Saturday, June 25, 2011

The myth of Wage Increments

Today let’s take a break from the statistical and option pricing articles and discuss something very close to probably every reader of this blog “Salary Increments”, I had almost finished an article on the farce of the PEG ratios however I would post it at some later date.

I would like to believe that I am one the most ardent votary of free markets and contrary to what many people have wrongly built an impression I think that Karl Marx is one of the most original thinkers in the field of economics and whose views are actually not anti-capitalist rather he just exposes the fallacies of capitalism, mind you there is a huge difference between free markets and capitalism. Certainly what has been happening since 1971 after the collapse of the Bretton woods system is hardly free markets, on the contrary it’s the worst form of Communism. The reason I say that is because atleast the communists are open about their ideologies and hence atleast are true to what they say. Our so called proponents of free markets i.e. the respective governments have been imposing centrally planned economies since the last 40 years. However this type of system is even worse because unlike in communism where government controls price of capital and labour, here the government certainly controls the price of labour and transfers that wealth to the capitalists. Let me explain this in a bit more detail by taking the example of “Salary Increments”.

So how was your Salary increment this year, Oh!!! Sorry did it hurt… didn’t get any?? Or were you that unfortunate one who got the middle of the band 10-14%, or were you that star performer who managed that 20% raise!!! Sorry to all but let me break it to you……….. you all have lost out!!!

The labour like in most other countries is paid in currency (government’s proxy banks controlled). So in essence like any competition the labour force is competing for the x amount of cash that exists in this economy. Now let’s say that these banks true to their nature induce an extra 20% cash in the economy, so just to be at par with what you were the last year you should get atleast x*1.2 cash for your labour, this is the minimum amount that you should get and even if you get this you are still not being rewarded for you improvement in productivity that would have happened because of the experience that you gained at work and the knowledge and skills you added in the last one year.

Compared to last year and extra 24-25% of fresh money was created this year, thanks to the base money of RBI and add to that the printing presses of the banks that create money because of the fractional reserve system. Assuming that an extra 4% people joined the Indian workforce and adding that to the workforce even the star performer getting a 20% raise has lost out and who actually ends up at the winning side… that’s right “the capitalists”. Remember price rise is not inflation it is just a symptom of inflation. Inflation is always more money chasing fewer goods so the myth that if the raise is atleast equal to the rate of inflation and hence you are not worse of is nothing more than a false propaganda.

The raise should atleast be equal to the increase in the money supply in the economy net off the increase in labour supply and if we add to that the increase in your productivity because of improvement in skills and knowledge only then we would truly say that you have been justly compensated.

However this is rarely the case that the extra cash ends up with the capitalists who get compensated more than warranted and thus widening the gap between the capitalists and labour. Please don’t misunderstand that I am against them, I am just stating the case as is. The real culprit are the global governments that have monopolized the issuance of base money. If this whole system has to become just then like any other product the issuance of money should be liberalized i.e. anyone should be in a position to issue money and let the invisible hand decide whose money is sound. Remember “money is nothing but a promise” and I certainly never trust the governments.

Alright so this looks like a solution that would not come about before another decade when the whole system would collapse, till that time what to do. Ofcourse the first solution is to start your own business (not everyone’s cup of tea) so the next is going to be based upon the old saying “If you can’t beat them then join them” i.e. invest your money with the capitalists i.e. by buying stocks, third and even better print your own money.. is that possible? Sure it is; taking debt is equivalent to printing your own money, hence take debt and invest, and if you can ride the rabid this fiat money system would ensure that you are much better off, or fourth (the best in my opinion) is to invest in commodities and precious metals… since the entire system is doomed to collapse ultimately the biggest loosers then are going to be the holders of financial capital and the biggest gainers are going to be holder of real/tangible capital (commodity owners) and lastly if one can face the stomach crunches go for the “Random Chalice option” buy those wealth cups (please refer to the very first article of this blog). Surely we all are mature people and capable of taking our own decisions but when you are being cheated in your face it’s important to be cognizant about it and do something about it.

Till next time…………

Friday, June 3, 2011

Statistical Follies

In the previous article I showed how the price of an At the money option is nothing but .8* σ or in other words more generally the expected price movement of the stock. Now I would like to show how we can compute price of any option with much more flexibility i.e “Out of money” or “In the money” and then finally introduce interest rates. The idea behind this whole song and dance is not to attack any existing model etc. because anyways in my opinion they are nothing more than epitome of Platonicity but to provide with sufficient flexibility to price these derivatives under the real practical market conditions which are highly volatile more often than not.
But before that let’s first have a look at what is fundamentally wrong with the financial modeling. As always if the design of the whole building is flawed but the problem lies in the basics or the groundwork and that is what we are going to explore in this article. Again the following content would be a little technical but not a whole lot, since this article series are going to continue for sometime, I have decided to alternatively put out more pleasant read articles after each one these.

With the progression of time it seems and more and more aspects of our society are becoming centrally planned rather than aligned to efficiencies of the free markets.  With everything denoted and measured in government controlled currencies it’s a big sham to call global economies as free markets. Closing the heels is education and knowledge. What awards like Noble Prize etc. ensures is that rather than the forces of free market discovering what type of knowledge/research paper/theory is good for the world, this whole notion ends up in the hands of a few people. Can you believe it a “few good men” I am sure deciding what the coming generations are going to study and based upon that would eventually the future of this planet would get shaped.

Let me pick up the most cardinal concept in statistics – “standard deviation (SD)”. In my last article I showed how the value of an At the Money option is nothing but equal to its Mean Absolute Deviation (MD), we eventually replaced it by 0.8*SD to get it inline with the Black Scholes. Infact as I would show in this article using Mean Absolute Deviation is a far superior method of use in social sciences than SD. So the question:
Why on earth is SD in widespread fashion?
Answer: Happens when few people decide the fate of learning.

In the field of statistics a “statistic” is used for measurement if it has the smallest probable error as an estimate of the population parameter. If the population is perfectly normal then the standard deviation of their individual mean deviations is 14% higher than the standard deviations of their individual standard deviations. Please note the bold italicized word, that’s it… so basically SD is a perfect lab rat however in the field of real social sciences it’s an abject failure. The icing on the cake is that this useless musings are imparted to millions of naïve souls in schools and colleges since almost a century.

Himanshu Jain: “SD as a useless measure in the field of economic science”
Wrong Knowledge is tantamount to a Fukushima whereby even the coming generations pay a heavy price. With these noble thoughts let’s have a look at it’s disastrous consequences. Since I started with the option valuations and the Black Scholes hoax let’s take this topic for example.
Thinking intuitively the price of an option should have been equal to the expected value of the stock or in other words mean deviation. In perfectly normal world of lab rats we replaced it with .8*SD, however stock market returns are anything but normal. Ofcourse with Central Planning of Stock Market these days there can be an illusion of normality. My point if I carry on with MD as the measure of option (instead of replacing it with .8*SD) we find that:
C+P = E[S]  - Eq 1
Expanding E[S] we get:
S*∑k=0n pk*abs(S-xk), Now if I assume that the distribution is leptokurtic (fat tailed – high kurtosis)
pkl lims->0(probability of leptokurtic distribution close to mean) ≤  pkm lims->0(probability of mesokurtic distribution (no excess kurtosis) close to mean).
-          In other words the option prices of At the Money options should be slightly less than what is being computed by using standard volatility measure i.e. SD (σ)
pkl lims->(probability of leptokurtic distribution far away from mean) >>  pkm lims->(probability of mesokurtic distribution (no excess kurtosis) far away from mean).
-          This implies that the prices of out of money options is far lower as estimated by using σ
For someone keeping a Platonic mindset let me put the proof below:
Since σ is calculated by squaring the movements of the deviations from mean, as the deviations increase σ basically explodes when compared to MD. To prove:
σ1  = √[∑k=0n ak^2+S^2]/n, S>> ak
MD1 (d1) = [∑k=0n ak + S]/n, S>> ak
σ2  = √[∑k=0n+1 ak^2]/n
MD2 (d2) = [∑k=0n+1 ak]/n
Since S>> ak d1 -d2 ≈ S/n
And σ1 - σ2 ≈ S/√n , Since n is large in other words it shows that σ explodes parabolically when the deviations  are more meaningful and if SD explodes parabollicaly then think what would happen to kurtosis!!!
The implications of the use of the most fundamental concept of standard deviation in option pricing are enormous. It leads to a clear under pricing of Out of money options while making At the money options slightly expensive and it is this very pricing that we are going to explore soon………..