09.12.2024

Hanging Up the Red Hat – What if Father Christmas Were to Retire?

Father Christmas has had a long stint. A good innings. A fantastic legacy. But all good things must come to an end. Delivering all of those presents for the past 1500 years[1] has been an exhausting endeavour for both him and the reindeer.

Last year, we looked at pricing an insurance contract for Father Christmas on his yearly trip around the world and came to a rather expensive conclusion (The (Pricing) Nightmare before Christmas). This year we look at Father Christmas’ job from a different actuarial light – how much money would he get yearly from a private pension scheme if he were to retire today?

Of course, in reality he would do no such thing! The job of bringing Christmas cheer to all the children in the world is an incredibly important and exclusive one – the show must very much go on. So fear not, children of the world; Christmas is yet to be cancelled.

Assumptions

As all actuarial models go, we must first decide on and critically assess our assumptions about Father Christmas. From our extensive research on the topic, we believe we have found (and can justify) the assumptions needed for this task. They are as follows:

Father Christmas is Immortal – Modelling Father Christmas on the story of Saint Nicholas would put his age at 1754[1]. Unfortunately for us, the mortality tables don’t go down quite that far. Further, we don’t want to begin thinking about how to adjust his mortality rates for lifestyle factors such as regularly piloting an open-top sleigh going incredibly fast! Given this, the only reasonable conclusion to come to is that Father Christmas is immortal.
Father Christmas is on a Defined Benefit (DB) Pension Scheme – This one took quite a bit of thinking. There are arguments to be made that Father Christmas is self-employed, or is a business owner himself. The issue with those assumptions, however, are the questions surrounding revenue. If Father Christmas does run his own show, where is the money coming from? This leads to the only reasonable conclusion: he has an employer who is heavily invested in spreading Christmas cheer! Given the longevity of his employment, and historical documentations of pensions, it makes most sense to say he has a DB pension.
Father Christmas has had no Breaks in Service – We all know of the seemingly endless supply of films where somebody takes over the job of Father Christmas for a year. Despite Father Christmas certainly being real[2], we shall be taking these films as pure works of fiction, as there is no concrete evidence for anyone else taking over at any point.
Father Christmas’ Pension is Managed in Britain – Ok, this one is harder to justify rigorously, and might be quite a leap. But with Britain’s history of financial establishments, and readiness of historical data about pensions, it feels like a completely reasonable choice to secure his financial future.
Father Christmas Joined his Pension Scheme in 1684 – We chose this date for two main reasons. Firstly, it was the year the first occupational pension scheme to provide lifetime support to retirees was started (earlier schemes existed such as the Chatham Chest, but these were primarily for people who were too sick as opposed to too old). Secondly, 1684 marks the payment of the first civil service pension. There is evidence of pensions earlier, but these were on an ad hoc basis and given on much different terms to the modern pension[3].

Now we have our assumptions, we can begin modelling the problem!

Finding Father Christmas’ Wage

To determine Father Christmas’s pension, we need to find out what his final wage would be. There are many different approaches we could take for this, each of which produce extremely different results. The three we chose to explore were:

He is paid the same as a postman per parcel delivered i.e. an employee,
He takes a cut from the delivery cost of each parcel i.e. a contractor,
He is paid as a delivery driver/courier for companies like Deliveroo i.e. a gig worker.

We will explore these each in turn. Full calculations for each method can be found in the appendix.

Postman Pat Kringle

Treating Father Christmas as a postman has many advantages. As he has an occupational pension scheme, it makes sense to base his pay off an employed job, and using a postman’s wage means we don’t have to account for things like distance travelled, as this (theoretically) will already be factored in. So how much would he earn?

We decided to use the delivery driver role at the Royal Mail as the baseline for this, and using this job listing[4] and accounting for Saturday/Sunday overtime, we found he earned £14.38 per hour. But this isn’t entirely fair on Father Christmas, as he has to deliver a lot more parcels per hour then the average postman, so it makes sense to apply some scaling based on the number of parcels delivered. Thanks to the work of last year’s Christmas article[5], we can assume Father Christmas delivers 700,000,000 parcels every year, while we calculated that the average driver delivers 143 parcels per hour. Dividing the hourly wage by this, each driver earns roughly 10p for each parcel they deliver. Scaling this up by the 700,000,000 parcels delivered every Christmas, we conclude that Father Christmas would earn a salary of £70,000,000 per year.

Contractor Claus

What about if, instead of his earnings being based on a fixed wage per hour, Father Christmas instead takes a cut from each parcel delivered? This arguably makes more sense as Father Christmas is the only known postman capable of delivering packages at the scale he does, and so would have a lot of bargaining power. It also provides him with an incentive to deliver all his parcels (if the magic of Christmas isn’t enough), meaning he won’t just clock off if he’s feeling too tired to cross the Atlantic. To find out how much he would earn as a contractor, we need to figure out how much a parcel costs to deliver.

To find this, we again turn to the Royal Mail[6] and their global delivery fees. There were lots of variables here, but we assumed the average gift would weigh 1kg, would be tracked (Thanks NORAD!) but not signed, and we then split the delivery fees based on whether they were in Europe or elsewhere in the world. This gave us an average parcel price of £19.17. Multiplying this by the 700,000,000 presents delivered, the overall income for the North Pole each year is £13,419,000,000. We decided Father Christmas would take a good share of this, due to his high demand and skill at sleigh riding, and earn 50% of this amount whilst his employer (and pension provider) takes the remaining 50% for paying the elves and other running costs. This means his pay using this method is £6,710,000,000.

Deliverudolph

A third option is treating Father Christmas as a gig worker. This makes sense as Father Christmas only works one or two days a year, so it does not make sense for him to earn a full-time job’s wage. Using the Deliveroo payment system (although other delivery services are available) allows for distance travelled to be considered, unlike in the previous methods. It also allows us to make up a fun name for this section. The main drawback with this method (which applies to the contractor method too) is that it is unlikely a gig worker would have a DB (or even a DC) pension, but we can assume Father Christmas has convinced his provider to give him one anyway.

Using The Money Builders[7] and The Penny Pincher[8] , we found that, per order, a Deliveroo driver earns a £3 delivery fee, a variable distance fee of roughly 28p per km, and tips – we can assume Father Christmas makes nothing from tips, as cookies, milk, and carrots are all he and his reindeers need! Deliveroo also has surge pricing at busy times (which Christmas most certainly is!), netting him a 50% pay boost to each delivery. The most complicated part of this method is finding how far the distance is for each order. For this, we took advantage of the multiple order multiplier, where a driver can collect multiple orders from a restaurant going to similar locations and earn a fixed 30% boost to their delivery + distance fee for each extra order delivered. To group together locations, we decided to use countries. We calculated how far the geographic centre of each country was to the North Pole, and then how many presents each country receives by splitting the total number of presents proportionally by population. This gives us the following formula to get his final salary for deliveries to any one country:

1.5 * ( 3 + 0.28 * (distance to NP)) * ( 1 + 0.3 * (# of presents - 1))

which was then summed over every country in the world.

We therefore find that Father Christmas’s wage if he was a gig worker would be… £662,600,000,000! Using this method, he earns roughly the market cap of Goldman Sachs each year[9], or the entire national debt of Argentina[10], or the total departmental budget of the UK government[11].

What About His Pension?

Now we have his final salary, we can find what his annual pension is. Recall we are assuming he has a DB pension, so the formula for his pension is:

Final Salary * Accrual Rate * Years of Service

We took the accrual rate to be 1/80, in line with many pension schemes, and based on his pension starting in 1684 that gives us 340 years of service. Using the above formula, Father Christmas’s annual pension for each of the methods is:

That’s £2.8 trillion each year, every year in the best case. Imagine how many mince pies and carrots he can buy with that amount of money! It would also give Father Christmas the largest pension in the world by a margin of approximately £2.8 trillion per year.

An Advent of Assets – Allocation for Our Scheme

For Father Christmas to enjoy his long, restful retirement eating lots of mince pies, we need to have a plan for how his assets will be invested. To do this, we need to consider the type of asset that we would like to invest in, the country the asset is based in, and the proportion of the money that is invested in each asset at retirement.

As we have assumed that Father Christmas is British, we looked at how UK DB Pension Schemes invest their assets. According to the Pensions Policy Institute (PPI), the asset classes can be loosely categorised into 4 main groups[12]:

Listed Equities
Bonds – including index-linked gilts, conventional gilts, corporate bonds, other government bonds and short-term debt instruments.
Alternatives – including private equities, property, secure income alternatives, private debt and venture capital.
Cash and Other – including cash, buy-in annuities, other unidentified assets, negative position on repos and derivatives.

Equities

The Office for National Statistics (ONS) presented data of the proportions of direct investment made by UK Pension Schemes in UK or overseas assets. It was found that 30% of equities investment was made in the UK with the remaining 70% happening overseas, predominantly in the United States (US)[13]. Therefore, we want to find a US index that best approximates the makeup of the equities portfolio. The S&P 500 index is an index of the 500 largest US companies, weighted by market capitalisation, so should be a good representation of our listed equities portfolio. Just like the joy of Christmas gifts, equities can bring great returns over long durations.

Bonds

The ONS found that UK schemes invest more in gilts than they do in corporate bonds and that most of the debt securities were invested in the UK[13]. As members approach the golden years of retirement, the PPI Institute shows that the portfolio consist more of bonds and less of equities[12]. This serves a couple of purposes:

Security – improves confidence that Father Christmas will receive his pension income.
Predictable Returns – Father Christmas’ income will be predictable and steady.

We chose the UK 5-year gilt because it best matches the timing of the approaching payments required in the short term.

Alternatives

The PPI found that in 2023[12] 14% of the alternatives class is property, whilst the remaining 86% is private equity and other alternatives. Moreover, 54% of the private equity assets was invested overseas at the end of 201925. Therefore, we decided to approximate this class by looking at the average return made on private equity across the state pensions market in the US.

Cash

Holding cash is important for maintaining a level of liquidity and to meet the immediate payments. We assume that it is held in a UK account that earns the risk-free rate of interest.

Asset Mix

Here is our approximation of Father Christmas’ portfolio at retirement:

Now that we know what the portfolio consists of, we shall now approximate the investment return of Father Christmas’ pension pot.

Investment Return

Here are the methods we used to obtain the returns. The values can be seen in the table below.

S&P 500 – The average annual investment return was taken over the period 1957-2023[14].

UK 5 Year Gilt – The gilt yield was chosen by taking the average gilt yield over the period 1998-2024[15].

Private Equity – Due to the lack of freely available data online, we found an article that calculated the average annual return of private equity over the last 21 years in the US state pensions market[16].

Cash and Equivalents – The 30-year government bond yield was used to estimate the future risk-free rate.

The estimated investment returns are as follows:

As Father Christmas is, of course, immortal, his pension income is paid every year for eternity. To mitigate the risk that the real value of the payments lose value if inflation is higher than investment return, we assume constant investment returns and inflation rates. We ensured that investment returns are greater than inflation rates. The overall average inflation used a similar weighting method to interest rates. We assumed an inflation rate of 2.67%. Now, Father Christmas can be assured that he will have enough money to enjoy those lovely mince pies forever!

Assuming all the investments are independent of one another, the real investment returns, after adjusting for inflation, are as follows:

Value of the Pension Pot

All that’s left to do now is the find out how much Father Christmas has in his pension pot! We first calculate the average yield of the portfolio, and then use the standard formula for the value of a perpetuity[17]. We get:

Eight hundred trillion pounds. That’s one mighty sum of money needed to be put aside for one man. Perhaps he would settle for just the state pension instead? Or perhaps he would take his pension in Christmas cheer instead of Sterling? However he accepts his pension, it surely reflects the hard work over the years he has put in to spread joy to all children in the world, and we think a peaceful and wealthy retirement would be appropriate.

Thankfully for us, that’s not going to happen and Christmas will go on as usual. And in that spirit, we wish you all a very Merry Christmas!

Ben Tocher, Alina Frost and Liam Gettins

December 2024

Appendix

In this Appendix we provide further detail on the calculations for Father Christmas’s salary.

Postman Kringle

Hourly Wage – We used the fact that delivery driver earns a base rate of £12.95 per hour (as it is fair to say Santa has completed his probation), with an extra £4.01 per hour on Saturdays and £6.01 per hour on Sundays. Assuming Christmas day has an equal chance of being on each day of the week, his average pay per hour will be £14.38.
Parcels per Driver per Hour – The Royal Mail[18] employs 5000 drivers, on an average annual salary of £25,679 before weekend bonuses. Dividing this by the hourly wage of £12.95 we found a postman works approximately 1,983 hours each year. Data provided by Statista indicates that the Royal Mail delivers roughly 1,416,200,000 parcels per year[19], and so the number of parcels delivered is:

1,416,200,200 / ( 5,000 * 1,983 ) = 143 parcels per hour per driver

Contractor Claus

The Royal Mail list prices for deliveries across the globe, separated by parcel weight and region. They are also split based on whether you order online or in person, but we will just assume a letter to Santa counts as an online order for ease. Using Royal Mail prices may not be the best assumption for costs as it assumes distances from the UK, but we believe it is fair enough as i) the North Pole is closer to the UK/Europe then it is to most of the rest of the world and ii) it allows us to better compare with the postman’s wage.

Weight and Tracking – We decided on the 1kg option for the parcels, as we assumed this would be the average weight for most gifts. Royal Mail further offers different prices depending on if you want the parcel tracked and signed, and as we can track Father Christmas and we know they will not be signed for (as Santa waking you up for a signature may ruin the magic of Christmas), we used the International Tracked prices.
Average Parcel Price – The two main delivery regions are Europe and World, both of which are further separated into 3 subregions. We took the average of each regions price and weighted them accordingly by population. We found the average price of a European parcel is £12.22 and that roughly 750 million people live in Europe[20], whilst the average price of a World parcel is £19.87 and roughly 7,440 million people live outside Europe[21]. Thus, the average price of a parcel will be the weighted average of these figures, which is £19.17.

Deliverudolph

Pay per Order – According to The Money Builders[22], there are four main fees – a £2 pickup fee, a £1 drop-off fee, a variable distance fee, and tips. We combined the first two into one £3 delivery fee, and assumed Santa makes nothing from tips. To calculate the variable distance fee, we used data from The Penny Pincher[23] which found a journey of a mile earns roughly £3.30, which represents 30p per mile, while a journey of 9 miles earns roughly £7.50, which represents 60p per mile. Taking the average of these, we found Father Christmas would earn 45p per mile he travels, roughly equal to 28p per km.
Method for Distances – Firstly, we found a dataset containing the centre of each country[24] and imported it into Excel, and similarly imported a dataset containing the population of each country[25] into another spreadsheet. As the shortest path from the North Pole to the centre of a country is the line of longitude connecting them, the distance Father Christmas travels on the way to each country is:

r * (π/2 - a)

where a is the latitude of the country’s centre in radians, and r is the radius of the Earth (6371 km).

Now we had a distance for each country, we used Microsoft Access to combine our datasets. However, there were inconsistencies between them. Using a full outer join, we found there were roughly 36 countries between the two sets that were not matched. After fixing issues such as spelling or territories being split (in these cases, we combined the split territories together), we were left with a list of 16 countries in exactly one of the datasets. The vast majority of these were small territories with populations at most in the tens of thousands, but often in the hundreds. In these cases, we simply removed the territories from the analysis, as it was unclear if the populations were included in that of the mother country. There were two exceptions:

Kosovo – Kosovo was not included in the population data. As it has a population in the millions. we added it separately with the most recent population data for it from Wikipedia[26].
Antarctica – Despite being a continent, it has no permanent population and all the temporary residents there are also citizens of other countries. As we assume these people are included in the total for their mother country, we removed Antarctica as we did for the other territories.