The cries of Plutus – Why Greece should exit the Euro

With each passing day the Greek economy is pushed deeper into to the abyss, a country halted by strikes; people burdened with taxes; a government saddled with debt and a nation with uncertain fate.

Not only is it unfair for the common Greek citizens to pay for the folly of the bankers but living under a flawed economic structure – “The Euro” that is destined to create disparity instead of parity, they are also paying for the misjudgments and hubris of their politicians and economic elites.

A single currency area is equivalent to a monopolised business where the consumer is at the mercy of the industrialist only that this type of system can be termed as a "foreign social monopoly”. As one can see that the name itself encapsulates all the possible social and economic evils. By giving away the right to the printing presses not only the Greeks and other European countries have given away their economic fates to foreign masters but have also possibly given away their democratic ethos.

Let me elaborate, a currency may be a store of value for an individual but for a society at large it is nothing but a way to transfer wealth. Remember a currency is nothing but a short term government liability and so a currency note printed by the Central Bank and given to banks increases the assets of the banks but at the same time increases the liabilities of the government by an equal amount, so net impact on global wealth; “zero”. However this increase in government liability now has to be serviced by ordinary citizens; and how do we expect the citizens to service it…. Well by either putting in more hours than usual at work at same pay or giving away more from their existing share of their income to the government in form of taxes. The net effect of this whole guerilla circus is that the citizens end up giving more of their personal income to the banks in form of taxes or in form of harder workload.

So an increase or decrease in the currency supply doesn't actually change the overall wealth of the society; it simply moves it from one person to the other. This phenomenon of wealth transfer is quite apparent and common these days when the Central Banks prints a lot of money so let me explain what happens when this supply reduces.

So let’s assume that 2 people A&B have one euro each and vie for a product, they both can acquire it for a euro each. Now as fate would have it, A loses his euro; it simply vanishes from the world, has the world become poorer... NO, as now B can buy two of the same product with his euro, in other words wealth has not been destroyed, just transferred from person A to person B. Governments and Central banks already have monopoly over money creation and thus can easily transfer wealth these days by creating money (here capital owners and debtors benefit over labours and savers) or by destroying it.

By giving away the power to print money this transfer of wealth is now happening not just between individuals but also between countries in Europe. Euro on a consolidated basis is a weaker currency for Germany and a much stronger currency for Greece in other words there are too few euros for Greece and too many for Germany, remember a loose currency transfers wealth from labour to holders of capital and strong currency transfers it back to the labour.

So with such a strong currency there is little incentive for the capitalists in Greece to setup industries and employ people as a result the government ends up employing too many people (over 40% is government contribution to Greek GDP) and government true to its nature ends up making lofty promises, running exorbitant debt that now it cannot repay. Such a condition is advantageous for a country like Germany; this is not to say that Germany and German workers are not good at their work but this provides an even extra edge as with little competition from Greek internal industries it ends up selling lots of its products.

Had Greece been able to use its drachma it would certainly have devalued its currency by printing more money and thereby transferring some of the wealth from its labour to its capital holders, thus unleashing the country’s entrepreneurial spirit and giving an incentive for more people to start industries.

A monopolised currency system in any case is flawed but a common currency area is structurally and economically wrong and as we are seeing today has disastrous consequences. This would never lead to convergence but always a divergence away from the normal equilibrium. The leaders must accept their past mistakes and bring an end to this euro experiment else it will not just bankrupt many nations and benefit just a few but it could seriously jeopardise not just our economic but even our democratic setup. It was this land of acropolis which was the cradle of our modern day democratic system; today Greece should again pick the baton to preserve the same very values that it stood for. It’s time for Greece to exit this common currency experiment and in the process pave the path for others to follow.

My Article Published in Hindu Business Line on Oct 1, 2011

Options - The Pricing Ways Continued.......

Today let’s take a break from economic issues and get back to option pricing. In continuation with my last piece on option pricing (Link) , wherein we explored a much easier way to price options and what was even better was that it allowed for the flexibility to have non-normal probability distribution in pricing. Today I would like to write about how we can develop the concept further to include in the money and out of money options. Well if one understands the basic premise of my last article on this topic it’s fairly simple.

As I wrote before, basically if I buy an “At the money” call and put, the price that I should pay is the expected movement of the stock in that period. So in essence

C+P = E[S] – Eq 1

Now for any option that is “In the money” for the buyer to make any money and for the seller to loose money would be when the Stock crosses the Strike price of the option, so in essence what we really care about are the probabilities wherein the Stock Price crosses the Strike Price of the option.

So the price of the option would be:

C = (S-K) +E[ ∑_x=kⁿ p_x*S]

The above formula gives the flexibility to the reader to assume different probability distributions and use them in the option pricing.

Please Note that If I try to simplify the Black Scholes model i.e. take the assumption of Normal probability distribution I would be only be approximating the pricing, but nevertheless let me put it down anyways.

The call price (assuming interest rates as negligible) c = SN(d1) – KN(d2), the put formula is also accordingly KN(-d2) – SN(-d1),

c= SN(ln(S/K) + σ/2*√t) – KN(ln(S/K) - σ/2*√t), Since We are taking volatility for the entire duration of the option so I am going to replace σ*√t with σ .

Also I would express S in terms of K and σ as that’s what we are concerned about, i.e.

S = K+ K*σ*Ɵ

Putting these values into the Black Scholes formula and expanding the log portion using taylor equation the log portion would be reduced to Ɵ – Ɵ^2* σ/2

Finally adding both these terms and using the Normal expansion and exponential expansion by taylor series

N(x) =[∫_-∞⁰exp^^{- (x)^2}  + ∫₀ ^σ/2exp^^{- (x)^2}]/sqrt(2 π)

The first part is equal to 0.5, to integrate the second part of the expression let me expand it using the Taylor series. The Taylor series expansion of the exponential term is

e^x = 1 + x + x^2/2! + x^3/3! ……

Replacing x by Ɵ – Ɵ^2* σ/2+σ/2 and then integrating we get

N(Ɵ – Ɵ^2* σ/2+σ/2) = 0.5+ [₀ ^σ/2 ∑₀ⁿ (-1) ⁿ (Ɵ – Ɵ^2* σ/2+σ/2 )²ⁿ⁺¹/2ⁿn!(2n+1)] /sqrt(2 π)

As SD is small number (in decimals) we can ignore the higher power of σ,

Please note that if σ is high the whole notion of Normality falls apart and as does the Black Scholes model.

So expanding this expression and putting it in Eq 1 we get

C = (2* Ɵ - Ɵ^2* σ/2 + σ) * √(1/2π)  

Or more simply C = (2* Ɵ + σ) * √(1/2π)

Again this is simplying Black Scholes using mathematical tools what’s more important to understand is that the genesis of any option pricing i.e. using any probability distribution is this formula below:

C = (S-K) +E[ ∑_x=kⁿ p_x*S]

Till Next Time………….

Failure is the option

Writing after a long time indeed, got stuck in some daily chores and also reduced travel in the last couple of months gave me less time to think. Anyways here it goes now; also I did put up this article at Business Insider yesterday.

The high unemployment rate that has engulfed the major economies of the world is not just serious but also bewildering and these moments of pain and awe among the population is when governments try to intefere and curb the freedom of the society, the case in point being the new excess stimulus plan of Obama. After all wasn't capitalism supposed to allocate the resources efficiently then why is that we have 16% unemployment in US (U6), over 30% youth unemployment in Spain, Greece, Italy. I mean the problem of this world is fall output and so isn't it ironic that with so much unemployment around we are taking about this problem. A garbage reason that I always listen on television by many analysts and CEO's is that of lot of policy uncertainty which is leading to this bemusing irony. Well this may be playing a very small part in e scheme of things as I find it hard to believe that policy makers of a few decades back were far idealistic, efficient and superior than what the are now. The real reason for this catharsis is that the world we are living in is no longer free markets or the economic order is no longer capitalist but "crony capitalist"

Recessions, fall in stock prices and asset prices in general and failure of big and mighty are features of capitalism wherein it reorganises resources and efficiently allocates it to new sectors, people and industries which then take it forward thus creating jobs and continuing the boom. Unfortunately now even a 10-15% stock market fall is followed up by printing of money by the Central Bank of US, companies like GE and GM are saved under the garb of avoid huge job losses and of course the banks and the financial institutions (the less said of those the better) these institutions that add very little value in this society but for continuing the ponzi currency scheme. What's worse is that with every time they being saved under the farce too big to fail these banks have raked in too much of the economic resources.

What's required is not another failed government induced spending plan but instead the government getting out of the way of this economic reset, let the markets crash if ey have to and the companies and banks go bankrupt... There will be brief period of chaos followed by a new reinvigorated order as new capable people take over those deflated resources and as the capital froth from those assets move to new places thus creating opportunities from our young entrepreneurs and providing jobs to millions. Socialism and today's crony capitalism suffer from the same problem "misallocation of resources" the only difference is that while socialism gives less to the competent, crony capitalism gives almost everything to the incompetent but not letting them fail.


In the next article (sometime this month only) probably we shall talk about how this increase in government debt ends up doing no good but preserving the existing world order of ponzi banks and its monetary system.

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…………

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 p_k*abs(S-x_k), Now if I assume that the distribution is leptokurtic (fat tailed – high kurtosis)

p_kl lim_s->0(probability of leptokurtic distribution close to mean) ≤  p_km lim_s->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)

Now-

p_kl lim_s->∞(probability of leptokurtic distribution far away from mean) >>  p_km lim_s->∞(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 a_k^2+S^2]/n, S>> a_k

MD₁ (d₁) = [∑_k=0ⁿ a_k + S]/n, S>> a_k

σ₂  = √[∑_k=0ⁿ⁺¹ a_k^2]/n

MD₂ (d₂) = [∑_k=0ⁿ⁺¹ a_k]/n

Since S>> a_k 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………..

Black Scholes Conundrum Concised

I have never been enthused by this model after I left college. Not only large parts of this model’s derivation is taken from the seminal yet unnoticed paper of its time by Louis Bachelier but also the assumption of normality reduces it to be worth for the books of economic and financial history than otherwise.  What’s even worse is that this started a trend that tried to bring this subject of financial economics more apt as a social science into the realms of physical sciences. Anyways for those inclined to use this model or still revere it with some awe let me make your life simple. In one of my insomniac nights I worked upon this derivation, I would cut the entire crap used in the derivation of Black Scholes band bring out the same model in a very simple form. So here we go.

PS: The content would be a little technical but can be easily understood with a few minutes of patience as the mathematics is pretty simple (as was the aim of this whole exercise)

Basically if I buy a call and a put, the price that I should pay is the expected movement of the stock in that period. So in essence

C+P = E[S]  - Eq 1

After time t, where t is the maturity of the option. Now in the realm of Black Scholes the distribution of the returns from the stock is Normal. So instead of using the expected return E[S] I have to be using the Standard deviation or √E[S^²] and the relationship between √E[S^²] and E[S]in the world of Normality is pretty simple:

E[S]/ √E[S^²] = √(2/π) – Eq 2

We can also represent √E[S^²]  by σ so in essence Eq 2 now becomes

E[S] = √(2/π) * σ

Hence Eq 1 now becomes

(C+P)/S =  √(2/π) * σ

For At the money options (the starting point from where deviations are computed can be taken as 0) and assuming interest rates as negligible C≈P. Hence

2C/S = √(2/π) * σ or C/S = √(1/2π) * σ

That’s it……….. the price of the option is the standard deviation of the underlying asset divided by the square root of 2π

Now let me get to this equation by reducing the Black Scholes model. Later some other day I shall give you the proof by using geometric interpretation.

The call price (assuming interest rates as negligible) c = SN(d1) – KN(d2), the put formula is also accordingly KN(-d2) – SN(-d1), We are taking the case of At the money option as it is convenient to show. So for At the money option.

c= SN(σ/2*√t) – KN(-σ/2*√t), Since We are taking volatility for the entire duration of the option so I am going to replace σ*√t with σ and K by S (as the option is At the money). Hence

c= SN(σ/2) – SN(-σ/2), N(-σ/2) = 1- N(σ/2),

c= S(2 N(σ/2) -1), Similary p = S(2 N(σ/2) -1), Hence

c+p = 2S(2 N(σ/2) -1), as c=p Hence,

c/S = (2 N(σ/2) -1) – Eq 1, Now

N(σ/2) =[∫_-∞⁰exp^^{- (σ/2)^2}  + ∫₀ ^σ/2exp^^{- (σ/2)^2}]/sqrt(2 π)

The first part is equal to 0.5, to integrate the second part of the expression let me expand it using the Taylor series. The Taylor series expansion of the exponential term is

e^x = 1 + x + x^2/2! + x^3/3! ……

replacing x by σ/2 and then integrating we get

N(σ/2) = 0.5+ [₀ ^σ/2 ∑₀ⁿ (-1) ⁿ σ²ⁿ⁺¹/2ⁿn!(2n+1)] /sqrt(2 π)

As SD is small number (in decimals) we can ignore the higher power of σ,

Please note that if σ is high the whole notion of Normality falls apart and as does the Black Scholes model.

So expanding this expression and putting it in Eq 1 we get

c/S = [σ]/ sqrt(2 π) as we got it earlier without this whole and dance.

This expression is for At the Money options at negligible interest rates. We can do it for out of money/in the money options as well and introducing a little bit of interest rates also. So in anycase, next time if you feel bound to calculate volatility or option price using the assumptions of Normality for At the money options your formula is

C/S = √(1/2π) * σ

I wasn’t able to write anything last month so the next one would hopefully follow soon…….