4-5-4 Calendar

The calendar exists because a calendar month is the wrong unit for trading. A 31-day month can hold four or five Saturdays, and a different count of each weekday from one year to the next, so a calendar-month comparison moves with the weekday mix before demand has changed at all. A 4-5-4 month holds whole weeks, which also lines it up with the weekly grain of the WSSI: the monthly merchandise plan and the weekly trading view sum to the same periods, and a receipt planned for a week sits inside exactly one month. The 4-4-5 and 5-4-4 variants move the five-week month within the quarter; the arithmetic is the same. The consequence for planning is that months are unequal. At an illustrative 100 units a week, a five-week month plans 500 against 400 for each four-week neighbour, so month-to-month reads are made on the weekly rate, not the month total.

The 53rd week is the correction for drift. A 364-day year falls about a day and a quarter short of the solar year on average, so the fiscal year end moves a day earlier each year, two after a leap day, until an extra week pulls it back — about one year in every five or six, since seven days of drift at 1.24 days a year takes 5.6 years. The rule that fixes the year end, such as the Saturday nearest a chosen date, decides which years carry the extra week, and the calendar decides which month absorbs it: that month runs a week longer, its quarter 14 weeks and its half 27. The extra week changes every total it touches. At the same 100 units a week, a 53-week year sells 5,300 against 5,200 — 1.9% more with no change in the weekly rate.

The planning rule is to compare trading week with trading week. In the 53-week year, the extra week is either reported on its own, with comparable sales measured 52 weeks against 52, or last year is restated so that each week is set against the matching trading week. The year after starts almost a week later in date terms, so every week number sits almost a week later against the dates than it did, and a date-fixed holiday can fall into the week number before the one it occupied last year. Copy last year’s weekly shape into this year’s sales plan without restating it and the peak lands a week out; read a WSSI against last year by date and every week the calendars disagree produces a variance nobody traded. The calendar also sets the season’s length before a single receipt is phased — receipts, markdown timing and the exit date are planned across the weeks the calendar actually has.