The Normal distribution is the symmetrical line at the center of the graph
Seydina M. Fall
July 30, 2007
Risk aversion is a concept in economics, finance and psychology that explains the behavior of consumers and investors under uncertainty. It is the reluctance of a person to accept a payoff with an uncertain outcome rather than another scenario with a more certain outcome but a lower reward. Often times, a situation defined as a moral hazard occurs. It is when an individual who is assumed to be risk averse buys a vast amount of insurance and subsequently, acts recklessly by choosing bargains that an otherwise risk averse individual without insurance would not choose.
This moral hazard highlights one of the many issues that economists have faced in trying to predict behavior under uncertainty. One of the most widely accepted theories of human conduct under risk was developed by Harry Markowitz, an economist who won the Nobel Prize of Economics in 1990. Markowitz, in his seminal paper first published in the journal of Finance in 1952, showed that under certain assumptions, risk can be measured, quantified and ultimately eliminated. Markowitz's model is known as Modern Portfolio Theory (MPT).
The MPT is based on the following pretensions: all individuals are risk averse, fit into an archetype known as the Homo-Economicus or economic man, face a tradeoff between risk and return in the short and long run, and reside in a world where time is two dimensional. The MPT model as is the case for the great majority of economics models has been tested using only the tools available in econometrics: a branch of economics that combines formal economics and statistics.
We propose in this essay to extent the scope of tests of the MPT model utilizing cross cultural literature as a tool for testing instead of econometrics. It is then interesting to ask the following question: Can the MPT model explain and predict the risk taking behavior of terrorists and anarchists depicted in the works of Orhan Pamuk (Snow), Marguerite Duras (Hiroshima mon Amour) , Alaa Al Aswany ( The Yacoubian Building), Joseph Conrad ( The Secret Agent) and Naguib Mahfouz (The Day the Leader was Killed. )
Markowitz's MPT model has had a far reaching impact in the world of finance and beyond. Markowitz is commonly referred to as the God Father of modern finance. The popularity of the MPT model is based on its representation of risk as a mathematical equation. The model attempts to assign numbers, specifically probabilities to human behavior under uncertainty. From this time forth, the range of all individual actions according to the MPT falls under a probability distribution called the normal distribution.
The Normal distribution is the symmetrical line at the center of the graph
The normal distribution was first introduced in 1738 by a French Mathematician named Frederic de Moivre. It is based on an archetype that supposedly encompasses all humans regardless of their cultural background. The prototype or model normal behavior is that of the Homo-Economicus also known as economic man. The Homo Economicus is seen as an unemotional self interested actor who desires wealth and avoids unnecessary risk and labor.
The use of the word “normal” implies that the Homo-Economicus is the customary and consensual type of individual in all societies regardless of cultural background or context. This creates a fallacy of the type “glittering generality” because it assumes that people who do not fit this archetype are non normal. This misleading notion is one of the main reasons why the MPT model has been unable to pass the litmus test of cross cultural investigation.
For instance, similar to the Homo-Economicus archetype, Joseph Conrad in his book The Secret Agent creates archetypes of anarchists. However, unlike Markowitz, Conrad does not assume that anarchists should fit a normal distribution of behavior. On the contrary, Conrad creates two different types of anarchists. On one hand, we have the character of Mr.Verloc, whose attitude towards dangerous and perilous events is unemotional like a robot. Mr.Verloc is described as cold calculative figure that does not take unnecessary precarious measures. Even while facing the death of is brother in law Steve and his own pending arrest by the police, he remained quiet, gentle and even seemed peaceful. Conrad says of Mr.Verloc: “His resemblance to a mechanical figure went so far that he had an automaton's absurd air of being aware of the machinery inside him.” On the other hand, the character of the professor who, although an anarchist, is not developed along the same archetype as that of Mr.Verloc. In fact, the professor is described as uneasy and filled with turmoil while facing uncertainty. He is the antonym of Mr.Verloc even though they both espouse the same ideology; their attitudes towards risk are at opposite ends. Conrad writes about the professor “It was vain of him to pretend that he was not disappointed.” It is not unexpected to note that Conrad chooses the use figures of speeches such as a metaphors “his resemblance to a mechanical figure” to describe Mr.Verloc. The deliberate use similes allow the author not to get deep inside the psyche of the Mr. Verloc. There is no need for an elaborate Proustian like description of Verloc's character. All that is needed is to compare him to a machine, he is that simple minded. Conrad describes the Professor in a more elaborate way. He uses verbs that connote with emotion. In the excerpt mention above the verb disappointed is used to show the professor's emotional side under duress.
We can see that MPT assumption of a unique, predominant and normal archetype when faced with risk does not hold in the world described by Joseph Conrad. In fact, the professor and Mr.Verloc's attitude towards risk could be depicted along the same graph as the Homo-Economicus but with different shapes to mark their distinctiveness.
Also, we note that that archetype of normal behavior under risk offered in the MPT can only hold when the author is taking a point of view that describes humans as mechanical beings devout of any emotions, like Mr.Verloc. We also note that The Secret Agent helps us observe that there is an emotional dimension to risk analysis that the MPT model omitted to take into consideration.
The use of archetypes and the normal distribution assumption towards risk is not the only point of divergence between the MPT model and the excerpts of literature of the 20th Century chosen in this discussion.
Another major assumption of the MPT model is its portrayal of paradise. Markowitz uses the term “efficient frontier” as his version of paradise. It represents a curved line, in a two dimensional graph where the most efficient and rational Homo-Economicus individuals are going to make their most efficient profit maximizing and risk minimizing choices. It is the zone of all the winners in the game of life.
According to the MPT, no wise and judicious person will ever choose assets that are below the efficient frontier. It would be tantamount to choosing an asset that had an inferior return but a greater amount of risk. The conclusion of the game in Markowitz's world is to reach the efficient frontier which is depicted as the gates of paradise. With this illustration, Markowitz achieves two very important goals. First, he establishes that there is clear tradeoff between risk and return. For instance, on the efficient frontier graph, if two points are one on top of the other, all individuals will choose the higher point (higher return) for the same level of risk.
Second, Markowitz shows exactly on the graph the location, the actual mathematical coordinates of each participant's paradise.
Marguerite Duras, in “ Hiroshima mon Amour”, offers a different take on the ideas behind the concept of an efficient frontier as a form of paradise. She does not explicitly mention Markowitz's efficient frontier but, she mentions paradise and its role in the constant search for a meaning of life. Instead of the efficient frontier, a scientifically derived form of paradise, Duras offers a more nuanced and abstract notion. In the book, the female protagonist proposes the following when asked to define her secret paradise :“Qu'est ce qui est ton secret? Douter de la moralite des autres. » . Duras introduces the ability to question a society's conventional wisdom, particularly its religious beliefs as the key to entering paradise on earth.
This contrast between the scientifically derived notion of paradise present in the MPT and Duras's take on the notion of paradise is part of a debate between two schools of thought that has been going on for centuries. On one hand, positivism is a philosophy that states that the only possible authentic knowledge is that achieved using scientific erudition. On the other hand, existentialism claims that human beings create the meaning of their own lives therefore their own paradise or hell. This truth-seeking debate is still current. When Markowitz received his Nobel Prize in 1990 he thanked the great philosopher Auguste Comte for making positivism a sine qua non condition to understanding life. Nevertheless, Markowitz deserves credit for being original. To depict paradise as a mathematical equation is archetypical in deed.
The efficient frontier is drawn on a two dimensional graph and is not a straight line. The main reason why the efficient frontier is not a straight line has to do with a concept in finance called the diminishing marginal utility. In layman terms we can just note that Markowitz is showing us that the path to paradise is not a straight line due to mathematical restrictions in his model. As byproduct of the diminishing marginal utility, one does not reach the efficient frontier by going straight from point A to point B.
Alaa Al Aswany and Naguib Mahfouz, both modern Egyptian writers have painted characters in their novels who believe in a linear path to paradise in contrast to the curved line depicted in the MPT model.
In his book The YacoubianBuilding, Al Aswany proposes a straight trajectory to paradise through the sacrifice of Jihad. For instance, in his depiction of the young and disillusioned Taha, El Aswany establishes a straight path to paradise for all martyrs that die during Jihad. Taha says: “I am not afraid of death any longer. I have made up my mind to be a martyr. I hope with all my heart to die a martyr and enter paradise. Jihad! Jihad!” Clearly, Al Aswany uses the word Jihad in its connotative meaning as a suicidal path to paradise through martyrdom.
In its expressis verbis denotative meaning, Jihad is simply “to struggle in the way of god and to improve ones self and society.” The fact that the reader is left to choose which meaning of Jihad is applicable in Al Aswany's text is a clever way for the author not to take position on the debate on how one enters paradise that we raised while analyzing the curved shape of the efficient frontier line. Furthermore, in Islamic tradition, Hadith #4 titled “The meadows of paradise”, the prophet Muhammad (Peace Be upon Him) has been known to have said: “When you pass by the meadows of paradise indulge freely in it! They said: O messenger of Allah! What are the meadows of paradise? He said: The circle of Ilm.” Is the prophet of Islam suggesting a path to paradise that is circular? It would be a stark contrast to the straight line suggested by martyrdom through Jihad in its modern day connotative meaning.
The efficient frontier or paradise that is being depicted in the MPT model is contained within a two dimensional graph. In fact all of the possible combinations of graphs in the MPT are all sketched within a two dimensional graph. Risk is on the x-axis and return is on the y-axis. A planting and payoff structure is established where one plants or invests in one period and receives the payoff in the following period. Hence, there exists a perfect temporal symmetry between planting and payoff. This brings us back to the normal distribution because it's a distribution that is perfectly symmetrical. The normal distribution also known as the bell curve is a perfectly symmetrical function where all values are centered around a mean or the central tendency.
Horan Pamuk in his novel Snow depicts a different concept: that of quasi symmetry or hidden symmetry in contrast to the perfect symmetry of the normal distribution. The process of writing poems for the main protagonist in the novel Kerim Alakusoglu or simply Ka is what Pamuk calls a hidden or quasi symmetry. He says: “When he had found the bottom and turned the light back on, he took one last look at the notebook and the title came to him: Hidden Symmetry.
What is mainly important to Ka, in Pamuk's book is the idea of creation. Ka uses his religious, sexual and political experiences in Kars a province in modern day Turkey located in the Northeastern part of the country as a means to and an ultimate end which is creation of poetry. We can see that Pamuk uses a planting and payoff structure similar to the MPT model. However, Ka is not an investor; he uses his experiences in Kars as seed and his pen as harvest.
As mentioned above, we have a different kind of symmetry than what is present in the MPT model which assumes perfect symmetry. If one were to define the concept of hidden symmetry, a sound bite of the latest single by the new age Jazz fusion group “The Hidden Symmetry” would be appropriate. Hidden symmetry is about fusion, it is the act of creation using ingredients from different sources. It can be found in literature, music and even the culinary arts. For instance, Japanese-French fusion cuisine is a form of hidden symmetry because it uses Japanese ingredients cooked using French techniques.
One major difference between Pamuk's planting and payoff and that of the MPT, is that the MPT assumes the planting and payoff is done in one continuous period of time. One plants in one period and reaps the benefits in the very next period.
This continuity in time present in the MPT model conflicts with the genre of Arab story telling which generally treats time as non continuous function: there are gaps between the beginning and the end of a story and the reader is deliberately left to imagine and fill in the blanks.
One of the most famous and most adept followers of this technique of non-continuous time is Naguib Mahfouz, a Nobel Prize of literature from Egypt . In his book “The day the leader was killed” , Mahfouz‘s protagonist says: “Then suddenly I wake up at a strange point in time. History and time corner me, saying: That is how the events you skimmed over through history took place.” This excerpt from Mahfouz symbolizes a stylistic as well as political choice on the part of the author. Just like a musical piece, Mahfouz's relationship with time is organized given a certain movement. The use of the word suddenly imposes to the reader a certain tempo. It goes from a state of rest (sleeping), to a journey through time in fast forward motion. The pace goes from an allegro to an accelerando pace quickly.
However, Mahfouz's horology is not as simple. Even though the rhythm is quick and abruptly changes, we can see in this passage that if we analyze Mahfouz's choice of words, there are some particularities in his style. For instance, the first sentence ends with the word time and the second sentence begins with the word history. It gives Mahfouz's style of story telling a linear sense of continuity while not telling the reader about all the details of president Saddat's assassination. Like a magician, Mahfouz pulls a neat trick because he deliberately chooses not to delve on the details of the assassination while creating semblance of continuity in time by using phrases that end and begin with a notion of time (time and history.)
Another example of this technique can be found in the writings of Sayyid Qutb, an Egyptian novelist, who has been coined as the “philosopher of modern Islamic terror”. In his book In the shade of the Qur'an he says: “to live in the shade of the Qur'an is a great blessing which can only be appreciated by those who experience it. It is a rich experience that gives meaning to life and makes it worth living. I am deeply thankful to God for blessing me with this uplifting experience for a considerable amount of time.” Nowhere in the book does Qutb mention what this considerable amount of time was. Considering that Qutb was in jail and subjected to torture for most of his adult life one can only conclude that he is yet another Arab author who practices the notion of non continuous time for political reasons perhaps.
We can call this original style a quasi linear style similar to Orhan Panuk's quasi symmetry when writing poems.
Through the works of the authors mentioned in this panoramic travel across different cultures, we showed that by relaxing the following assumptions: the two dimensional nature of the MPT model, the Homo-Economicus paradigm, the depiction of the efficient frontier as paradise, the intrinsic definition of risk as a “normal” probability distribution function: the MPT model in most cases fails the test of cross cultural diversification.
It is important to widen the debate to not just to a simple critic of the MPT theory but to also introduce the discussion of how economic models that claim to predict human behavior should be tested.
Using Econometrics alone as a testing mechanism of the MPT's veracity has earned Mr. Markowitz a Nobel Prize. We can see that some of his assumptions become glaring fallacies when tested in the context of the real world. A combination of econometrics based tests and cross cultural literary tests such as the one done in this essay can go a long way in giving MPT model empirical as well as true real world cross cultural authenticity.