In today’s financial system, double-entry bookkeeping is the cornerstone of accounting, as the measure of the exactitude and truthfulness of financial accounts. The accuracy of these accounts is critical, as it is only through the veracity of, and trust in, these accounting records that companies can attract investment. And it is the prerequisite of trust in these accounts, as a critical necessity in the financial system, that has served as the foundation for the growth and importance of the entire accounting fraternity – as well as the increasing dominance of the large international audit firms that comprise this fraternity.
The man who today is commonly credited as being the “father of accounting” was the Italian monk, mathematician and amateur magician, Luca Pacioli, or simply Friar Luca. As a young man, Luca Pacioli moved to Venice from the small Tuscan town of Sansepolcro to continue his education and to train as a Franciscan friar. To support himself, Friar Luca tutored the children of wealthy merchants in numeracy and literacy, and it was during this time that he became interested in the mathematics and accounting of Venetian traders. In the 15th century, Venice was a hub in terms of culture, trade and finance. As an important link between the Byzantine Empire and the Muslim world, Venice was a critical commercial centre for the trade of commodities, such as silk, grain and spice, as well as a cultural mecca, with wealthy Venetian merchant families acting as patrons for some of the most influential artists of the Renaissance. And it was from within the hustle and bustle of the chaotic activities that occupied the Venetian waterways that emerged one of the most significant advancements in trade and commerce history – that of double-entry bookkeeping.
Thanks to its status as a commercial hub, Venice attracted the most ambitious and experienced traders from across the globe, including Middle Eastern merchants who used a notably different record keeping system to that commonly used in the Byzantine region. Walking along the docks one day, Friar Pacioli encountered this innovative form of bookkeeping first-hand and took a keen interest in its mechanics. Fortuitously, this inherent curiosity and penchant for numbers ultimately led the Friar to write down these activities in manuscripts that were originally meant to serve as textbooks for his students. Thus, while Luca Pacioli may today hold the title of the “father of accounting”, it would be inaccurate to credit the Friar with the sole invention of double-entry accounting. In fact, at least 200 years before the method was printed in Friar Luca’s manuscripts, the earliest roots of the double-entry system can be traced back to Jewish bankers residing in Cairo, Egypt, in the 11th century. Despite this, however, Friar Luca was indeed the first to officially record and distribute written descriptions and examples of this new bookkeeping technique, captured forever in his Summa de Arithmetica, Geometria, Proportioni et Proportionalita (Summary of Arithmetic, Geometry, Proportions and Proportionality) published in Venice in 1494.
Before the use of double-entry accounting, most merchants used multi-purpose journals to mark down sales and record any credit extended to customers. But the unstructured nature of these early traders’ bookkeeping made calculating profits an uncertain affair and made optimising their business a very difficult task. Once the double-entry method cleanly divided different types of inventory and each of their associated sales, it became far easier to see exactly how well various products were selling compared to others, as well as to ensure an accurate tallying up of debits and credits to ultimately summarise daily, monthly, quarterly and annual profits and losses. It was largely thanks to this important development that trade and commerce became far more scientific in approach and significantly more measurable in terms of profitability.
The method recorded by Friar Luca in 1494 is surprisingly similar to the accounting we still use today. As described in the Summa de Arithmetica, assets, liabilities, capital, income and expenses must all be recorded as separate entities in a merchant’s journal, relevant to either the debit or credit side of the balance sheet, with a corresponding entry that will “balance” the books. Pacioli even explained how to calculate year-end entries to carry over to the next period, as well as proposing a trial balance to prove that the ledger is balanced. And, importantly, the Friar stressed in his book that a merchant should never go to sleep before the debits equalled the credits on his daily accounts.
Whilst Pacioli’s explanations of the Venetian accounting method he witnessed are impressive, without the invention and adoption of Johannes Gutenberg’s printing press just a few decades before Friar Luca wrote his manuscripts, the significance of the double-entry method could easily have been lost. Fortunately, however, Pacioli’s book was extremely well received and eventually mass produced. It became the most-read mathematics book in Europe, spreading the revolutionary technique of bookkeeping far and wide in the Renaissance world. Pacioli’s work became so popular, in fact, that he received an invitation from the Duke of Milan, Ludovico Sforza, to work under his patronage. Coincidently, Sforza had also been Leonardo da Vinci’s financier and famously commissioned one of the artist’s most renowned works, the Last Supper.
In Milan, Luca Pacioli and Leonardo da Vinci would meet and the Friar would teach da Vinci mathematics. It is even rumoured that da Vinci used principles and guidance with regards to geometry, proportions and proportionality from Pacioli’s Summa de Arithmetica to aid him in creating the depth and three-dimensional perspectives that are so prominent in the Last Supper. This intimate friendship between the two Renaissance men eventually resulted in them living together for a period of time in Milan, prompting some historians to surmise that they may also have been lovers. More than 600 years after Jewish-Egyptian bankers and Venetian merchants first started using double-entry bookkeeping, the most complex financial institutions in the world still use precisely the same underlying techniques described by Pacioli.
Interestingly, unconnected to his detailed descriptions of double-entry bookkeeping, in the Summa de Arithmetica reside also the earliest roots of probability theory. In a separate chapter of the Summa, Pacioli presents the puzzle that would become the seed for all later developments in estimating probabilities and making predictions, but not before confounding mathematicians for almost two centuries. The example Pacioli describes, challenges readers to determine the fairest way of splitting a pot between two gamblers who are interrupted during a best of five dice game, when one of them is two games to one ahead – a question that necessitates the application of statistical methods that would only come to the fore with the emergence of probability theory and predictive modelling, centuries after Pacioli’s death.
Today, probability theory dominates financial mathematics, serving as the basis for key financial theories, such as options pricing and the Capital Asset Pricing Model. Without probability theory, the world of banking would look very different. For one, without it, the explosion of derivative instruments and markets would not have happened in the 1970s, which drastically changed the banking landscape. And furthermore, without probability theory, there would be no scientific basis for the calculation of the risk-weighted asset value, as the foundation upon which banks calculate their required capital. This complex calculation makes use of forward-looking predictive probability-based models to estimate, per obligor, factors such as probability of default (PD) and loss given default (LGD). Probability theory therefore sits at the heart of banking, embedded in the tools that ensure banks’ balance sheets are risk sensitive to future expected and unexpected events.
In the modern history of banking, these two worlds – that of backward-looking accounting and the forward-looking forecasting of risk – have been largely divergent. On the one hand, banks have for decades been forecasting risk using advanced mathematical models, to predict for example the probability of an obligor defaulting on their loan, or to predict future movements in interest rates and exchange rates. And on the other hand, the auditing fraternity, that underlies the veracity and trustworthiness of every accounting record in the financial system, has largely ignored – until very recently – the forecasting of future risk.
After the financial crisis of 2008, the world’s two largest accounting regulation setting boards, the International Accounting Standards Board (IASB) and the US-based Financial Accounting Standards Board (FASB), began working together to address issues around the fair value reporting of financial instruments. However, due to disagreements on several key elements, what was once meant to be a joint set of regulations, has eventually resulted in the two boards taking vastly differing regulatory approaches. Whilst the FASB decided to develop a single, comprehensive set of regulations, at once capturing the classification and measurement of financial instruments, as well as impairment and hedge accounting standards all in a single set of rules, the IASB has opted for a phased approach, releasing each component separately in what has become known as the International Financial Reporting Standards (IFRS).
The ninth phase of the IASB’s new financial accounting standards, called IFRS 9 – effective since 2018 and relating specifically to the accounting of financial instruments – has finally resulted in the convergence of accounting methodologies with probability-based forecasting methodologies. Specifically, in the estimation of future credit losses that a bank could face, IFRS 9 necessitates a forward-looking impairment methodology which seeks to estimate losses on a probabilistic, expected loss basis and to recognise them in a timely manner. In doing so, the aim is to forecast the future deterioration in the credit quality of financial assets using complex predictive mathematics, as well as to make use of the probability-based metrics that underlie the Basel II capital requirement rules that were globally introduced in 2006. Thus, despite the critical importance of accounting as an historical record of a company’s performance and the basis of trust upon which the financial system rests, the backward-looking nature of traditional double-entry bookkeeping did not solve the problem of what was going to happen in the future.
And so, as these two philosophically disparate economic perspectives finally converge, the fundamentals for both backward-looking accounting and forward-looking risk prediction ironically resided side-by-side in the ancient textbook of an Italian monk, Luca Pacioli. It seems retrospectively serendipitous that one scholar, over five hundred years ago, would have created the primary text for both the accounting discipline and the statistical discipline that dominates modern finance. And today, the Friars’ legacy has not been forgotten. On 12 June 2019, a first edition of the Summa de Arithmetica will be auctioned at Christie’s in New York for an estimated $1.5 million. It may go for far more, should the bidders fully understand its importance.