truth, but the benefits of being believed higher when it's true; again, the sign of the net benefit should be positive if it's true and negative if it's false.

finance conventions

I've asserted at various times that finance is easy, so they have to invent strange conventions to make it hard.[1]  In his Tuesday column, Matt Levine gave an example, sort of:

The difference is that if you buy a $100 Venezuela 9.25 percent bond a day before the semiannual interest payment is due, and the price is $20, then if it trades clean you pay the seller $20 for the bond plus like $4.60 of accrued interest, while if it trades flat you just pay the seller the $20.

This is correct in some sense, but the emphasis is not what I think a person not steeped in finance conventions would find natural; the way I would put it is

The difference is that if you buy a $100 Venezuela 9.25 percent bond a day before the semiannual interest payment is due, and you want to agree to a price of like $24.60, then if it trades clean you call the price $20 with like $4.60 of accrued interest, while if it trades flat you just call the price $24.60.

The effect of "accrued interest" is to smooth out price drops; for a bond trading at par, the day before a $2 payment, you'll pay $102 (more or less), while the next day you'll pay $100 (because you aren't getting the $2 payment, the seller is), and if it trades "clean" then, by convention, you call it $100 on both days. Stock traders just accept that the day a stock goes "ex-dividend" the price drops, and I think in a day when traders are sitting in front of computers, it's more straightforward to call the price the price instead of adopting weird rules to make it seem to behave differently from how it actually does.

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[1] The hardest parts of finance, though, are law.  Conventions are second.

information and interaction

A point that I've made, but that has perhaps been better illustrated by Borges, is that extra information is less information; if you have 4MB of data, from which you need to find the 1k you want, you have, on some level, less information than if you just had the 1k.  (Maybe 12 bits less?  I don't know.)  As a related matter, if I need information from you, we may well be able to transmit it efficiently if we can go back and forth a bit than if not.  If I send one of 2ⁿ messages indicating a broad category, and you respond with one of 2^m responses to help me clarify my next request, and that request is l bits, and the final answer is k bits, then we've exchanged a total of n+m+l+k bits; if I had to send a single request, I would need to send l bits for each of the 2^m responses you might send to my initial message (plus perhaps the n bits as well); my request is 2^ml bits, which is huge. If you know I need the information, but have to send it without my request, that's 2^2mlk bits you have to send me to make sure I get what I want.

I kind of got to thinking about this in the context of the Mars rover, for which two-way communication is possible, but with latency.  If the latency doubles, to the extent that analogues for n and l are appreciable, you've basically just halved the rate of information transmission; the ability to recover from that latency by transmitting extra information on spec is basically negligible.