“If
you are out to describe the truth, leave elegance to the tailor.” – Albert
Einstein
Since hundreds of years, academics in the
field of the philosophy of science among the globe discuss on the trade-off
between simplicity and detailedness of theoretical models and mathematical
equations. Theories on this question date back to middle ages like the famous law
of parsimony, also called Occam’s razor, stating that the most
obvious and simplest solution is mostly the correct one and therefore,
theoretical models should be kept as straightforward as possible. On the other
hand, many scientists, like Einstein in my entrance quote, oppose this kind of
view and are convinced that the truth is way too complex and therefore mostly
not possible to be described in efficient and simple formulas (Ironically this
is coming from the man who delivered the mathematical proof for “e=mc²”, maybe
the most known and elegant equation in the world).
Especially relating to modern financial
theory, commonly used and accepted models among academics and professionals like
the capital asset pricing model (CAPM) that build the cornerstone of finance
as an econometric exercise (Dempsey, 2013) are under severe critique of being oversimplified
and not applicable at all. Arguments that underpin this critique highlight
false CAPM assumptions like observable market inefficiencies. Besides CAPM, one of the most popular but also
heavily criticised and furthermore Nobel Prize winning financial theories is known
as the Black-Scholes Model (BS). Published in 1973 by Fischer Black, Myron
Scholes and Robert Merton, the three economists claimed to have found a way to
value option prices correctly and therefore creating the possibility to
eliminate risk completely by using dynamical hedging strategies. Nonetheless,
also Black and Scholes elegant equation was constrained by several key
assumptions creating the same trade-off problem between parsimony and
detailedness.
I asked myself several times during my
studies of quantitative finance and economics: Are there any real-life consequences
of the application of models with insufficient assumptions? Or is it enough
that the people and the markets unitary believe in them, creating
self-fulfilling prophecies. One case in history might indicate where the boundaries
of financial modelling are and how these insufficiencies could affect everyone,
being way worse than CAPM and poorly calculated benchmarks for managers or
inappropriate discount factors (Dempsey, 2013).
The instance refers to the already
mentioned Myron Scholes and Robert Merton. In 1994, years after their
publication of the Black-Scholes Model, the 2 academics and a Hedge Fund
manager named John Meriwether decided to operate on the global markets on their
own and founded Long-Term Capital Management (LTCM). Within a few
months, the team raised 3 billion dollars (Barbu, 1999) as investors were almost
proud to give their money to 3 of the most popular luminaries in finance. The
fund managers invested mainly in options in the field of Fixed-Income
Arbitrage by applying the same dynamical hedging approach they used in
their model. In the following 3 years,
LTCM generated an exorbitant return after costs between 30% and 40% per year (Barbu,
1999) and it seemed like the impossible had happened namely that science had cracked
the code of the financial markets by using mathematics.
 |
| Figure 1. $1000 investment in LTCM . Reprinted from Wikipedia, by R. Lowenstein, 2000, https://en.wikipedia.org/ |
Although, it came different as the Russian financial crisis of 1998 hit the global markets completely unexpected. Investors all over the world reallocated their capital in the safest way possible, mainly in securities like US Treasury Bills. The consequences were an increase in the spread between interest rate swap derivatives and their underlying Treasury Bonds – the exact opposite way to LTCM’s investments. The hedge fund began to lose hundreds of millions every day till their liabilities reached an unimaginable amount of $1.25 (Barbu, 1999) trillion causing the possibility of a collapse of the global financial markets.
Lastly, the markets did not crash as the
USA organised the biggest bail out of history prior to the 2007 financial
crisis, nonetheless, the story of LTCM raised many questions concerning the
reasons how one single company could create a systemic risk of this scale and
what role the financial models like Black-Scholes played in this context.
A main implication of the simplicity of
models like BS and CAPM is the common usage among finance professionals. One
could say that this is a good thing because not applicable models are worthless
in real life. On the other hand, models that are followed by everyone and finally
turn out to be wrong lead to much greater downturns as everyone is betting on
the wrong horse. The major problem that occurs when people criticise the utilisation
of financial and econometrical models is in my opinion the lack of alternatives.
I doubt if it would be truly socially desirable if we could force traders to stop
listening to academics and let them invest only because of their gut feelings
and instincts. Moreover, the dystopian idea of stopping academics research in order
to prevent investors from using their ideas would be even worse, leading to a complete
standstill of human and social development. Whereas what we need instead of thoughtless
criticism of mathematics is the efficient regulation of markets through legislation
to prevent excessive risk-taking, illegal exploitation of asymmetric information
distributions and all the other cases where markets fail to regulate on their
own.
Having analysed the downfall of Long-Term
Capital Management, a company that could not even be managed by 2 of the
greatest minds in modern economics, makes me even look more critical on financial
theories like CAPM and their assumptions. Professors all over the world teach
about the models’ limitations, but the excessive usage of them makes the
students, me included, often forget about the obvious imperfections. Although,
I am in the opinion that academic models are an important cornerstone for
modern investment management, as long as they are not applied thoughtless and
get steadily falsified and improved as academics gain more and more knowledge every
day.
Bibliography
Barbu, G. (Director). (1999). Horizon
– The Midas Formula [Motion Picture]. United Kindom: BBC. Retrieved from
https://learningonscreen.ac.uk/
Dempsey, M. (2013). The Capital Asset
Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance?
Abacus, 49, 7-23. Retrieved from https://onlinelibrary.wiley.com
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