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Margin requirement calculations for complex options portfolio

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Summary

Equity option margin requirements in the U.S. markets are usually determined by either a Regulation T rule for regular customer accounts, covering most retail customers, or by Customer Portfolio Margin covering more sophisticated option portfolios.

The result is a fragmented, inconsistent options margining framework in the U.S. that needs an overhaul, recommendations for which are provided at the end.

Click here to download the paper.

The Good Life Compass

We have learned about the Purusarthas with the different activity spheres represented by Dharma, Artha, Kama and Moksa.  We have read many texts with stories of characters navigating each of these.  We now need to design our “Good Life Compass” incorporating these along with a description on how to use it. The word “compass” however is be taken figuratively and not literally as it could represent some other form of a device or guide.

To design a compass, we need to first understand if all these spheres should be included.  We have seen constructs of just dharma, artha and kama with moksa either on top of them or off to the side with some form of connection.  In the texts we do notice that there is a lack of theorization of the group of 3 or 4, but focus on each one individually. Scholars offer varying opinion on this.  Halbfass1, says “..[all four of ]the puruṣārthas are simultaneously essential attributes and constituents of humanity. It is in the nature of humanity to be an arthin [a being with goals].”  In the text themselves, we see in MDhŚ2 it says that  “…the established teaching is that the triple path is the best”, leaving moksha aside.

Is moksa even an activity sphere at all? Moksa is understood to be the cessation of suffering, the attainment of bliss, release from the cycle of rebirth, etc. and thus devoid of actual activity as understood by the other 3 activity spheres.  Even Yudhiṣṭhira in the MBh3 says of moksa. “One cannot attain moksa by doing any deed. Know that what is going to be all comes to be. Even he who lacks some of the group of three finds moksa”

This suggests it should stand on its own.  Malamoud4  says “…it is always possible to make dharma, artha or kdma into the + 1 that encompasses the two other terms in the list, and the moksa to boot..”  and continues to say  “..in the usual interpretation, it cannot encompass the other purusarthas, specially artha and kama, as not only does it transcend them, but, also negates them. Their functioning may be taken as a positive sign of the fact that not only has moksa not yet been achieved, but that it is not even being striven for.” This suggests that moksa is mutually exclusive to the others in a way.

To determine how to incorporate moksa into our compass, I prefer to look at it from a contemporary life perspective, as after all, we are trying to define a good life compass for our life now.  In our pragmatic good life compass, instead of looking at moksa as a practice to lead one to an “ultimate felicity” such as nirvāṇa or think of this activity sphere as a form of renouncement for  achieving liberation from suffering in the cycle of rebirths, I prefer to look at it as a sense of freedom and lack of attachment. Not freedom within the socio-political world, but freedom from the strivings that generate and sustain agents in this world. Freedom from strivings and the great sense of power that this creates in oneself.

With this context, in the construct of the compass, I choose to have all the 4 together.  This is also suggested by Professor K. J. Shah5, in which he says that the purusarthas as goals of human life should be treated as interactional in character, and says, “We must realize that artha will not be a purusartha unless it is in accord with kama, dharma and moksa’, kama in turn will not be kama, unless it is in accord with dharma and moksa; and dharma will not be dharma, unless it too is in accord with moksa. Equally moksa will not be moksa without the content of dharma; dharma will not be dharma without the content of kama and artha. The four goals, therefore, constitute one single goal, though in the lives of individuals the elements may get varying emphasis for various reasons.”

So now we have our construct. But any good compass or guidance system requires, by definition, some objective measures.  These measures inform the compass and the user when something is out of balance, when one measure too large or too small – and these objective measures work together by way of a set of rules and logic.

Does such objectivity exist when it comes to the activity spheres in our compass, so that our compass knows how to guide us into living a good life?  There are certain qualities of objective measure, e.g. hierarchy in order to define the logic and exactly what defines balance. In additional a good guidance system will have achievable metrics and goals and “next steps” based on these. Do the components of our compass have such hierarchy, measure, metrics, rules etc.  We turn to the texts now to look for these.

First let us look at dharma. From the MDhŚ2 we see that dharma is about who you are (as a member of a corporate group) and where you are in your phase of life. It is broad and capacious and thus very context sensitive. From the Ramayana we see several scenes in which dharma seems highly subjective and open to individual justification, such as the killing of Valin by Rama or the treatment of Soorpanaka by Rama and Lakshman.

In the Mahabharata, even with the clearly adharmic treatment of Draupadi, Bhiṣṃa can only say that, “As dharma is subtle, my dear, I fail to resolve your question in the proper way”
In addition, there is the plurality of authority in dharma with sva-dharma and sadharana dharma as we see when Bhima challenges Yudhishtra’s view when in the forest or when Arjun puts down his bow at the beginning of the Bhagawad Gita.

Throughout the texts we see little or no evidence of a measure or objectivity of dharma, in fact we even see the need to forsake dharma for the sake of dharma. This leaves us with a picture of dharma that is highly subjective, context sensitive, open to justification and very subtle – making it difficult to put into an instrument like a compass.

Now to look at artha, which is described as the means of life, and includes material prosperity, security and health of oneself and those one feels responsible for. The thriving of humans requires artha – that is, economic activity, wealth and its creation, worldly success, profit, political success and all that is necessary for human existence. Thus, it seems that artha should be measurable.  However, referring to the texts, once again we see no mention of a measure of prosperity or success.  In fact in the first chapter of the Panchatantra6 it says Earning the money when you don ‘t have it, guarding what you have earned, increasing it as you guard it, and then giving it away to worthy people when it has increased- that is the way to live in this world” implying that having the wealth based on ones own needs and not the accumulation of wealth is one of the essence of artha. 

But Kautilya in the MR7 shows us that besides the instrumentality of artha there is a non-instrumental artha and for the sake of artha it could be required to put aside artha.

We also see that artha, like dharma, is justifiable and not always objective, as in the Panchatantra6 when Damanaka justifies having Pingalaka kill Sanjivaka because of what he considers bad policy.

Is there a hierarchy of dharma and artha?  In the MBh3 we are alerted to the dangers of setting aside Dharma for Artha as it leads to pretty much the destruction of the world, caused by Duryodhana who believed, “…the way of kings differs from the way of the world, and that therefore the king should endeavor always to think of his own profit (artha).”  The MBh3 suggests without maintaining Dharma, nothing is held together, pursue Artha, violate Dharma, and see, everything will fall apart.

But then we see episodes in the Ramayana of Rama forsaking his dharma when he banishes Sita in order to please the polity, thus for the sake of artha. In the MBh3 We see several incidents of deception, such as the killing of Drona, in which even Krishna says “…. we must put aside dharma and resort to stratagem to conquer him..”

So once again we come away with little objectivity and no clear metrics for even the artha activity sphere as well as no clear hierarchy between dharma and artha and their juxtaposition being highly contextual.

Turning to Kama, which means desire, wish or longing. While often used to refer to sexual desire, it largely refers to any sensory enjoyment, emotional attraction and aesthetic pleasure such as from arts, dance, music, painting, sculpture and nature.  In the MBh3, Bhima says Without Kāma, there cannot be any striving on any activity sphere. Seeking Dharma and Artha are entirely dependent upon Kāma. Even the seers were joined to Kāma when they were intent upon their asceticism…”.

Throughout the texts, there seems to continuous push and pull of extolling the virtues of kama with warnings of the dangers of kama. In the MBh3every imaginable form of uncontrolled kama and its consequences is depicted. Shantanu’s inability to control his longing for Satyavati.  Karna’s yearning for recognition and lust for status resulted in possibly unhealthy attachments. In the Gita, Krishna praised Kama but warned us against it too. So long as Kama is under your control, it is divine. When it goes haywire, it turns demoniac, which he advised Arjuna to renounce.
So once again we are left with little to no objectivity on the extent of kama as an activity.

The hierarchy between all the purusarthas has been the continuous subject of discussion and debate. Even in the Mahabharata, Yudhisthira, the four brothers and Vidura all have very different views on the relative position and importance of each.

Given the distinctive nature of each of the purusarthas and the lack of a prescriptive hierarchy,  the good life compass is highly context sensitive to each of us individually. Thus, it is clear that we can’t design an objective measuring instrument like a compass or a gyroscope or a FitBit to guide us to a good life. However, is there something than can still be designed? It is possible that our compass is purely informational, with no judgement, no recommendation, no guidance or advice.  Possibly a place where we can record our activities and it informs us of whether we are been more focused or involved in one or there (or several). This would then let us rebalance our activities and not let any one get out of hand or destroy the others. This seems like it would be a useful device or say app.

But then, I would venture to say, after the realization and use of such and app, one should simply throw it away.  Let this become innate to us, in our minds, hearts and souls, such that we don’t need something to tell us that we may be out of balance, but we know and sense that from within.  So, when you get too busy in the rat race at work, you reflect on this and take time for your spouse, kids and some enjoyment. When you are out hanging out with buddies and playing poker too often, you remember your obligations as a provider to your family.   Then the compass becomes within us and is always helping guide us in these spheres of human activity, maintaining balance and harmony and leading us through this life as a good life.

  • References
  • 1. Wilhelm Halbfass India and Europe. An Essay in Understanding.
  • 2. MDhS: Manavadharmasastrs, Manu’s Code of Law
  • 3. Mbh:  The Mahabharata
  • 4.Charles Malamoud, On the rhetoric and semantics of purusartha
  • 5.Daya Krishna. Indian Philosophy, a counter perspective
  • 6. Patrick Olivelle, Panchatantra, The book of India’s Folk Wisdom
  • 7. Mudrarakshasa

It’s our time to serve

Our family received some stimulus money, received a refund from the insurance company and my kid’s colleges gave us money back.  I am spending no money on commuting or eating out and dry cleaning and so on.  My job is secure (at least I hope so) and so things are going well – expect for the minor inconvenience of being cooped up at home. So, it feels odd taking this money.

Do you remember going to a restaurant with friends and family and being served a nice meal; do you remember sitting at a bar and having the bartender make you a fantastic cocktail; do you remember your barber and the banter about sports and local politics. When you needed some new clothes, do you remember the store clerk that helped you out or the nameless barista who made your weird coffee drink each morning before work.  Well now is time to remember all these people and many more who helped make our day to day life a little easier, a little better. They are out of jobs, struggling to put food on their tables and not sure what lies ahead for them.  Sure, some may have got a stimulus check, some are getting unemployment, but that is not a replacement for a regular job. They are living with the worry of making ends meet today along with the distress of how they will manage tomorrow. And then there are thousands that will get nothing at all, for example a kid I know, son of a waitress and father that cannot work, putting himself through college by working odd jobs – will not get any government aid and has no job.

So, we decided to donate any money we got to help our local community.  And  I urge all of you that may be getting some money back and are lucky to have a steady job still, please remember all those who served you – it is now our time to serve them and help them in their time of need. Find a local community organization that is directly helping to put food on their tables, helping to support their families and give whatever you can. It is our duty and the right thing to do.

Model for Covid-19 in the US

Using some assumptions driven from recent data and current response rate, I have built a fairly simple model to predict the number of COVID-19 cases that will be seen in the U.S.

The model starts with Seattle which reported its first case around Jan 21st.  It didn’t go into an emergency state till the end of February.

The model assumes an average rate of infection after the average incubation period.  It also assumes a ratio of local infection and infections that travel to other areas. This leads to the model’s idea of clusters.  When an infection travels to another area, it creates a cluster.  In a cluster, once a certain number of cases are detected, the area typically goes into a state of lockdown and emergency.   The result of this should be a quickly declining spread and stopping of creating of additional clusters. The model assumes a more and more aggressive reaction response, based on recent data where some places when into emergency or lockdown mode after just 4 reported cases.

The further modeling of areas that are in actual or virtual lockdown is the difficult part as there is no clear data on how quickly the spread will stop. 

The model shows that currently there are close to 19,000 people in the US that are already infected.  Most of them were infected in the 1st week of March and thus are starting to show symptoms now. Thus over the next week or so, the number or confirmed cases will rise dramatically from the last reported 2500 or so.

The model estimates that the total number of infected cases will rise to somewhere between 22,000-25,000 after which the transmission will slow down significantly and essentially be contained. It is estimated that this will happen around the second week of April.

Below is a graph of the estimate from the model.

Of course, no one knows exactly what will happen. The model was built was a rather simple, but logical, set of assumptions and was driven by observed data so far in the US and other countries, but this data is what I found on the internet, which in itself is a bit flawed.

Nature

I was in Kentucky visiting friends who took me on a short hike on Berea forest trails. These friends are “bird” people – bird watchers and photographers.  So, on the hike, we would stop often when they heard some bird and they would look up to try and capture a photograph – which I also got into and starting pointing out birds in the canopy of the trees. When I saw them my description limited to “…a small black one there..” or “…a large black one over here…”.  They would look at it and say something like, “…that’s a yellow rumped warbler…” and then my friend would take some pictures with the huge lens attached to his camera.

These are what my “little black birds” really looked like!

They live on a 13 acre farm in rural Kentucky, with a view of a pond and lots of trees and vegetation. When I walked down their stairs to their living room I see five cats looking up at me (they are also “cat” people); in the morning the back yard is full of birds looking for food; in the evening the raccoons come around to their porch and eat all the cat food.

My friend, a close buddy from college, got his first SLR a few years ago and now has become a really good bird photographer.  Just around where he lives, and mostly from his porch itself, he has photographed and identified over 130 different bird species.  Some of these are just magnificent, a few pictures below.

The fact that over 130 species in that area of KY alone was mind boggling – well it turns out there are over 10,000 bird species in the world. Add to that all the different mammals, sea creatures, reptiles and the 10 quintillion insects – and we are reminded how vast the living world of nature is.  Human beings share this earth with all these living creatures and only represent one species out of tens of millions.  While it is no doubt that we are the dominant species in modifying, building creating and overcoming our environment to make it easier for us to live, we still only represent a small fraction of all the co-inhabitants of this earth both in numbers and even in actual mass. 

All this is a constant reminder that humans, representing such a small portion of all living beings, have http://simpleyrico.com/31228-dte58853-bumble-dating-website-san-marcos-robby-roden-tx.html no right to destroy the environment, the nature of this world, due to their activities. As Spinoza says, God is Nature and Nature is God. So, let us never forget the environment and our duty to protect it

Action and dharma

Our actions are what define us.  Just thoughts, however good they may be, unless proceeded by action, remain just theoretical.

The philosophical study of action and its motives dates back to Ancient Greece and India.  To be clear, my reference to “action” is intentional action or things that people genuinely do.  

As Aristotle said, in order for a man to perfect his humanity, he must be the best man he can be. To be his manly best, a man not only needed to cultivate proper intentions and an appropriate disposition, but put those intentions into real virtuous action.

In ancient Indian philosophy, the goal of the early portion of the Vedas is action, in particular moral or dharmic.  A human being is defined by his or her actions and the actions are what defines the persons’ dharma.

Even if we aim for virtuous actions, the world has become so complicated that it is hard to know if the action is truly virtuous.  The degrees of freedom between an action and it’s consequence or consequences can be so numerous that it is impossible to know if the action was good. This problem of unintended consequences could have the effect of making almost all actions non-virtuous. So, what is one to do? The only real practical answer is to still act in good faith within one’s cognitive visibility or horizon. Otherwise if we try and analyze too many possibilities it could result in paralysis by analysis.

I personally have always tried to act in a way that is purposeful.  My actions are usually preceded by rational thought and logic, which is somewhat consequential or utilitarian in that I would try and evaluate the course of action by what it can achieve vis a vis other choices.  This has largely been my principle, my dharma and has mostly served me well and it suited my predominantly analytical mindset.

But not too long ago there has been somewhat of a change.  Recently an old colleague asked our college class group for money to help his son’s education, having fallen in difficult times in his career. This was not the first time he had asked, and we all came to know that he has asked other family and friends for money in the past. I thought about this – rationally and logically – and argued against contributing, citing that this has become a ritual and habit of his, that there are better places to put my money, why can’t he send his son to a college within their means and so on and so forth. It all made sense based on the principles that have normally governed my actions.  Then suddenly I contributed. Not out of guilt or coercion, rather it dawned on me that all my analysis was really to serve myself – the only thing that mattered at that time was there was a friend in need and that I could take a small action to help. Period,

Soon after that another incident happened in which an aging family member was raising a fund to support their special needs son so he can live in an appropriate institution.  The immediate analytic assessment was why have they not been planning for this for the last fifty years and so on.  But I stopped short in my tracks and chided myself –  who was I to question their life and their lack of setting enough aside for their son, neither do I know the complete picture and neither am I qualified to judge them.  They have a need and I can help, so I should act, and I did.

The analysis, the justification, the rationalization is sometimes how we attach ourselves to the results or fruits of the action – it seems like we do that more for ourselves, thus in a way it is for selfish means.  While action based on the analysis of the results is clearly still needed in order to achieve certain goals, needs and comforts in life, it was truly liberating to simply act without any analysis, purely on the basis of the need to act, completely without attachment.  I am sure in life there is a balance of the two, which I am yet to figure out. I am not planning on abandoning the dharma that has served me, but the new dharma, if I may call it that, has been satisfying.

Dharma truly is subtle.

Skew Vega

Skew Vega is the exposure of an options portfolio to a change in the implied vol skew, e.g. change in the risk reversal level. While teaching my daughter trigonometry, I realized that using some basic trigonometry, I could easily calculate the Skew vega in the case where there is no functional form (parameterized) volatility surface. Here is a simple and elegant model to calculate the skew vega

Calculating Skew Vega model