In the face of highly adverse moves, when risk managers are faced with the need to liquidate an equity portfolio, they often face significant slippage and additional losses due to lack of liquidity. Thus, it is common for firms to assess a liquidity addon component to the margin or capital requirement for a portfolio that holds large, concentration positions in illiquid securities. The common technique for this is to compare the size of a position in a security with the Average Daily Volume (ADV). In this paper I discuss the inadequacy of a simple ADV and propose a new method for calculating Liquidity addons.
The article was published in Risk.Net in Sept 2021 and can be found here:
He spent his entire day lying in bed at the age of 88, suffering from multiple age related ailments, needing assistance with mobility, eating and for basic hygiene functions. Alone with just a male attendant for company, his estranged younger son lived upstairs with no time for him, he thought of his wife who had an untimely death a year ago. His other children lived in faraway lands and despite visits, with little ability to communicate; he mostly just shed some tears. While not a religious person, you could hear him cry, “Hai Ram1, please have mercy and let me go.”
Was death bad for him? Thomas Nagel, the contemporary American philosopher would say definitely yes. In his chapter “Death”2, Nagel believes that all deaths are bad and he defends “…the natural view that death is an evil because it brings to an end all the goods that life contains…”
Death could be bad due to the separation of friends and family as well the process of death could be bad, but when discussing the badness of death, we want to talk about what is bad about death for you. Death is not intrinsically bad because when you are dead, there is no you for it to be bad for; death cannot be instrumentally bad as nothing else can happen after you are dead so it can only be comparatively bad, as Nagel says “If death is an evil at all, it cannot be because of its positive features, but only because of what it deprives us.” He states that it is the loss of life, rather than the state of death that makes it bad. This is the “deprivation account” view of death that Nagel holds in which death deprives a person of all the goods that life contains, and he states “..death, no matter how inevitable, is an abrupt cancellation of indefinitely extensive possible goods..” Nagel does little in the way of discussing the value or quantity of deprivation as it pertains to the badness of death, and we will discuss this some more later.
The main objection to Nagel’s view comes from the thoughts of ancient philosopher Epicurus3 who says “So death, the most terrifying of ills, is nothing to us, since as long as we exist, death is not with us; but when death come, then we do not exist..” Thus, Epicurus believes that death is not really bad and we should not worry about it. Epicurus’ argument is rather simple and elegant: 1) There is an existence requirement for something to be bad for you, 2) when you are dead you don’t exist, 3) So death cannot be bad for you. We see similar views about death not being bad in other ancient philosophies, such as Taoism4 which sees death as a part of the eternal force which all of us need to accept and live with peacefully and it encourages people to focus on life rather than death, as it is inevitable.
We now have a view of death being bad, regardless of the conditions, and we have a view that death cannot be bad. How do we reconcile these and how do we thus think about death in our lives? Most humans do think about death at some and often many times in their lives. Most of us have some level of worry, fear and at the minimum, concern about death, so it is very difficult for us to simply accept that death is not bad and ignore it. How should we think about death so that it influences the way we live our actual lives? As Spinoza says, “Insofar as the mind understands all things are necessary, so far has it greater power over the effects, or suffers less from them.”5 An understanding of how to think about death, could avoid unnecessary anxiety and suffering caused during our life despite deaths inevitability.
Religion offers one solution, most of which maintain a dualistic stance, i.e. they believe in some form of soul and some form of an afterlife or continuation of something after the body dies. In this account, death is not an end, the soul will go to heaven or hell, the soul will reincarnate or transforms into some other life form. There are multiple versions of these, but they tend to either create a further fear of death (in the heaven or hell version) or a complete resignation (in the reincarnation version}. For a physicalist of course, there is no solution offered here.
If we have difficulty completely rejecting that death is not bad, to understand the badness of death, we need to return to the deprivation theory and look at it a little deeper. Nagel says “There are elements which, if added to one’s experience, make life better; there are other elements which if added to one’s experience, make life worse. But what remains when these are set aside is not merely neutral: it is emphatically positive.” Kagan, in his book “Death”6, helps to make sense of this in his explanation of the value of life and Nagel’s believes in the valuable container version which assigns value to being alive itself along with the contents. Thus, following Nagel’s view, regardless of the contents of the container of life, since the container itself has value, death, no matter when it happens, deprives us of something.
One criticism on Nagel’s approach is that he seems to view at the topics of life and death on the average, despite that fact that death is unpredictable, has a range of time of occurrence, has many forms it can take and has very different processes leading up to it. The average approach gives us little real insight into dealing with the topic of death on an individual level and thus I believe that we should also be concerned about the particular badness at death, i.e. based on individual conditions and circumstances.
To create a model of the value of life and relate it to death, we look at alternative deprivation theories. Kagan expresses support of the deprivation theory but believes in a neutral container model of life, in which just being alive does not have value in itself without the experiences to fill it. This leads to a fairly simplistic model of the value of life and thus the deprivation when death occurs, which decreases with age, the largest being just after birth. This model can be represented by a graph that could look similar to this:
On casual observation, this works quite well – the longer the life, the greater the loss due to death and thus greater the badness of death. One major objection to this is the issue of transitivity at the time of birth. The maximum value of life is just after one is born, with no value just before, thus leading to a discontinuity. Several contemporary philosophers have weighed in on this and offered alternative models on the value of life and the badness of death, including Jeff McMahan, with his Life Comparative account7 and John Broome, with his Critical Level Utilitarianism model7. A complete discussion of these are outside the scope of this paper, although incorporating some of their thoughts, I suggest by own model in which the value of life for the average person, who lives a normal 80-90 year old life would look something like this:
When death occurs, the right hand area of the graph from that point on, would represent the potential of goods and experience that the person was deprived of, thus represents the value of the badness of the death. For a person that say has a terminal illness at the age of 40, the graph would descend very quickly from that point on and the deprivation value thereafter drops significantly. Thus viewing the value of a life conditional on a life’s circumstances with a similar model provides a basis for the value of the deprivation in case of death.
The entire discussion so far has focused on the value of the goods and experience that is lost on death, which is the basis for the deprivation model. However it seems worth exploring the life one has lived in determining the badness of death. Tolstoy’s Ivan Ilych8 is only about 45 years old and is suffering from an accident related life threatening ailment. He suffers mental anguish from his condition and asks “Why me?”, which can be interpreted as a lament about dying too young and thus the loss of life’s potential – i.e. the right hand part of his life graph. But he also looks at the life he has lived and realizes it has been shallow and unfulfilling. Ivan’s death is not just bad from the deprivation of potential goods but is also bad because he has not experienced or lived a fulfilling life. Thus I would like to venture to add another variable to the value of a life relating to the live lived.
If you are told you will die tomorrow – ask yourself – “have you had a life worth living – has your life been fulfilling?” Then look are what you are being deprived of by death. Given the latter being non-negligible, if the former is much more than the latter, then your death may not be bad for you and you can go in peace. If you are like Ivan and with a shallow, unlived live and the deprivation is also large – your death will be bad for you as you will not have the chance to live a fulfilled life. This may see counterintuitive, but it measures the badness of death not only on the deprivation, but also with the view that everyone deserves the opportunity to LIVE life. This sentiment is also echoed by Kagan in his chapter on Living in the face of death. One objection to this account would be the implication that a life better lived is a less objectionable death. This is actually untrue as the necessary condition is the difference between the live lived and the amount of potential deprivation. This in no way encourages seeking death but gives a formula for confronting death. In the chapter on Suicide, Kagan’s rationality argument also follows a similar thought as it is possible somebody’s life would be so full of suffering, failure, with no serious prospect of recovery, that death would be better on balance. Gillian Bennet9 in her note said, “I have had a husband beyond compare, and children and grandchildren who have outstripped me in most meaningful ways”, showing how she has had a fulfilling life, yet also says, “Dementia is taking its toll and I have nearly lost myself”, thus stating the forward value she will be deprived of was very little – so death to her was not bad and arguably good.
Thus I conclude that it not rational to describe death in the binary version of bad or non-bad, but rather death, while often bad, has a range of levels of badness that are conditional on the individual and in some cases can actually be good.
I return to my father who I opened this paper with. He finally did die. He had lived a life as well as he could and given his condition there was no value in his continued living – so death was definitely not bad and as like Gillian, while it hurts me to say this, his death was good.
References
1. Ram is an Indian diety, often worshiped as a god
2. Nagel, Thomas. “Death.” in Mortal Questions. New York: Cambridge University Press, 1979
3. Konstan, David, “Epicurus”, The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.)
