A wise ruler decided that he wanted to reward his servant for an extraordinary act of bravery. The servant said:
‘Master I ask you for just one thing. Take your chessboard and place on the first square one grain of rice. On the first day I will take this grain home to feed my family. On the second day place on the second square 2 grains for me to take home. On the third day cover the third square with four grains for me to take. Each day double the number of grains you give me until you have placed rice on every square of the chessboard. Then my reward will be complete.’
The master swiftly replied:
‘This sounds like a small price to pay for your act of incredible bravery, I will ask my servants to do as you ask immediately.’
Seems like a pretty straightforward agreement, right?
The fact that you multiply the number of grains of rice, by two, every time doesn’t really matter for the first 15 squares. The amounts are 1, 2, 4, 8, 16, 32, 64, 128, 256; all the way up to 16,384 grains of rice. No bother.
But it really starts to hit you at square 30 – which equates to 536,870,912 grains of rice, or about 31 metric tonnes of rice. There’s 34 more squares after that to go!
By the time you get to the 64th square the total is a mind-boggling number – because mathematically you have 264 grains (minus one). It would look ridiculous just to write it down and clearly the Master didn’t anticipate this outcome.
The point is that this is the human condition and a bias we carry, we simply don’t see exponential growth and our brains struggle to think in such abstract terms.
This Cognitive Bias Affects Our Ability to Save
There was a paper written by the National Bureau of Economic Research in 2016 and it studied how human biases affect people’s ability to save for retirement.
Essentially according to this study we suffer from two distinct biases that hamper our ability to save.
Bias 1 – “Exponential Growth Bias”
Summary: This is a perceptual bias around compound interest, where many of us underestimate the power of compounding.
Data says: In the study 70% of respondents either believed growth to be linear (28%) or under-estimate the future growth potential of the money that they save. Only 30% correctly recognized compound growth.
What you can do: Put your mind to work and try setting yourself a savings target. Let’s say you have $5000 and you sock away $365. Visit an online compound interest calculator and see how much you will have in 20 years if you do so. Want to venture a guess?
After 20 years of socking away $365 a month, you’ll end up with $241k after having deposited only $92k in savings.
Bias 2 – “Present Bias”
Summary: In evaluating a trade-off between two future options or events, a person will favour the earlier option as it gets closer (and feels more real for them). For example you might decide that you’re going to invest that $365 from your pay check, but when it comes time for pay day, you spend it on booze, pizza and a new video game.
Data says: 54% of respondents suffered from the Present Bias and would be inclined to, in the example above, change their mind as the pay-day nears.
What you can do: We have written about the importance of institutionalising how you invest and save. It needs to become a habit, that you do every single month, or if you get paid weekly, every single week. The money needs to be set aside and put into savings. Ideally you would automate the process as a standing order so that the money comes straight out of your account.
Exponential Growth of Covid-19
I can’t get away without briefly referencing the coronavirus outbreak as it enters full swing.
The reality is that as we all start working from home this week, the idea that Covid-19 is going to continue to spread exponentially is a difficult one to grasp. I see people at the parks, going to school to collect their kids, and driving around the roads in the U.K.
Yet the data is everywhere and easy to see:
Between March 7th and March 16th worldwide cases have accelerated. The reason that governments have decided to start to shutter the economy, and in some cases forced citizens to stay at home, is due to compound growth. They expect that if Italy is anything to go by, the UK will have tens of thousands of cases and at least a few thousand deaths by the end of this public health crisis.
The US may have 5696 cases today, however expect that to grow substantially over the next three weeks with 20-25% daily rises in cases and fatalities until it starts to taper off. That is difficult to imagine, but it is coming.
How to Reduce Those Biases
One thing that helps is to think ahead to what you’re going to save and invest when this is all over and run a very basic projection of how it will grow over the coming 20 years. Instead of focusing on the present (with red ink and losses) perhaps focus on the future.
(1) There are free online compound interest calculators that you can use to do this. Use 8% forecast annual growth (assuming an all-stock portfolio) and if you deposit cash month, then input that too.
Assuming you live in the UK and you have – let’s say – an average £65,500 pension pot. You are forty-five and you’ve decided, suddenly, you’re going to retire early. So you’ll deposit £500 into your pension every month and get 20% tax back from the government (higher earners can get up to 40%!) Here’s where you end up by 65:
A staggering pension pot of £678,473 after twenty years. And you started somewhat late, at 45, but managed to really gain a lot of ground over 20 years! Just by visualising and planning ahead, you’ll manage to motivate yourself to think in terms of compound growth.
(2) Follow our Market Timing Model and get into stocks after this major market meltdown has subsided. It is entirely possible that today was the bottom of the market. However, we believe there is more to come. Either way – equities are now, finally, going on sale. Start planning ahead because the buying opportunity of a lifetime is not far away.
(3) Dollar cost average in. For the majority of people who perhaps don’t have a huge amount of savings now, the best course of action is actually to start saving your money on a monthly basis and to start buying low-cost and passive investments.
Follow our Global Dividend Aristocrats (Canadians here) Portfolio, or start investing in one-click asset allocation funds like the Vanguard LifeStrategy or Vanguard FTSE All-World.
When it comes to investing it pays to have a system, to stick with it, and to truly understand the power of compound growth!
