Flight to Quality

Every time I hear that bond investors are flocking to quality, and that quality = lending to the U.S. government, I think the following:

• what’s so high quality about U.S. government debt?
• is this really just because business schools use Treasury’s as the canonical example of a “risk-free” asset?
• what’s a “good” debt-to-income ratio for a government, anyway?

The U.S. economy is big

The U.S. produces roughly $10 trillion worth of goods and services per year, and its government can tax that — to a degree. But other countries also can tax their citizens. And if you added together some smaller countries you could find another $10 trillion of taxable income. (Governments can tax old assets too, like real estate.)

If you’re not a giant fund looking to plunk all your money in one place, you could lend money to 5000 municipalities or cities or something, and is California really any more interested in defaulting than the U.S.? And California is like the world’s 4th largest economy, if you broke it off from the rest of the States. Not only that, but “diversification” is the buzzword for panacea in finance.

“I’ll believe in whatever they believe in”

I get that, like, people think the US Government won’t default on its debt. Partially that’s due to a feedback loop—so many people believe it to be the case that the government can cheaply borrow to cheaply pay back the current debts with cheap future money. After the “financial meltdown” people and institutions from all over the world were shoveling so much money into the Treasury’s coffers that the government would have been stupid to turn them away. This when Uncle Sam was spending, what, $2 trillion on the bailout?

But a feedback loop the other way — a sudden loss of trust — could cause Uncle Sam’s lenders to jack up the API on his credit card, and each dollar of interest might spike to $1.05, $1.15, $1.25, who knows. The laws of calculus would no longer apply, i.e., small changes might become huge jumps and suddenly the default looks a lot more attractive — thus raising the interest due even more.

_Why?

Really, I don’t get it. I have never invested in a bond in my life. I have never analyzed a municipality’s balance sheet, a county’s, a state’s, or a country’s. I’m not even sure if I should be writing Treasuries, Treasurys, or Treasury’s. But still I wonder, why do people consider an investment in U.S. Treasurys to be risk-free?

This really puts my mind at ease as far as whether it’s an economically doomed strategy to pursue quantitative finance:

The Efficient Markets Hypothesis is neither necessary nor sufficient for the Random Walk Hypothesis.

Apparently the Cowles Commission was the first to discover a Gaussian pattern in stock market returns—and its members thought it was proof that financial markets are irrational.  Later on, Paul Samuelson established the connection between EMH, greed, arbitrageurs, and random walks of the price of a publicly traded stock.  (Benoit Mandelbrot figures into this story too.)

Anyway, Eugene Fama eventually coined the phrase “Prices fully reflect all available information” which is the story I got in Economics 101.  But like most bite-sized wisdom, apparently it’s more complicated than that.  (Phew, said the hedge fund investor.)

(Source: http://www.amazon.com/gp/product/0691092567?ie=UTF8&tag=hiremebecauim-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0691092567)

Leverage & Derivatives

Derivatives contracts allow you to make bets on an asset without owning it. Like a side bet. I don’t have to own, watch, or like the Dallas Cowboys to bet on their success / failure.

You can bet on a company by buying its stock, or you can bet someone that it will go up. The latter is a derivative contract. Today the $$$ value of side bets exceeds the trading in original securities by a factor of 40.

For example there is $800 million worth of wheat (3 million metric tonnes) in the world — or at least that’s this year’s production of hard red winter wheat #1, ordinary protein.

But on the Chicago Board of Trade alone there were 22 million bets this year, betting about those 3 million MT.

Supposedly there are $1 quadrillion worth of derivatives contracts being traded today.

People talk about it like it’s a bad thing — but it’s neither good nor bad, by itself. It’s scary for regulators because they can barely measure, much less control, what people are doing with their money. They worry about systemic collapse on the one hand, if people make correlated mistakes — but on the other hand, if they over-regulate then they will choke off freedom of property.

Highly Nontrivial

Only a mathematician would say something is “highly nontrivial” rather than just plain “difficult”.  And it’s surprising how many people actually say “highly nontrivial”, which doesn’t make any more grammatical sense than “extremely unpregnant”.  Get a grip, guys.

Bilinear maps and dual spaces

Think of a function that takes two inputs and gives one output. The + operator is like that. 9+10=19 or, if you prefer to be computer-y about it, plus(9, 10) returns 19.

So is the relation “the degree to which X loves Y”. Takes as inputs two people and returns the degree to which the first loves the second. Not necessarily symmetrical! I.e. love(A→B) ≠ love(B→A). * It can get quite dramatic.

An operator could also take three or four inputs.  The vanilla Black-Scholes price of a call option asks for {the current price, desired exercise price, [European | American | Asian], date of expiry, volatility}.  That’s five inputs: three ℝ⁺ numbers, one option from a set isomorphic to {1,2,3} = ℕ₃, and one date.

A bilinear map takes two inputs, and it’s linear in both terms.  Meaning if you adjust one of the inputs, the final change to the output is only a linear difference.

Multiplication is a bilinear operation (think 3×17 versus 3×18). Vectorial dot multiplication is a bilinear operation. Vectorial cross multiplication is a bilinear operation but it returns a vector instead of a scalar. Matrix multiplication is a bilinear operation which returns another matrix. And tensor multiplication ⊗, too, is bilinear.

Above, Juan Marquez shows the different bilinear operators and their duals. The point is that it’s just symbol chasing.

* The distinct usage “I love sandwiches” would be considered a separate mathematical operator since it takes a different kind of input.

(Source: http://en.wikipedia.org/wiki/Bilinear_operator)

Contrary to the recently popular “behavioral” approach which proposes to take advantage of economic “irrationality”, I suggest that value-added comes from creating investments with more [psychologically] attractive risk-sharing characteristics.

Andrew Lo & Craig McKinlay, A Non-Random Walk Down Wall Street

43 252 003 274 489 856 000

I respect the cube. I cannot fathom it. I do not want to learn how to do it from anybody else. Instead I want to experience the simple moves that hopelessly and mercilessly turn order into disorder.  Whichever way I turn, disorder gives way to more disorder. It seems as hopeless to restore order as it is to get the spilt milk back into the jug.

—György Marx

Imagine a solved Rubik’s cube.  Now imagine just one of the corners mis-coloured. You have imagined an impossible state.

It’s impossible to twist just one corner of the cube clockwise or anticlockwise.  It’s impossible to twist just two corners of the cube clockwise or anticlockwise. The minimum change is three corners twisted clockwise, or three corners twisted anticlockwise.

Quarks are like that too. (Solomon Golomb noticed this first.)  The universe never makes just one quark alone, or just two quarks alone.  The universe only makes three quarks together all at once.  

There’s more. The universe does put a quark and an antiquark together. (Instead of making a proton or neutron this makes a “meson”).  And likewise, the cube allows a twist and an anti-twist on just two corners.

What does quantum chromodynamics have to do with Ernő Rubik’s invention? There is just something similar in their group structure.  Just as a particle’s baryon number must be conserved, so a similar SU(3) like property characterizes the cube. Spooky.

And. 43 252 003 274 489 856 000.

There are 43 252 003 274 489 856 000 possible arrangements of the cube, only 1 of which is correct.

43 252 003 274 489 856 000 states of disorder and 1 state of complete order. Need I say the word?  Entropy.

(Source: http://www.amazon.com/gp/product/0198532024?ie=UTF8&tag=hiremebecauim-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0198532024)

Thanks to Ed Leamer, a saint and anti-mystic at once.

(Source: http://www.springer.com/cda/content/document/cda_downloaddocument/9783540463887-c2.pdf)

Trackback

Yo tumblr users.  You may have noticed that tumblr does not have a TrackBack field. But you want to use it anyway.

Here is how to do it. Only works if you use Linux, Mac, or Windows PowerShell, and you know how to open a terminal.

I wanted to submit a TrackBack request to the arXiv, which told me to aim my ping at http://arxiv.org/trackback/gr-qc/9712019 in order to cite http://arxiv.org/abs/gr-qc/9712019.  It’s a free general relativity textbook that gave me the idea for the post Time Is Like Space.

Here is what I did to convey that:

1. Open a terminal.
2. Type curl -d url="http://blog.hiremebecauseimsmart.com/post/806785036/s4" -d title="Time Is Like Space" -d blog_name="Human Mathematics" -d excerpt="in the old view, time was something separate and distinct from space: S³×T. Now, in the modern view, time is another kind of thing that's just like space: S⁴." http://arxiv.org/trackback/gr-qc/9712019.  (No line breaks, or if you do, precede them with a ).
3. Hit enter.
4. Receive confirmation that looks like:
<?xml version="1.0" encoding="utf-8"?>
<response>
<error>0</error>
</response>
.  If you get something much longer, ur doin it wrong.

A simpler version would have been curl -d url="http://blog.hiremebecauseimsmart.com/post/806785036/s4" http://arxiv.org/trackback/gr-qc/9712019.

One thing the curl utility does, is it allows you to send POST requests from the terminal.  Normally when you type an address into your browser or click on a link, the browser (Safari or whatever) sends a GET request and that is what tells ty.com to send you the latest on Beanie Babies.

For more details on the utility, type man curl into your terminal.

No-arbitrage conditions are so often assumed in economics papers that they’ve come to seem magical.  As I read more books by arbitrageurs, the obvious has become apparent:  real people have the job of making financial markets equilibrate.

Given that companies are trying to raise funds for their projects by offering shares of the profits on public exchanges — which is the state of things* — it’s not at all obvious that various mathematical balancing conditions should come about.  It takes hedge funds and stat arbs spending their days looking for profit opportunities to smooth these markets out.

For example, take high-frequency traders.  They learn the nitty-gritty trading rules (aka market microstructure) and look for tiny opportunities to hold a security for just a little longer (intraday) and then sell it for more than transaction cost a wee bit later.  Effectively they act as a short-term warehouse holding the security in between the person who wanted to dump it and the person looking to pick it up.

Knightridge Capital and Jesse Livingston both advised traders not to fight the market, but to go where it wants to go.

As with most ways of making money, to extract it over the long term you have to make the world more like people want it.  (So I believe.)

* but not necessarily the way things would have to be done.  For example I could just call people up and ask them if they wanted a share of my company; or I could auction shares on eBay; or I could post a message on Craigslist to get local people to meet up and talk together about various people buying various proportions of the company.

(Source: “http://www.amazon.com/gp/product/0956399207?ie=UTF8&tag=hiremebecauim-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0956399207)