Wednesday, August 9, 2017

How much money will you spend in a lifetime?

A version of this question is often asked: how much money do you need to retire? Let's make a simple yet believable calculation.

The main expenses you incur are housing, transportation and healthcare. The prices change over time: transportation gets cheaper, housing depends on where you want to live (can find cheap options), but price of healthcare seems to be growing, and in fact much faster than the inflation rate. Which makes you wonder why do they define inflation rate as they do. So let's focus on healthcare. If you save money by putting it in the stock market, your wealth grows approximately as fast as the healthcare prices, so you can use the nominal value on your paycheck and add it up over the years you work. Specifically, you add up the amount you manage to save. And then you compare it to the amount Americans spend on healthcare today per person per lifetime (~300k$). This is how much you need to save. So saving up 1k$ a month, you need to work 25 years to provide for yourself and just yourself. Of course, that implies that you take advantage of all the retirement benefits of your work, insurance and social support. And also move to the place in US with the cheapest housing and living expenses. So we get the right ballpark. You're spending about 4 times more than that, so total per lifetime in US you will spend 1.5M$ per lifetime. That is just for an average job. Many people struggle to reach this number, and enter and endless circle of exploitation by companies.

Now another important question: when do you actually want to work those 25 years? Do you want to spend your 20ies and 30ies working and then spend your time with kids in the 40ies and 50ies? Would you rather party away the 20ies and see little of your kids in your 40ies? Would you prefer to work 40 years but not too hard or 25 years very hard, and then retire at 40? Would you not stop at 40 and keep working hard to earn a better, more comfortable living conditions, like many Americans do?

Saturday, October 29, 2016


Is a good way to value companies. There are several main methods, all producing different value, well, values. This one involves finding similar companies, and averaging over them the ratio of market cap (not sure if that's the right term, but essentially all that company is worth right now not counting the debt) to this EBITDA number of that company. Then one looks at the EBITDA of company of interest, calculate the worth of it using the averaged ratio, and then uses the result -debt/ shares outstanding to get where the stock price should be.

This method does not work for fast-growing tech companies, because for one thing, they don't have anyone to compare to. Sometimes it can be circumvented by splitting a tech company into sectors doing different things, each one of them comparable to existing companies (like Apple can be split into phone company and computer/software company).

This method is more robust than the seemingly more reasonable DCF (Discounted Cash Flow), where the company is valued depending on the cash it generates for the owner. The DCF is very sensitive to internal parameters, for instance the way the discounting is done (without discounting, any company naively generates infinite cash so has infinite worth). It also doesn't work for natural resource- related companies, because then what's important is how much resources is in the land they own, not how much cash they decided to generate this year. Also note that coal mine companies typically have lifespan of about 10 years, whereas "usual" companies effectively stay around forever (except for a few rare cases).

Method #3 is to look up expert opinions. Typically they are either public or available with your broker. Experts are a bit biased in a sense that they prefer to write about companies they think are good to buy, even though the typical company you find on the market is not any good. So if you put together all expert opinions on all companies, there will be 90% of opinions that tell you to buy something, just because the negative opinions do not get written. Nonetheless, when they talk about specific companies they do not lie, and they probably have spent a month of their lives looking into this company's internal workings, so it's good to check with them.

There's another very good method that seems to be more relevant to what's actually going on in the stock market, but unfortunately it's not available unless you're "in the know". It's called LRO or something, I don't seem to find it on the web. The idea is to see what big investors are actually buying. Look at the big transactions, look at how many offers are out there to buy some kind of company. Having that information, one can estimate how much money can be made if the company was to be bought now and resold in a year, or something like this. Maybe in five years. From that, one can figure out what's a good price. But since only big players are involved in such transactions, you really need to know what they are doing to predict like this.

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:
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. 

Monday, May 23, 2016

Low income strategy

So you have that minimal wage 2k$. You live next to your job and can get by without a car. You share a house with a few roommates so your rent is <1k$. You are healthy so you don't need insurance (or you have subsidized insurance). Your family is all fine so you don't have any financial burden from them. It goes without saying that you don't spend on alcohol and have inexpensive hobbies. Then you're good to go - saving money actually makes sense for you.

You get 1k$ net profit every month. You get credit cards from different banks and accumulate promotions and credit line. You get 0-interest first X month loans and pay them back on time. You hold your money in both liquid and illiquid investments. The amount you loan is equal to twice your current worth that is invested in liquid part of your portfolio. Let's do a calculation:
M is the money that you own. 0.5M of it is in illiquid investments with 5% yearly rate. 0.5M +M owed are in liquid investments - stock market and high rate savings accounts. They say Goldman now has a saving account everybody can open with them. The return rate is 2% for savings, random for stock market, but we assume it is roughly 3% expectation value in the current economy. With a more advanced algorithms small amounts of investment can easily get 20% return rates, but the taxes may be an issue for those ones. So if you don't use our algos, you are stuck at 3% expectation value. If you do, it is let's say 10%.
So over a year you get 12k$ of wages, and (0.025+ 0.045)M= 0.07M of investment income. After taxes it gets reduced to 11k$ and 0.05M. So our new M' = 1.05M + 11k$. The amount of money you save living this way is (for the first 10 years):
One group of people that easily fits the requirements are gradstudents. They stay for 6 years, and then typically get a postdoc for 2, and then forced to leave their field. With this strategy, they can instead retire :) the 5% income from 100k$ is 5k$/year - enough to have a comfortable life in one of those third world countries. They can even keep doing science - their dream job - in their free time.
Seriously, 5k$/ year is not enough. You don't expect to be able to support your family with that. There are also other nice bonuses like promotions from all those credit cards (500$ a year?), and extra 40k$ of postdoc salaries over those 2 years. So you can maybe get to 150k$ by year 8. Or 200k$ if you get a second postdoc. Moving to another country will mess up your loan game, so 5% interest rate will not be available anymore (however, the interest rate in that country may well be comparable). Also if you are a foreigner, you will need to figure out immigration by then.

Now let's consider an idealistic scenario. You use our algorithm and you get 10% yearly returns on it. Then it doesn't really make sense to use illiquid investments - their rate is lower. You may still do it to diversify your portfolio. But let's say you don't, and put all 3M into this algorithm (email us for details, there should be a form on the right). You get 0.3M yearly returns. Lets say you somehow figure out your taxes, so you just pay 1/3 on stock trading income - your returns after taxes are 0.2M. Let's see what the formula M' = 1.2M + 11k$ spits out after 8 years :)))
Now you get 181k$ savings (+44k$ extra from postdoc salary and credit card promos). Also your yearly return is much more noticeable: 45k$/year. That is a decent salary! Our only assumptions are that the algorithm will still be working at 10% yearly returns expectation value, and that the banks will still give out those 0-rate loans as a way to attract you as a customer. If you play the credit card game (see website "dr. credit"), your credit line should be pretty big at year 8, and the banks should be willing to loan you sums like 400k$ with no interest rate for a short amount of time (because they expect you to forget to pay on time). Both assumptions are very feeble. But at least they show that financial stability is possible for those who want to stay in Academia. In the same way they are possible for other low-paying jobs.

Wednesday, March 16, 2016

Installing Python 3.3

So there are two ways of installing python such that the nice Mathematica-like iPython notebook environment works. In the above, it's hardcore console. Here's a related blogpost. Here's a better one. For me I installed Python 2.7 on an older Mac.

I needed to say "pip install ipython[all]" instead of what's in the video.

Then running "ipython notebook" worked. You also need to "pip install" numpy, pandas etc.

Alternatively, and avoiding console for the most part, one may go to Anaconda website. There they have a file you can download for consoleless installation. Ideally "ipython notebook" console command then just gives you what you want.

Wednesday, March 9, 2016

The Big Short, and loans in the modern day

The movie shows how knowing that something for sure is gonna happen, big money players can negotiate instruments that allow them to make much bigger returns than what one would expect. Let's see. Naively, if you know that the price is going to go down or up 5%, you can make 5% returns. If you find a way to borrow money at a rate <5% of interest payments for that period of time, then you can increase your returns. The typical rate for a trustworthy borrower is 5,69% per year. If you know about 5% price move that's gonna happen over 1/2 a year, then you should borrow as much money as they are willing to lend you and get roughly 4% of that after all. Unfortunately, there's not so many places you can borrow big sums of money for stock market purposes. Maybe it changes when you have a lot of money already, and some legal status, Idk. But in essence, one would not expect that a hedge fund can borrow much more money than what investors already gave to it, or else it would do it all the time. So naively you expect that your returns will still be of order 5% of what your investors gave you, even if you are a hedge fund.

But there are plenty of financial instruments that circumvent it, most of which are not available to simple people. One thing would be leverage. As far as I understand, hedge fund can make an agreement with a broker about investing money 1:20 into this opportunity. Then, if the actual price reaches -5% at any point in that 1/2 a year, hedge fund loses everything. But if it actually goes +5% as expected, hedge fund doubles the money, getting +100% out of known 5% change of a given instrument. Another way of thinking about it: hedge fund finds a person who is willing to make a bet on all this money that the price is not gonna go move 5% that direction.

Christian Bale plays Michael Burry in ‘The Big Short.’

So when one of the main characters (played by Christian Bale?) was drawing numbers on the board: first -119% when the price did something unexpected, but then +440% when it went the way he expected, this is essentially what was happening. The housing prices dropped, say by 60%, after rising by 30%, counting from the moment he shorted the housing market. His bare returns are +30%. If he used the leverage instrument, he needed 1:14 to get his 440%. So he could only afford prices going up by 1/14, or 8%. If they went 9%, he'd lose everything. How could he afford 30% rise on his leveraged short position? And still be only in -119%, not in -440% as the symmetry would suggest?

First of all, he did not put all of his fund's money into shorting the housing market. But that doesn't help: to have 440% returns, he needed to have -440% loss when the price went the opposite direction. Which would bust him. The resolution is that, first, even though the housing market that we see was down by 60%, he shorted some more extreme instruments that were down by almost 100%. Second, to short them, he used Credit Default Swaps, that has been around for decades, just that nobody thought of using them on a housing market.

It is good to note that he made his decision to trade based only only the publicly available information. Using insider's information about upcoming price motions to make money is something you can go to jail for.

Another concept that movie covers are CDO's: a packs of loans that are offered by a bank to investors to provide money for. The movie drives the point home that anyone who was working in the bank on getting those CDO's approved and sold insurance on them was acting completely irresponsible and should go to jail (although almost noone did).

Much blamed CDO's still exist, although in a heavily regulated fashion. Banks still don't do a proper investigation of individual borrowers. However there are web-based platforms Lending club and Prosper that do the bank's job of connecting capital and borrowers without "black boxing" where the money goes. Careful investors can review every single loan app. For big investors, there's even a startup Theorem LP, that's a third party optimization/machine learning that helps quickly scan all the loan requests for reliable ones. They managed to double the return of a naive investment.

Their fees are twofold: there's a 1% fee for putting money into account, and standard hedge fund 10% fee on profits. The minimum account value is 1M$. So essentially what this company is doing is what big banks failed to do during the 2008: carefully review each loan application. It also claims to sometimes provide liquidity to those who want to withdraw (option not available to regular investors on Lending Club), and identify recession years and be even more stringent in the screening during those years. The defaults usually lag 0.5 years behind the economy collapse. Here's a neat data visualization by Bloomberg.