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The Birthday Paradox

By Stefan Starr, published 18 March 2021.

Firstly, I’d like to introduce myself. I’m Stefan, one of the three graduates (along with Andy and Mat) who joined Candid in September last year.

Ian recently challenged me to come up with an interesting blog for our website which, you’ll be comforted to hear, prompted some intellectual conversation in the office (it does occasionally happen).

Ian had remarked “I can’t believe how many clients I share a birthday with, what are the chances of that?

A quick google search coupled with Mat’s maths degree introduced us to the Birthday Paradox. If you have 23 people in a room, the chances of two sharing a birthday is around 50%.

Many people (me initially included) would calculate the probability by comparing the other birthdays against your own, resulting in 22 comparisons in a room of 23. I’ve shown this idea on a smaller scale in my diagram below.

But in reality, every birthday gets compared against every other birthday, so the number of comparisons in a room of 23 is actually over ten times that amount – 231. As there are 365 days in a year, and 231 chances of a match (minus a little for people with the same birthday), the probability of a shared birthday is over 50%. Again, I’ve shown this on a smaller scale below.

As you add more people into the mix, the chances of a match compound.

Probability takes a bit of time to get your head around, and I think the same can be said for investing. Both concepts show the value of compounding, and more significantly, they demonstrate that we are not as rational as we think we are when it comes to assessing the effect of compounding.

Compounding the return of your portfolio over the long term has an enormous impact on the size of your original investment, but still, many do not see the potential of investing money from a young age. Investing early means more compounding and a greater potential return. As does cutting costs.

That being said, life needs balance, and I am definitely not planning on putting all my money away in my 20s and sacrificing great life experience.

During lockdown there have been fewer opportunities to spend my money, so I set aside a small pot to punt on some speculative investments (sorry Ian and Justin) - but I won’t be losing sleep over them.

For the bulk of my savings, I am planning on keeping it simple. Buy the globe, keep your costs to a minimum and let the markets do the hard work. The Candid ethos is starting to take hold.