Financial Miscalculations - A Permanent Solution
One set of problems thrown up by the Gregorian calendar is the so-called “day-count problem.” For example, to determine how much interest accrues on financial instruments— like bonds, mortgages, swaps, and forward-rate agreements—day counts, the number of days interest accrues, are required. With the Gregorian calendar, complexities and anomalies exist that create difficulties, which give rise to day-count problems.
In an attempt to maneuver around these difficulties and simplify accrued interest calculations, a variety of conventions have been created. For U.S. government bonds, the interest earned between two dates is computed based on the actual number of days between interest payments. This is called the actual/actual convention. It’s simple enough. But, that’s not the end of the story. In the interest of simplicity and convenience, U.S. corporate, municipal, and many agency bonds use a 30/360 day-count convention. This artificial convention assumes that each month has 30 days and all years have 360 days, even though this is simply not true. These different day-count conventions have been spawned by the Gregorian calendar. They create confusion, errors, inefficiencies, and arbitrage opportunities.
For example, discrepancies occur between the actual/actual and 30/360 day-count conventions in those months that do not have 30 days. The clearest example of this problem is illustrated when calculating interest accrued on bonds held through the end of February, a month with 28 days. A corporate bond held from February 15th to March 1st (in a non-leap year) accrues 16 days of interest between February 15th and March 1st because the 30/360 day-count convention is used for corporates. In contrast, a government bond only accrues 14 days of interest because the actual/actual day-count convention is used to calculate interest on government bonds. In consequence, February gives rise to arbitrage opportunities between corporate and government bonds.
Day-count conventions also affect swaps. Consider two companies entering into a swap contract. One company is a fixed-rate payer; it pays a fixed rate of interest to the other company on a specified date. The other company is a floating-rate payer; it pays, for example, the 6-Month London Interbank Offered Rate (LIBOR) on the same principal amount as does the fixed-rate payer.
It would seem that a swap between the two companies is a straightforward transaction. But, it’s not. Yet another day-count convention must be introduced: the actual/360 day-count convention. This is the convention used for all U.S. dollar and euro-denominated money market instruments as well as money market instruments quoted at the LIBOR rate. So, floating-rate payments for U.S. dollar and euro-denominated swaps use the actual/360 day-count convention. Conversely, fixed-rate instruments denominated in the U.S. dollar or the euro use the 30/360 day-count convention. So, for swaps, a fixed-rate payment calls for an entirely different day-count convention than a floating-rate payment. Therefore, additional calculations must be made to ensure that the payments required for both companies engaging in the swap are comparable.
Multiple day-count conventions clearly make for tedious calculations and room for plenty of errors. Indeed, the confusion, miscalculations, and errors associated with the use of multiple and seemingly arbitrary day-count conventions that are spawned by the Gregorian calendar cost time and money. But, there is a solution: a permanent calendar that I, along with my Johns Hopkins colleague and Academy Professor of Astronomy Richard Conn “Dick” Henry, developed. It’s the Hanke-Henry Permanent Calendar (HHPC). When it replaces the Gregorian calendar, the errors thrown up by the Gregorian calendar will be history.
The HHPC adheres to the most basic tenet of a fixed calendar: every date falls on the same day of the week every year—forever. For example, New Year’s Day always fall on a Monday, and birthdays always fall on the same day of the week—forever. The HHPC divides each year into four three-month quarters. The first two months of each quarter contain 30 days; the third month of each quarter contains 31 days. So, each quarter contains 91 days, resulting in a 364-day year comprised of 52 seven-day weeks. The uniform, 91-day quarters are important for quarterly business financial reporting. And, the seven-day weeks turn out to be another vital feature of the HHPC. They preserve the seven-day Sabbath cycle. So, the HHPC abides by the Fourth Commandment and avoids the major ecclesiastical objections that have doomed all other attempts at calendar reform.
With the adoption of the Hanke-Henry Permanent Calendar, the multiple, artificial day-count conventions will no longer be needed. Indeed, they will be eliminated and replaced with one standard actual/actual convention. And, with that, interest will always be accrued on the same basis for all financial instruments.
In addition to solving the accrued interest day-count problem, the HHPC solves other financial problems associated with the Gregorian calendar. With the Gregorian calendar, each year (except leap year) has 365 days. Because each year contains an odd number of days, the number of days contained in each quarter vary. This is confusing and creates errors for businesses and analysts who must reconcile internal accounting procedures with external reporting requirements.
With the Gregorian calendar, not only do the number of days in a quarter vary, but the number of high-sales traffic days vary, too. Retailers are most susceptible to this Gregorian calendar quirk because weekends and holidays account for a significant portion of their sales. In consequence, problems arise when analysts make sales comparisons across quarters and years where the number of high-traffic, weekend days differ between periods, or where important holidays don’t align evenly.
The Hanke-Henry Permanent Calendar solves these day-count problems, too. The HHPC contains consistent 91-day quarters. In addition, it contains the same number of all-important weekend days each quarter. As for holidays, with the HHPC, they predictably fall on the same date and day of the week year-after-year. For example, seven existing federal holidays fall on Mondays. The HHPC also pins down floating holidays, like Memorial Day, which will eternally fall on Monday, May 27th, and Labor Day, which will fall on Monday, September 4th—forever. The calendar places both Christmas Eve and New Year’s Eve on Sundays. So, the HHPC facilitates sales comparability across quarters and years.
The Gregorian calendar not only results in a varying number of days for each quarter, but also a varying number of weeks. This creates another set of problems. Many companies define their fiscal quarters as 13-week periods instead of three calendar months. This makes for a 52-week fiscal year with 364 days. But, it leaves out one day a year (the 365th day) and two days during a leap year. To reconcile a company’s fiscal years with the Gregorian calendar, an extra week is added every five or six years to compensate for days that are left out each year with the 52-week, fiscal-year format.
Interestingly, there is no particular rhyme or reason as to when companies add back the extra week. While all companies add an extra week every five or six years, they do not do so during the same quarters, or even during the same sequence of years. Just where the extra week is placed on the calendar for any particular year is at the discretion of each company and is arbitrary. This ad hoc practice of adding weeks leads to confusion and accounting errors for analysts and investors.
Apple provides illuminating examples. Like most other companies, Apple defines its fiscal quarters in 13-week periods and adds an extra 14th week to one of its fiscal quarters periodically. For Apple, the extra 14th week shows up in Q1 every so often. Apple’s Q1 2013 was one week shorter than the extra-long, 14-week Q1 in 2012—a year in which Apple added back its extra week. Wall Street analysts failed to take notice and account for the fact that apple switched back to a normal 13-week quarter in Q1 2013. As a result, Wall Street’s expectations for Apple’s earnings were missed by a country mile and Apple’s stock experienced its worst one-day loss in four years, with a share price plunge of 10%.
In 2018, due to calendrical confusion, Apple suffered again. In Q1 of fiscal year 2018, Apple sold fewer iPhones and Macs than in Q1 2017, a quarter with an extra 14th week. The number of Macs sold declined by 5% from Q1 2017 to Q1 2018, and the number of iPhones sold fell 1.2%. Apple reported its Q1 2018 results, missing the consensus estimates for unit sales. As a result, Apple’s share price declined by more than 4% in just one day. But, on a per week basis, Apple’s iPhone unit sales had actually increased by 6.4%, and Mac unit sales had increased by 2.4% from Q1 2017 to Q1 2018. Indeed, Apple’s Q1 2018 performance was superb. But, the analysts failed to catch the calendrical quirk, and Apple’s share price suffered. The HHPC will sweep all these day-count problems into the dustbin.
The Hanke-Henry Permanent Calendar accounts for the disparity between its yearly length of 364 days and the length of the astronomical calendar (roughly 365.24 days, the duration of one full orbit of the Earth around the Sun) by tacking one additional full week to the end of every fifth or sixth year (specifically, 2015, 2020, 2026, 2032, 2037, 2043, 2048, and so on). Contrary to the current ad hoc convention adopted by companies, the HHPC extra week occurs at the same point: after the last week of December, every five or six years. So, with the HHPC, everyone will know exactly when to expect an extra week, and the problems that were visited on Apple and its share price will be eliminated.
As it turns out, some of the financial problems generated by the Gregorian calendar are well known. In an attempt to correct them, the National Retail Federation (NRF) recommends their own calendar guide—the 4-5-4 calendar. The 4-5-4 calendar is a voluntary guide for retailers. It takes into account the need for comparability of retail sales between years. The NRF calendar divides each year into 52, seven-day weeks. These weeks are allocated into four, 13-week quarters. Each quarter is divided into three months. The three months consist of 4 weeks, 5 weeks, and 4 weeks. Each quarter contains 91 days, so each year has 364 days. The NRF’s calendar greatly improves sales comparability across quarters and years. Fine. But, the HHPC already addresses all of the problems that the NRF 4-5-4 calendar attempts to solve, and more. And, it does so with more accuracy, standardization, and scientific rigor than does the NRF calendar.
The adoption of the Hanke-Henry Permanent Calendar will solve many of the problems thrown up by the quirks associated with the Gregorian calendar. Confusion and financial errors associated with a myriad of day-count problems will be swept into the dustbin. It’s time for a simple, astronomically sound, permanent calendar that is exactly the same year after year—forever. The HHPC is just what the doctor ordered.