Monday, June 20, 2016

Macroeconomics doesn't make sense

The purpose of this post is to present IS-LM model and also my own made-up model, just to demonstrate how arbitrary are some assumptions made in economics, and how it obscures the truth. The models like IS-LM and the conclusions drawn from them have their criticism within economic community as well, but the criticism is being no less obscure than the models themselves.

So here's a theoretical physicist's take on IS-LM model. We aim to describe a country with a government, a bunch of banks, businesses and people. Their economic activity is exchange of money and goods/services. It is measured by following well-defined quantities:

CPI -  price of a fixed list of goods that are supposedly the most common consumer choices. Is used to adjust for inflation, so all other quantities get the adjective "real": real GDP, real interest rate. We talk about real values without mentioning it from now on.

GDP - every time money is exchanged for goods/services this year, the amount is added to GDP. Buying shares in a company (or stock) is also counted. Taking/paying loan in a bank, and paying taxes are not counted.

r - interest rate. Reflects what kind of loans are available. Is set by either government, or some agreement/competition between banks (depends on a country).

MS - money supply. Counts how much money (how many bills) the government has printed.

I - investment. Part of the GDP that involves buying shares (or stock).

C - consumption. The rest of the GDP. For economists in the room, we ignore export and government spendings.

Then economists write several equations to determine the equilibrium values of these quantities, and also see how they change if some of the internal mechanics of the system changes. First equation follows directly from definitions:

GDP = C + I

Second equation follows from a simple consideration about Investment and interest rate. Supposedly for investors there's a "safe" option to put their money in a savings account that has rate of return that follows the interest rate r. So some of the investment opportunities are not interesting (if their rate of return is smaller than one of savings account). So investment depends on the interest rate with a negative coefficient:

I = Io - a*r

Here Io and a are describing how many investment opportunities are there, They may, and in principle should, depend on what's up in the economy. If people tend to spend more money, there should be bigger investment opportunities, and more profitable ones. But for some reason IS-LM model doesn't consider that, and instead fixes Io and a to be constants.

Consumption, on the other hand, is allowed (in IS-LM model) to depend on how much money people and businesses got. What they got this year is GDP. They probably have paid taxes, so the amount decreased by a bit. Then they have decided which fraction of the rest to spend this year (or possibly overspend and reduce their savings):

C= c0 +c1*GDP

Here c_1<1, or else we can't balance the equation for GDP. If we collect our knowledge so far, we get the IS (investment-savings) part of IS-LM model:

(1-c1)*GDP  = c0 + I0  - a*r

it's a line with \ slope on (GDP,r) axis. Note that somewhat in spite its name, IS equation doesn't actually talk about savings. What's going on is that of total amount of money MS some part have been circulating (possibly several times) to count towards GDP, while other part were people's savings. Some people made money, some people lost this year. GDP by itself does not really tell us anything about savings. We can imagine a year when two monkeys are selling a banana to each other ad infinitum for a dollar, while the rest of MS in never used. In this case, GDP may be arbitrary huge, but at the same time MS-1 dollars never left people's savings.

To describe savings, one needs to involve heavier math. Suppose that MS is split between people according to a distribution m(i) - how much money does i'th person/business have. Everyone wants to consume c(i) and invest I(i). Also this year they earn g(i). In case m(i)+g(i)>c(i)+I(i), this particular individual/business can achieve it's goals. In fact, the quantities c(i) and I(i) should probably depend on m(i) +g(i). But we ignore it for now. If there's not enough money, then an individual can take a loan, or decrease its consumption goals. In the end, we get an inequality:
 m(i)+g(i) + l(i)>c(i)+I(i)
In fact some individuals also need to pay for older loans, so:
 m(i)+g(i) + l(i)>c(i)+I(i)+p(i)
If we sum these inequalities, we don't get anything interesting:
MS+GDP + LOANSissued>GDP+LOANSpayed
Any significant MS will allow this to balance always.

But the breakdown into individual agents has taught us an important lesson: investment and consumption depends on their savings. Economy where people have tons of savings will grow until they start spending most of them every year, but or IS-LM model doesn't capture that.

Finally, the LM ("liquidity preference/money supply")  part of the model describes how the interest rate is set. Looking at the above, intuitively more consumption means more loans (because for more people their savings are not enough). As we noted, this cannot be seen in the aggregates, one actually needs to consider a distribution. Roughly half of the agents will not need loans this year. But how big will be LOANSissued really depends on the economic inequality accumulated from the past, this year's salaries and this year's desire to consume. We assume that both salaries and consumption depends linearly on GDP for those who are in debt. So
LOANSissued = a + b*GDP
Here b>0. We then make a simple assumption about bank operation (that is very far from what they actually do). The global interest rate is set by the following procedure: they look how many loans are requested this year, and think: ok, the bigger the demand, the bigger we can set the "price". The "price" of loans is the interest rate:

r = a' + b'*GDP

Here b'>0. This is the LM part of the IS-LM model. Together these equations can be solved, and if we assume that all the used coefficients except one are constant, then we can find the dependencies between different economical indicators. Like, when we change c0, we observe that if the GDP grows, I  decreases. Other parameters would lead to other relations, so for instance GDP and I can both increase.

What one can do to check that the above makes sense, is to try other things. For instance, one can fix r=0, and instead develop a relationship between I and people's savings. Unfortunately, as soon as savings are involved, the simple line-crossing economists do is not applicable anymore, instead one needs to run numerical simulations. I have run a simple one and observed the relationship between the supply of shares of a specific company (people willing to sell their shares) and the GDP. It turns out that the supply is bigger when GDP is bigger, which would imply that the corresponding stock price is anticorrelated with the GDP.

Saturday, June 4, 2016

Two levels of understanding of the Market

New traders start approaching the market as an object of scientific method. They think it is a black box that is given to us, like in a problem statement in high school. They absorb all the knowledge they can find about it, believe successful people and their models of efficient market and stock price somehow representing the value of the company. They probably learn to avoid scam, but they are sure that the truth is out there. That the market will be operating forever according to yet undiscovered laws. That if they see contradictions in different known results and theories, they should just ignore it. And such optimism pays off - they do find relations in the historic data and utilize them to trade in the future. If the market were a static black box, they would do just fine.

Yet there is one situation where looking at history and black box approach may lead you in trouble. Quite literally, imagine a trail of candies lying on the ground. The above strategy is like picking up the candy without questioning who left it there. One may easily get into trouble at the end of the trail.

But once one starts asking questions like "who left the candy", it's really easy to stop trading and be overwhelmed by the complexity of what's inside the box. During meetings of our local investment club, I rarely say anything at all. Many other people jump into arguments, but to me none of their arguments are convincing at all. There is absolutely no reason to trust or believe into any principle that somebody tells you about the market.

So who left the candy? In fact, people like you did. Other traders who believed in similar things that you believe in made "mistakes", and you are getting their money now (assuming that you win). That is a simple picture. Once one starts to dig deeper, it is even more disturbing.

It will probably not be too far off to say that 90% of the money in the market is managed by people called "portfolio managers". That means this is their full-time job, they often have business and economy background and they are put in charge of large sums of money. It is generally not completely automated, it's more like a machine-human interface. Human still does the steering, and the machine takes care of the details.

Now these guys do not actually take money from you. You don't even have enough money to feed their greed. Most of their wins is money taken from each other. That is, even though these people have lengthy resumes with tons of accomplishment and expertise in the area, roughly 50% of them end up losing every year. Stock market does not "generate" money by itself. The only way for someone to win is for someone to lose.

It's ironic then that all of them were able to convince their rich employers that their portfolio management skills are above average. In fact, they are not even rational players. If one tries to use game theory to this problem, one sees that many of the portfolio managers never really tried to optimize their game strategy against other portfolio managers, like they should optimally. Instead, they have empirically collected a huge body of knowledge about how to do their job, that was based essentially on the first approach described above (black box) plus some evolutionary dynamics that made them slowly abandon the methods that do not play well against other players. They still probably have tons of methods used daily that make absolutely no sense from the point of view of game theory. And they will keep using them for a while.

The problem is how fanatic they are on this erroneous path. An ideal game theory strategy against them involves studying their thought process, however inappropriate for the problem, then modeling them by a few math equations and coming up with optimal strategy. But their thought process is so sophisticated (and probably not even deterministic) that it defies any simple modeling. In this way, even though they are not getting closer to the better 50% of their crowd (the winning one) by indulging in all those economy studies, they somehow protect themselves from bright people who would want to attack them with correct math tools. And as a bonus, they also manage to charm their rich employers with the obscure language of finance.

I find this field to be not in the realm of science, it more resembles alchemy, where you secretly develop outlandish recipes that do not actually work, and make colorful sparks to awe the king so he does not think of beheading you this time. Over the years, alchemists developed some kind of understanding of nature, but they also had tons of misconceptions that held them back.