# The Investors vs. the Tabby

There’s an amusing article making its rounds of the internet today, about the successful investment strategy of a cat named Orlando..

A group of people at the Observer put together a fun experiment.
They asked three groups to pretend that they had 5000 pounds, and asked each of them to invest it, however they wanted, in stocks listed on the FTSE. They could only change their investments at the end of a calendar quarter. At the end of the year, they compared the result of the three groups.

Who were the three groups?

1. The first was a group of professional investors – people who are, at least in theory, experts at analyzing the stock market and using that analysis to make profitable investments.
2. The second was a classroom of students, who are bright, but who have no experience at investment.
3. The third was an orange tabby cat named Orlando. Orlando chose stocks by throwing his toy mouse at a
targetboard randomly marked with investment choices.

As you can probably guess by the fact that we’re talking about this, Orlando the tabby won, by a very respectable margin. (Let’s be honest: if the professional investors came in first, and the students came in second, no one would care.) At the end of the year, the students had lost 160 pounds on their investments. The professional investors ended with a profit of 176 pounds. And the cat ended with a profit of 542 pounds – more than triple the profit of the professionals.

Most people, when they saw this, had an immediate reaction: “see, those investors are a bunch of idiots. They don’t know anything! They were beaten by a cat!”
And on one level, they’re absolutely right. Investors and bankers like to present themselves as the best of the best. They deserve their multi-million dollar earnings, because, so they tell us, they’re more intelligent, more hard-working, more insightful than the people who earn less. And yet, despite their self-alleged brilliance, professional investors can’t beat a cat throwing a toy mouse!

It gets worse, because this isn’t a one-time phenomenon: there’ve been similar experiments that selected stocks by throwing darts at a news-sheet, or by rolling dice, or by picking slips of paper from a hat. Many times, when people have done these kinds of experiments, the experts don’t win. There’s a strong implication that “expert investors” are not actually experts.

Does that really hold up? Partly yes, partly no. But mostly no.

Before getting to that, there’s one thing in the article that bugged the heck out of me: the author went out of his/her way to make sure that they defended the humans, presenting their performance as if positive outcomes were due to human intelligence, and negative ones were due to bad luck. In fact, I think that in this experiment, it was all luck.

For example, the authors discuss how the professionals were making more money than the cat up to the last quarter of the year, and it’s presented as the human intelligence out-performing the random cat. But there’s no reason to believe that. There’s no evidence that there’s anything qualitatively different about the last quarter that made it less predictable than the first three.

The headmaster at the student’s school actually said “The mistakes we made earlier in the year were based on selecting companies in risky areas. But while our final position was disappointing, we are happy with our progress in terms of the ground we gained at the end and how our stock-picking skills have improved.” Again, there’s absolutely no reason to believe that the students stock picking skills miraculously improved in the final quarter; much more likely that they just got lucky.

The real question that underlies this is: is the performance of individual stocks in a stock market actually predictable, or is it dominantly random. Most of the evidence that I’ve seen suggests that there’s a combination; on a short timescale, it’s predominantly random, but on longer timescales it becomes much more predictable.

But people absolutely do not want to believe that. We humans are natural pattern-seekers. It doesn’t matter whether we’re talking about financial markets, pixel-patterns in a bitmap, or answers on a multiple choice test: our brains look for patterns. If you randomly generate data, and you look at it long enough, with enough possible strategies,
you’ll find a pattern that fits. But it’s an imposed pattern, and it has no predictive value. It’s like the images of jesus on toast: we see patterns in noise. So people see patterns in the market, and they want to believe that it’s predictable.

Second, people want to take responsibility for good outcomes, and excuse bad ones. If you make a million dollars betting on a horse, you’re going to want to say that it was your superiour judgement of the horses that led to your victory. When an investor makes a million dollars on a stock, of course he wants to say that he made that money because he made a smart choice, not because he made a lucky choice. But when that same investor loses a million dollars, he doesn’t want to say that the lost a million dollars because he’s stupid; he wants to say that he lost money because of bad luck, of random factors beyond his control that he couldn’t predict.

The professional investors were doing well during part of the year: therefore, during that part of the year, they claim that their good performance was because they did a good job judging which stocks to buy. But when they lost money during the last quarter? Bad luck. But overall, their knowledge and skills paid off! What evidence do we have to support that? Nothing: but we want to assert that we have control, that experts understand what’s going on, and are able to make intelligent predictions.

The students performance was lousy, and if they had invested real money, they would have lost a tidy chunk of it. But their teacher believes that their performance in the last quarter wasn’t luck – it was that their skills had improved. Nonsense! They were lucky.

On the general question: Are “experts” useless for managing investments?

It’s hard to say for sure. In general, experts do perform better than random, but not by a huge margin, certainly not by as much as they’d like us to believe. The Wall Street Journal used to do an experiment where they compared dartboard stock selection against human experts, and against passive investment in the Dow Jones Index stocks over a one-year period. The pros won 60% of the time. That’s better than chance: the experts knowledge/skills were clearly benefiting them. But: blindly throwing darts at a wall could beat experts 2 out of 5 times!

When you actually do the math and look at the data, it appears that human judgement does have value. Taken over time, human experts do outperform random choices, by a small but significant margin.

What’s most interesting is a time-window phenomenon. In most studies, the human performance relative to random choice is directly related to the amount of time that the investment strategy is followed: the longer the timeframe, the better the humans perform. In daily investments, like day-trading, most people don’t do any better than random. The performance of day-traders is pretty much in-line with what you’d expect from probability from random choice. Monthly, it’s still mostly a wash. But if you look at yearly performance, you start to see a significant difference: humans do typically outperform random choice by a small but definitely margin. If you look at longer time-frames, like 5 or ten years, then you start to see really sizeable differences. The data makes it look like daily fluctuations of the market are chaotic and unpredictable, but that there are long-term trends that we can identify and exploit.

# Bad Arithmetic and Blatant Political Lies

I’ve been trying to say away from the whole political thing lately. Any time that I open my mouth to say anything about politicians, I get a bunch of assholes trying to jump down my throat for being “biased”. But sometimes, things just get too damned ridiculous, and I can’t possibly let it go without comment.

In the interests of disclosure: I despise Mitt Romney. Despite that, I think he’s gotten a very unfairly hard time about a lot of things. Let’s face it, the guys a rich investor. But that’s been taken by the media, and turned in to the story through which everything is viewed, whether it makes sense or not.

For example, there’s the whole \$10,000 bet nonsense. I don’t think that that made a damned bit of sense. It was portrayed as “here’s a guy so rich that he can afford to lose \$10,000”. But… well, let’s look at it from a mathematical perspective.

You can assess the cost of a bet by looking at it from probability. Take the cost of losing, and multiply it by the probability of losing. That’s the expected cost of the bet. So, in the case of that debate moment, what was the expected cost of the bet? \$0. If you know that you’re betting about a fact, and you know the fact, then you know the outcome of the bet. It’s a standard rhetorical trick. How many of us have said “Bet you a million dollars”? It doesn’t matter what dollar figure you attach to it – because you know the fact, and you know that the cost of the bet, to you, is 0.

But… Well, Mitt is a rich asshole.

As you must have heard, Mitt released his income tax return for last year, and an estimate for this year. Because his money is pretty much all investment income, he paid a bit under 15% in taxes. This is, quite naturally, really annoying to many people. Those of us who actually have jobs and get paid salaries don’t get away with a tax rate that low. (And people who are paid salary rather than investment profits have to pay the alternative minimum tax, which means that they’re not able to deduct charity the way that Mitt is.)

So, in an interview, Mitt was asked about the fairness of a guy who made over twenty million dollars a year paying such a low rate. And Mitt, asshole that he is, tried to cover up the insanity of the current system, by saying:

Well, actually, I released two years of taxes and I think the average is almost 15 percent. And then also, on top of that, I gave another more 15 percent to charity. When you add it together with all of the taxes and the charity, particularly in the last year, I think it reaches almost 40 percent that I gave back to the community.

I don’t care about whether the reasoning there is good or not. Personally, I think it’s ridiculous to say “yeah, I didn’t pay taxes, but I gave a lot of money to my church, so it’s OK.” But forget that part. Just look at the freaking arithmetic!

He pays less than 15% in taxes.

He pays 15% in charity (mostly donations to his church).

What’s less than 15 + 15?

It sure as hell isn’t “almost 40 percent”. It’s not quite 30 percent. This isn’t something debatable. It’s simple, elementary school arithmetic. It’s just fucking insane that he thinks he can just get away with saying that. But he did – they let him say that, and didn’t challenge it at all. He says “less than 15 + 15 = almost 40”, and the interviewer never even batted an eye.

And then, he moved on to something which is a bit more debatable:

One of the reasons why we have a lower tax rate on capital gains is because capital gains are also being taxed at the corporate level. So as businesses earn profits, that’s taxed at 35 percent, then as they distribute those profits as dividends, that’s taxed at 15 percent more. So, all total, the tax rate is really closer to 45 or 50 percent.

Now, like I said, you can argue about that. Personally, I don’t think it’s a particularly good argument. The way that I see it, corporations are a tradeoff. A business doesn’t need to be a corporation. You become a corporation, because transforming the business into a quasi-independent legal entity gives you some big advantages. A corporation owns its own assets. You, as an individual who owns part of a corporation, aren’t responsible for the debts of the corporation. You, as an individual who owns part of a corporation, aren’t legally liable for the actions (such as libel) of the corporation. The corporation is an independent entity, which owns its own assets, which is responsible for its debts and actions. In exchange for taking on the legal status on an independent entity, that legal entity becomes responsible for paying taxes on its income. You give it that independent legal status in order to protect yourself; and in exchange, that independent legal status entails an obligation for that independent entity to pay its own taxes.

But hey, let’s leave that argument aside for the moment. Who pays the cost of the corporate taxes? Is it the owners of the business? Is it the people who work for the business? Is it someone else?

When they talk about their own ridiculously low tax rates, people like Mitt argue that they’re paying those taxes, and they want to add those taxes to the total effective tax that they pay.

But when they want to argue about why we should lower corporate tax rates, they pull out a totally different argument, which they call the “flypaper theory“. The flypaper theory argues that the burden of corporate taxes falls on the employees of the company – because if the company didn’t have to pay those taxes, that money would be going to the employees as salary – that is, the taxes are part of the overall expenses paid by the company. A company’s effective profits are (revenue – expenses). Expenses, in turn, are taxes+labor+materials+…. The company makes a profit of \$P to satisfy its shareholders. So if you took away corporate taxes, the company could continue to make \$P while paying its employees more. Therefore, the cost of the corporate taxes comes out of the salaries of the corporations employees.

You can make several different arguments – that the full burden of taxes fall on to the owners, or that the full burden of taxes falls on the employees, or that the full burden of taxes falls on the customers (because prices are raised to cover them). Each of those is something that you could reasonably argue. But what the conservative movement in America likes to do is to claim all of those: that the full burden of corporate taxes falls on the employees, and the full burden of corporate taxes falls on the customers, and the full burden of corporate taxes falls on the shareholders.

That’s just dishonest. If the full burden falls on one, then none of the burden falls on anyone else. The reality is, the burden of taxes is shared between all three. If there were no corporate taxes, companies probably would be able to pay their employees more – but there’s really no way that they’d take all of the money they pay in taxes, and push that into salary. And they’d probably be able to lower prices – but they probably wouldn’t lower prices enough to make up the entire difference. And they’d probably pay more in dividends/stock buybacks to pay the shareholders.

But you don’t get to count the same tax money three times.

# Facts vs Beliefs

One of the things about current politics that continually astonishes me is the profound lack of respect for reality demonstrated by so many of the people who want to be in charge of our governments.

Personally, I’m very much a liberal. I lean way towards the left-end of the political spectrum. But for the purposes of this discussion, that’s irrelevant. I’m not talking about whether people are proposing the right policy, or the right politics. What I’m concerned with is the way that the don’t seem to accept the fact that there are facts. Not everything is a matter of opinion. Some things are just undeniable facts, and you need to deal with them as they are. The fact that you don’t like them is just irrelevant. As the old saying goes, you’re entitled to your own opinion, but you’re not entitled to your own facts.

I saw a particularly vivid example of this last week, but didn’t have a chance to write it up until today. Rick Perry was presenting his proposal for how to address the problems of the American economy, particularly the dreadfully high unemployment rate. He claims that his policy will, if implemented, create 2.5 million jobs over the next four years.

The problem with that, as a proposal, is that in America, due to population growth, just to break even in employment, we need to add 200,000 jobs per month – that’s how fast the pool of employable people is growing. So we need to add over two million jobs per year just to keep unemployment from rising. In other words, Perry is proposing a policy that will, according to his (probably optimistic, if he’s a typical politician) estimate, result in increasing unemployment.

But here’s where he goes completely off the rails.

Chris Wallace: “But how do you answer this question? Two and a half million jobs doesn’t even keep pace with population growth. Our unemployment rate would increase under this goal.

Rick Perry: “I don’t believe that for a minute. It’s just absolutely false on its face. Americans will get back to work.”

That’s just blatant, stupid idiocy.

The employable population is growing. This is not something debatable. This is not something that you get to choose to believe or not to believe. This is just reality.

If you add 2.5 million jobs, and the population of employable workers seeking jobs grows by 4 million people, then the unemployment rate will get worse. That’s simple arithmetic. It’s not politics, it’s not debatable, and it has nothing to do with what Rick Perry, or anyone else, believes. It’s a simple fact.

The fact that a candidate for president can just wave his hands and deny reality – and that that isn’t treated as a disqualifying error – is simply shocking.

# Stupid Politician Tricks; aka Averages Unfairly Biased against Moronic Conclusions

In the news lately, there’ve been a few particularly egregious examples of bad math. One that really ticked me off came from Alan Simpson. Simpson is one of the two co-chairs of a presidential comission that was asked to come up with a proposal for how to handle the federal budget deficit.

The proposal that his comission claimed that social security was one of the big problems in the budget. It really isn’t – it requires extremely creative accounting combined with several blatant lies to make it into part of the budget problem. (At the moment, social security is operating in surplus: it recieves more money in taxes each year than it pays out.)

Simpson has claimed that social security must be cut if we’re going to fix the budget deficit. As part of his attempt to defend his proposed cuts, he said the following about social security:

It was never intended as a retirement program. It was set up in ‘37 and ‘38 to take care of people who were in distress — ditch diggers, wage earners — it was to give them 43 percent of the replacement rate of their wages. The life expectancy was 63. That’s why they set retirement age at 65

When I first heard that he’d said that, my immediate reaction was “that miserable fucking liar”. Because there are only two possible interpretations of that statement. Either the guy is a malicious liar, or he’s cosmically stupid and ill-informed. I was willing to accept that he’s a moron, but given that he spent a couple of years on the deficit commission, I couldn’t believe that he didn’t understand anything about how social security works.

I was wrong.

In an interview after that astonishing quote, a reported pointed out that the overall life expectancy was 63 – but that the life expectancy for people who lived to be 65 actually had a life expectancy of 79 years. You see, the life expectancy figures are pushed down by people who die young. Especially when you realize that social security start at a time when the people collecting it grew up without antibiotics, there were a whole lot of people who died very young – which bias the age downwards. Simpson’s
response to this?

If you’re telling me that a guy who got to be 65 in 1940 — that all of them lived to be 77 — that is just not correct. Just because a guy gets to be 65, he’s gonna live to be 77? Hell, that’s my genre. That’s not true.

So yeah.. He’s really stupid. Usually, when it comes to politicians, my bias is to assume malice before ignorance. They spend so much of their time repeating lies – lying is pretty much their entire job. But Simpson is an extremely proud, arrogant man. If he had any clue of how unbelievably stupid he sounded, he wouldn’t have said that. He’d have made up some other lie that made him look less stupid. He’s got too much ego to deliberately look like a credulous drooling cretin.

So my conclusion is: He really doesn’t understand that if the overall average life expectancy for a set of people is 63, that the life expectancy of the subset people who live to be 63 going to be significantly higher than 63.

Just to hammer in how stupid it is, let’s look at a trivial example. Let’s look at a group of five people, with an average life expectancy of 62 years.

One died when he was 12. What’s the average age at death of the rest of them to make the overall average life expectancy was 62 years?

$frac{4x + 12}{5} = 62, x = 74$
.

So in this particular group of people with a life expectancy of 62 years, the pool of people who live to be 20 has a life expectancy of 74 years.

It doesn’t take much math at all to see how much of a moron Simpson is. It should be completely obvious: some people die young, and the fact that they die young affects the average.

Another way of saying it, which makes it pretty obvious how stupid Simpson is: if you live to be 65, you can be pretty sure that you’ll live to be at least 65, and you’ve got a darn good chance of living to be 66.

It’s incredibly depressing to realize that the report co-signed by this ignorant, moronic jackass is widely accepted by politicians and influential journalists as a credible, honest, informed analysis of the deficit problem and how to solve it. The people who wrote the report are incapable of comprehending the kind of simple arithmetic that’s needed to see how stupid Simpson’s statement was.

# Shocking Fraud from Financial Scum

Against my better judgement, I’ve ended up writing a lot about the
financial mess that we’re currently going through. If you’ve read that, you
know that my opinion is that the mess amounts to a giant pile of fraud.

But even having spent so much time reading and studying what was
going on, the latest news from the financial mess shocks me.
Even knowing how utterly sleazy and dishonest many people in the financial world
have been, even knowing about the stuff they’ve been doing, the kinds of
out and out fraud that they’ve perpetrated, the latest news makes them
look even more evil than I could have imagined.

# Financial Shenanigans: the Repo 105

I’m glad to report that electricity has been restored to the Chu-Carroll
household. So now I’m trying to catch up.

During the outage, I got a bunch of questions about the latest news coming
out of the big financial disasters. A major report came out about the failure
of Lehman Brothers, and one thing that’s been mentioned frequently is
something called repo105.

The whole repo105 thing is interesting to me, not so much because of what
it actually means, but because of how it’s been reported. The term has been
mentioned everywhere – but trying to find any information about just what the
hell it means seems to be next to impossible. It’s absolutely amazing how many
places have reported on it without bothering to explain it.

# Bill O'Reilly on Life Expectancy: Dumbest Man on Earth?

An alert reader just sent me, via “Media Matters”, the single dumbest real-life
video clip that I have ever seen. In case you’ve been living under a rock, Bill O’Reilly is
a conservative radio and TV talk-show host. He’s known for doing a lot of really obnoxious
things, ranging from sexually harassing at least one female employee, to sending some of
his employees to stalk people who he doesn’t like, to shutting off the microphones of
guests on his show if he’s losing an argument. In short, he’s a loudmouthed asshole who
gets off on bullying people.

But that’s just background. As a conservative commentator, he’s been going off on
the evils of Obama’s supposedly socialist healthcare reform. That’s frequently
taken the form of talking about how horrible medical care is under Canada’s
the insanity follows.

The question came from a viewer named Peter from Victoria, BC, who asked: “Has anyone noticed
that life expectancy in Canada under our health system is higher than the USA?”

Bill’s response:” Well, that’s to be expected Peter, because we have 10 times
as many people as you do. That translates to 10 times as many accidents,
crimes, down the line.” Delivered, of course, in BillO’s trademark patronizing
style.

# Bad Healthcare Cost Models Produce Silly Results (anyone surprised?)

This morning, my good friend Orac sent me a link to an interesting piece
of bad math. Orac is the guy who really motivated me to start blogging; I
jokingly call him my blogfather. He’s also a really smart guy, not to mention
a genuinely nice one (at least for a transparent box of blinking lights). So
when he sends me a link that he thinks is up my alley, I take a look at
the first opportunity.

Today, he sent me a link to a guy who claims to have put together
a mathematical model showing that it’s impossible to create a national
healthcare system without rationing. The argument is a great example
of what I always say about mathematical modeling: you can’t just
put together a model and then accept its results: real mathematical models
must be validated. It’s easy to put together something that looks
right, but which produces drastically wrong results.

The common way of saying it is “Garbage In, Garbage Out”. I personally
don’t like that way of describing it – because in the most convincing examples
of this, it looks like what’s going in isn’t garbage.

# More Stupid Graphs

Remember the post I made a couple of weeks ago, flaming the wall-street idiots for
They were comparing the value of financial firms before and after the current
mess. But they way that they drew it was using circles, where the diameter of the
circle was proportional to the values, but the way it was drawn strongly suggested that
the area was the metric of comparison.

Well, an astute reader sent me another example of the same error – but it’s even
worse. This one is misleading in two ways. Take a look and see if you can figure out
what the two errors are. I’ll explain beneath the fold.

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