Supportive Quantitative Methods

To Err is Human

Ah ne'er so dire a Thirst of Glory boast,

Nor in the Critick let the Man be lost!

Good-Nature and Good-Sense must ever join;

To err is Humane; to Forgive, Divine.

(Alexander Pope, An Essay on Criticism, Part II, 1711)

Why all this Mathematics?

• Living in small groups is easy…

• With some basic mental accounting we can keep track of property rights.
• It is also possible to have some barter trade.
• But not much more…
• One cannot organize a city of thousands without some form of bookkeeping.

The Sumerian City of Uruk

wikipedia

• Ancient Sumer is one of the earliest cradles of civilization.

• It emerged between the fertile lands of Tigris and Euphrates around 5000 BC. in modern-day Iraq.
• The abundance of crops led to surpluses and created a need to build storage facilities for the stockpile.
• The first early urban settlements were formed.
• Among them was Uruk.
• It is estimated that Uruk may have had 40000 residents in 3100 BC., making it the largest city in the world at the time.

Bookkeeping

wikipedia

• How did the people of Uruk keep track of their stockpile?

• The earliest proto-writing (elaborate bookkeeping system) texts come from the city of Uruk c. 3500 BC.
• They consisted of symbols scratched on clay tablets.
• They record the distribution of bread, wheat… and beer.

The Accountant

• Some of the records were written by a person named Kushim.

• Their signature on 18 tablets indicates that Kushim was responsible for a warehouse with beer brewing materials.
• Nisa, their supervisor, also signed these tablets.
• To fulfill their roles, Kushim and Nisa had to perform a lot of mathematical calculations.
• They were not always correct!

The Oldest Mistake Ever Recorded

(Parker 2019)

(Parker 2019)

Costly Errors in Finance Mathematics

• Errors in mathematics can get very costly.

• In 1999, the $125 Million Mars Climate Orbiter crashed due to a conversion error between the imperial and metric measurement systems.
• An integer overflow led to the explosion of the European Space Agency’s Ariane 5 rocket in 1996.
• Although mistakes in large engineering projects receive more attention, mistakes in finance and economics can also be very costly.

The Great Recession

• After the collapse of Lehman Brothers in 2008, monetary authorities in the US and the EU strengthened their regulatory supervision.

• Up to 2007, stress tests were used internally by banks for their self-assessment.
• After the crisis, central banks started conducting their own stress tests to assess how well banks are able to cope with financial and economic shocks.
• For instance, ECB is conducting multiple stress tests for the EU banking sector each year (Bank 2023).

Some Good News

• In March 2014, Bank of America (BoA) announced its very positive performance for the recently conducted stress tests.

• It was the first time that BoA passed the Federal Reserve's (Fed) stress test since the 2008 financial crisis.
• The results were so good that the bank announced
  • it will boost the dividend payments to its shareholders, and
  • buy back stocks up to $4 billion.
• Neither the dividends were paid, nor any buyback operations were conducted.

Structured Bonds

• In 2009, BoA acquired structured bonds owned by Merril Lynch.

• An accounting review of the stress test data revealed certain inconsistencies in the valuations of these bonds (Christina, Dan, and Ryan 2014).
• BoA reported that it miscalculated a measure of the capital on its books due to an incorrect adjustment on the bond's future values.

A Math Error with a $9 Billion Valuation

• In April 2009, BoA retracted its previous announcement.

• Fed required BoA to resubmit its report and capital action plans.
• The bank's shareholders were not very happy with this error.
• The day when the news of the error went public, the bank's stock value plummeted by $9 billion (5% of its total value).