On the Markets, US Dollar, and Inflation

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I hadn't planned on prognosticating on the financial markets here, in my journal. These are unusual times, however, and I have been entertaining unusual thoughts lately. But first a little about where I'm coming from..

Background: Trading Activity

I play mostly individual stocks, and luckily (for me, that is) I have been on the right side of the recent market action. I've been in the market for over 20 years now. I first started as a broker on wall street where I became good at selling mortgage backed instruments (CMOs) and such derivatives as "residuals". Actually, no. I wasn't good at selling them; I was good at explaining how the pricing model was supposed to work. I made okay money, but a year or so after the crash of '87 (my best trading day ever), my interest wandered back to painting and I left the business shortly thereafter. I was young, and had yet to try many other things. Through it all, though, I've always had skin in the market.

Over time, I have developed some trading/investing habits. I summarize them below.

• Whatever the overall strategy, it has to be simple to execute. This means, for instance, that I wont consider a trading strategy that involves anything more than a few trades a day.
• I generally prefer to be market neutral: that is, I like to hedge my long positions with short positions in other stocks.
  
• I like to maintain anywhere from 6 to 9 positions at any one given point in time. This policy does a few things for me. One, it helps me focus on what I believe are the best opportunities by narrowing down on a few. Two, it makes following the news that I have exposure to easier. Three, it makes trading the positions easier. (Trading 20 different stocks is considerably more challenging than trading 3.)
• I prefer to speculate on medium term trends: 6 months to 2 years out. I will not enter a position for which I have no medium term prognosis.
• I trade around core positions. I do this in an attempt to increase profits while minimizing my average downside exposure over time.
• I accept that to win you must also prepare to lose.
• The only number on the screen that matters is the one on the corner: your account's value.
  
• I begin everyday with one mantra: "I don't know anything; I'm just a speculator in search of an edge."
  

Inflation or Deflation?

What's the nasty end game? That's what everyone is quietly wondering.

Will the dollar plummet, as in the unraveling of an elaborate confidence scheme to which foreign traders of goods and capital are just waking up to? Or will the dollar plummet as the treasury prints more money to stave off a financial crisis which itself was a product of another credit bubble? Or does the master plan (the one nobody knows about but which is written in stone) involve cheating our creditors by wiping off the real value of all this toxic debt with an inexorably steady dose of inflation?

Or is deflation in the cards? The US government does not print money; it doesn't have to. The world's creditors run to the protection of the one "true" thing they still believe in, the US dollar. Economic activity contracts in the developing world and takes the emerging economies down with it. Unemployment rises, interest rates fall, and the treasury finds yet more willing foreign buyers for Treasury debt. And the currency confidence scheme of international trade and national current account deficits continues.

Turning and turning in the widening gyre

The falcon cannot hear the falconer;

Things fall apart; the centre cannot hold;

Mere anarchy is loosed upon the world..

-W.B. Yeats

The future, it seems, can have both outcomes in the cards. For now, while fear is in charge and world markets price in economic contraction, deflation is the theme of the day. As a horrible as it might get, we will eventually meet our demons, and fear will first be replaced with ambivalence, before greed's comeuppance. Somewhere along that path, I expect inflation to rear its nasty head. I hope it doesn't, but a dollar is an IOU, and that's what happens to IOUs issued by borrowers who can't balance their books.

A more efficient shorting tactic?

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The recent SEC curbs on shorting a select list of financial stocks got me thinking about ways to avoid these silly procedural rules. I was short some of these financials, and in deciding whether or not to cover, I had to also consider the fact that I would likely be unable to short the stock again.

I called my broker, and they confirmed my suspicion: there was no stock available for shorting--for the time being. I asked whether it was likely that my short position might get called away--that is, that I might be forced to cover: highly unlikely, was the answer. I described my predicament (a juxtaposition of fear against greed), that I wanted to cover (fear), and still keep the borrowed shares around for shorting later (greed), and they said there would be no guarantee that there'd be any more shares to short after I had covered. How about if I bought the stock in my long account, didn't touch my short account, and later sold the shares in the long side of my account? I suggested. Can't do that either, they said. Once I bought the shares on the long side, they would be in a boxed position, and I would not be able to sell any more shares. I thanked the broker and hung up.

The solution to my problem had already presented itself in that last question. All I had to do was to go long the shares in another account I own at another broker: the combined account positions could exactly offset each other, and I would be able to later return to a net short position simply by selling the shares in the long account at the other broker.

I doubt the procedure described here is illegal, [ Ignorantia juris non excusat warning and other usual IANAL, IANAIA disclaimers go here], and if it is, I certainly couldn't find anything about it on the web. (Truth be told, I didn't ask either of my brokers: I had heard enough stupid "No"s for one day.)

My solution to this short term problem, created by a seemingly capricious regulator, led me to consider its more general application. For the regulator, by making shorting difficult, has created artificial scarcity. A short position, then, by virtue of its scarcity, must have more value than its nominal value. How much more?

Let's call this double account tactic, where your long shares in one account are exactly offset by your short shares in another account, an open boxed position. I suggest the scarcity value of a short position might somehow be connected to the cost of money (e.g. as employed in the Black-Scholes model) required to maintain an open boxed position in the same number of shares. I say "somehow", because while I can easily quantify how much it's currently costing me to maintain my open box, there is no general way to determine what it might cost another person (the cost of borrowing shares varies from broker to broker).

To put it another way, I suggest an open boxed position is a store of all the regulatory overhead associated with shorting. A speculator wishing to short hard-to-borrow shares, must consider both price movement and the availability of shares to short in the timing of their trade. It is a well known fact that open interest tends to increase at price peaks, making shorting at the best price a double challenge. This puts the short trader at a tactical disadvantage to the long trader. In order to mitigate that disadvantage, a speculator who plans to short shares at, for example, some future higher price might build a (net neutral) open boxed position, to be unboxed (net short) at a future time when the price or trend is right. In building the open box position, you are satisfying all the regulatory overhead of shorting ahead of time (whether that overhead is the requirement that your short never be naked, the now defunct up-tick rule, or some other silly red tape impeding your ability to short at the precise time of your choosing). Alternatively, as described at the beginning of this post, a short position can evolve into an open boxed position.

That you can easily skirt the intent, if not the letter, of regulatory restrictions designed to impede shorting is a testament to the fact that shorting is a natural, organic outgrowth of market activity. It is not an activity born of the invention of some new fangled derivatives instrument; rather, people have been shorting stuff for centuries. So I guess it shouldn't surprise us if we later find that the new SEC curbs on shorting only worked temporarily. The market always finds ways to correct artificial scarcity.

Differential equation estimating the distribution of primes

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Let me begin with this disclaimer, first: though mathematically trained (physics background), I am not a mathematician. OK, got that out of the way.

*

I have found a simple way to derive Gauss's estimate of the prime density function using probability heuristics, alone.

Background

Excerpt From MathWorld: http://mathworld.wolfram.com/PrimeNumberTheorem.html

..
In 1792, when only 15 years old, Gauss proposed that , the prime density function

Gauss later refined his estimate to

where

..

I have not seen a simple derivation for this estimate, and if it exists, I am surprised why it is not more widely used in expositions on the subject of the distribution of primes. What follows is a very short argument based on a probability model. According to this model, we'll find that the distribution of primes is governed by a delay differential equation of the form

Q'(x) = - Q(x) Q( √x ) / x

which has a solution

Q(x) = 1 / 2 ln x

Anyway, to me, what's interesting is how using some specious probability arguments about the distribution primes I was able to set up the equation and try a test function inspired by Gauss's estimate to solve it. This hints at something more meaningful in my Clouseau-esque accident.

The setup

The setup, I have come to find, is similar in spirit to Harald Cramer's probabilistic, heuristic arguments for estimating of the distribution primes (the difference here being that we don't use any other results from number theory). Here it is..


Equ. 1:
The joint probability of a randomly chosen positive number n not
being divisible by two relative primes p and k is (1 - 1/p)(1 - 1/k).

Equ. 2:
Define Q(x) = ∏(1 - 1/p)
taken over all primes p ≤ x.

Equ. 2a:
The joint probability of a randomly chosen positive number n not being divisible by any prime p ≤ x is Q(x).

Using Equ. 2a, vigorous hand waving, and a pinch of salt, we can say

Equ. 3:
The probability that a randomly chosen positive number x is a prime is Q( √x ).

What we're saying here is that for x to be prime, it suffices to show that it is not divisible by any prime less than the square root of x. Equ. 3 says that in the neighborhood of x, the 'average' distance between primes is 1 / Q( √x ).

Now the d.d.e. above comes from trying to approximate Q(x) using this probabilistic model. The idea is to use that approximation in order to estimate a prime counting function:

∫ Q (√x) dx

But we don't have an analytic expression that approximates Q, yet. Instead of setting up an integral equation, we try a differential approach. Consider the change in Q as x passes over 2 very large consecutive primes p₁ < p₂:

ΔQ = -Q(p₁) / p₂ ~ -Q(x) / x
Δx ~ 1 / Q( √x )

Dividing the top equation by the bottom one, you get

Q'(x) = - Q(x) Q( √x ) / x

the d.d.e. I described above.


The solution

I had read somewhere how the 15 year old Gauss had been able to come up with his logarithmic integral for estimating the number of primes less than n. Was his integral inspired by a similar probabilistic argument? Maybe, but googling it, I couldn't find much. So, I plugged in C / ln x and solved for the constant C (=1/2).

Q(x) = 1 / 2 ln x


Does it mean anything?

I suspect it might, which is why I posted it. I did a bit of cursory reading on the topic, but alas, I'm an amateur. My claim that

Q(x) = ∏( 1 - 1/p) ~ 1 / 2 ln x

does not agree with Mertens' asymptotic formula (1874)

∏( 1 - 1/p) ~ exp(-C) / ln x,

where C is Euler's constant.

Still, there's something here that piques my nose. My result, when plugged into the prime counting integral, agrees exactly with Gauss's estimate:

∫ Q (√x) dx ~ ∫ (1 / ln x) dx
What do you think? Is this interesting, or is this old?


7-09 Addendum: Interestingly, if we adjusted the model so that Q'(x) = - Q(x) Q( x^1/n ) / x

then Gauss's estimate would still hold for most n. It's as if the forward distribution constrains that back distribution.

On the line that divides private from public

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It used to be hard to dig for information--before we had the web, that is. Even if the information you were digging for was public, finding it was often difficult, laborious, or costly. So we didn't mind, for instance, that a copy of the deed to the house was available to anyone who bothered to walk over to the local Recorder's office, look up the lot number, thumb through the books in the stacks, and expend a nickel a page on the Xerox machine. Few citizens actually visited these offices. So you likely didn't know what your neighbor owed on his property (unless it somehow became your business to know); nor did your neighbor likely know what you owed on your property. This information was public, but it was tucked away in a hard to get corner of a government office.

Finding your neighbor's phone number in the phone book, on the other hand, was much easier than finding out how much they owed on their property. (After all, that's what phone books were used for, back then.) So in a very practical sense, your phone number was more public than the publicly recorded lien on your house. While it was understood that there was no legal basis to consider one piece of public information more public than another, it was also understood that some information was harder to find than other information. The harder it was to find the public information, the less it was apparently public.

Contrast the above with the situation today. Finding out how much the neighbor owes on their property is about as many mouse clicks away as is finding their phone number. In a very real sense, both pieces of information (the amount owed, and the phone number) are equally easy to reach.

As more personal information--some of it public--comes online, and as search technologies improve, I predict, you'll soon be able to type a name into a search engine and instantly receive a synopsis of personal information about the individual[s] with links that drill down to their finances (e.g. home purchase/sale price, and amount owed), blog pages and comments, photo albums, listed phone number, date of birth, resume, and so on. Every word ever written, every link ever created, on the public conversation that is the web will take on added significance as it will be attributable to its author.

Today, there's still plenty of hard-to-find, public (or practically, public) information. In the future, I predict, information will either be easy or impossible to find. The impossible-to-find, will be private information; the easy-to-find will be everything else. So when a piece of private information leaks, the search engines will be able to quickly assimilate and contextualize the information, and attribute it to a person or group of persons. Search engines will be able to do this, no matter how [apparently] tenuous the link between the information morsel and the person[s] attributed to.

The line dividing private from [practically] public information is becoming razor thin: it is the other edge of the search technology sword. Like time and entropy, information has an arrow along the private/public dimension--from private to public (a piece of public information cannot ever be made private again). This has always been so. Only now, thanks to the web, the rate at which information is becoming public is increasing in leaps and bounds. (And the transition states, as it were, from the private to the public end the information spectrum are becoming fewer and fewer, until there will be but 2: private and public.)

It is easy to imagine a dystopia in which we find ourselves imprisoned in the very public image each of us has projected on the web, where past projections are hard to displace, where labels are hard to peel off, where you must blog in order to protect and enhance your personal brand. But wait a minute! Aren't we there already? And is it so bad?

We're well along the way to such a future, I would say--only, the future needn't be so dystopian. I actually welcome this new landscape, where everyone competes on a more or less equal information footing, where what you know and how you know are more important than your access to information. The problem, I suspect, will be that many will have come to expect their relative anonymity today to continue well into the future. That, I'm afraid, would be unrealistic. I cannot expect this blog post to remain forever unattributable to my real name.

Microsoft and the OLPC deal

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I have been following Microsoft's courting of the OLPC project on Slashdot. Ever since my involvement with the FaunOS project, I've slowly convinced myself that it will be "portables" that pave the way down to ever cheaper, commoditized computing. And Linux has always figured prominently in my speculative conceptions of likely, future computing landscapes. So now what to make of Microsoft selling $3 copies of Windows [on OLPC]?

I believe a simple rule of markets is that once a producer breaks the price of its product in one market, it will eventually have to break prices for the product in other markets as well. (I tried googling for some such succinct rule but, alas, I couldn't come up with the right query terms.) From a long term investor's point of view, this cannot be good news for Microsoft. It is a short term coup for Redmond: having OLPC run on Linux risked cultivating a new cadre of non-Mr. Softies. A $3 copy of Windows thwarts that threat: few children would opt for the Linux version of OLPC--for obvious reasons not worth enumerating. But this sets up a bad precedent. Will Microsoft fight Linux with $3 licenses wherever Linux enjoys a clear cost advantage? My guess is that wherever a user interface is involved, Microsoft will fight to keep market share. Today the battle is staged on what I'll sweeping characterize as ultra-portables, like OLPC and Eee PC. (Okay, maybe it's not a full scale battle, yet, but hear me out..) From Microsoft's perspective, the distinguishing characteristic of the ultra-portables is price: that they are portable is irrelevant. But hardware prices inexorably fall, and we can safely assume to see hardware the size of an ordinary laptop selling at today's Eee PC prices. Cheaper hardware means either a free OS like Linux, or significantly lower Windows licensing costs. This deal is an example of the latter, and is a reminder that Microsoft's fat margin's and pricing power are receding.

Now don't mistake this entry for a Linux fan's attempt at finding a silver lining in a deal that effectively ditches Linux. In fact, I am very worried. Imagine a world in which Microsoft still makes a decent living selling mostly $3 operating systems. Somehow they figured out how the business model could work--e.g. leverage their monopoly position less obviously, or make up the lost margin through greater volume. Whatever. Microsoft could even be a lot smaller company and still control the desktop.

I doubt that is how history will unfold. Linux will win the desktop, but it'll likely be a long and dirty battle in which Microsoft will make a lot of noise while quietly imploding as its pricing power wanes and margins collapse.

Idea: Wave power without moving parts

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When I was an undergraduate in applied physics, I had this idea about using the conductive and dielectric properties of sea water to convert wave motion directly into electricity. I recently googled the topic and came up naught. (May be because it's a bad idea?)

Any way, the idea comes from 2 observations about capacitors.

1. It takes work to slip out a dielectric slab sandwiched between charged capacitor plates.
2. It takes work to increase the distance between charged capacitor plates.
   

Now if we can set up a large scale capacitor with the ground plate placed horizontally underwater, close to sea wave troughs and the "positive" plate well above wave crests, and a suitable timing mechanism to apply and draw voltage to and from the capacitor as the wave enters and leaves the contraption, then some of the wave power can be converted to electricity.

You don't actually need capacitor plates: a mesh of conductive wires should suffice. The power generated by such a contraption is proportional to the area of sea surface covered. But because of its simple design (all the smarts and expensive parts can be centralized), it should scale well.

Numbers? I'll try to add a back-of-envelop calculation, later..

Addendum: 3-20-2010

I'm beginning to think this might not work as decribed. Even if it did, from a practical standpoint, the wires would soon be covered with debris, barnacles or other insulating stuff. A better approach might be to create a giant, barely floating, sealed "waterbed" filled with a suitable dielectric liquid. Two wire meshes spanning the top and bottom walls of the bed from the inside would be used to create the effect of an array of capacitor plates. A component of the [gravity] wave hitting the side of this bed would continue to propagate through this bed, creating a moving bulge through it as it passes. As before, an adaptive control mechanism would time a voltage increase across the cascading, virtual capacitor plates ahead of the approaching bulge and draw power as the wave leaves the region.

Greetings

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Years ago, before marriage and kids, I used to keep journals. I still write, on occasion, for my own pleasure, but in recent years this writing is mostly scattered across email conversations I've had with family and friends. The nice thing about the meat-space journal was that at least it was all accessible in one place (not to mention all the other obvious advantages of a real notebook). The downside of writing in a notebook, well.. is that only you read it.

I don't know if this journal will find an audience. I hope it will, but if it doesn't, the thought that my kids might one day read whatever crap I wrote here is enough to sustain me. That the digital footprint we leave behind in our lives is for posterity, I think, is an under-appreciated facet of online activity.

This will hardly qualify as a blog. Little that I write, I suspect, will be timely. Nor will it likely be focused on any few topics. This is more like an online notebook..