Recently I watched a lecture that Monish Prabai gave to Boston College (full video here) and while he talked about many other interesting things in the video, there’s one thing which stood out for me.

**Rule of 72**

The ‘Rule of 72’ is something I learnt quite early on. It’s a nice and easy approximation to figure out how long it takes to have an initial amount double.

72 = Rate of Return per year x Number of Years

With that equation, all you have to do to figure out how many years it takes to double your money is to take 72 divided by the Rate of Return. For example, with a rate of return equal to 8%, it takes 9 years to double your money. Obviously, you could also figure out the rate of return required per year in order to have an initial sum double within a certain number of years. For example, if you want to double the initial sum in 10 years, you need a 7.2% return per year (72 divided by 10 years) for the next 10 years.

**What I learnt from the video**

In his lecture, Monish talked about ten ‘doubles’ which is 2^10 (2 to the power of 10). That’s equal to 1024.* That got me thinking. Going with that, for $1,000 to become $1,000,000, you need that $1,000 to double 10 times.

And putting the ‘rule of 72’ and this together, if you know your rate of return, you can easily calculate how many years you’ll need. Or conversely, if you know what kind of timeframe, you want to achieve this in, you can calculate the rate of return per annum necessary to achieve this target.

Basically,

Initial Sum x 2^n = Final Sum

n = No. of doublings.

Quick example:

Let’s say n = 10.

Using the rule of 72, if we can get 8% return per annum, that’ll take 9 years for the initial sum to double once. So if we require 10 doublings to reach the final sum, the total time taken will be 9 x 10 = 90 years.

**What it all means**

The math above means that there are essentially two variables that impact the road to a financial target- rate of return per year and the initial sum

**(a) Varying the initial sum**

For someone passively invested in the market, per annum returns can be approximated (for easy math) to be 8% per year (assuming all dividends reinvested). This means that being passively invested will require just under 10 doublings or, take you roughly 90 years to become a millionaire.**

Starting with a much larger sum of $10,000 requires only 6.6 doublings or roughly, 60 years. That’s pretty good if you’re planning to leave something substantial for your grandchildren. Start with a $100,000 and that only takes 3.3 doublings or roughly, 30 years. Thing is, starting at 30, you still have to stick with it until you’re almost at the official retirement age.

The other flaw with the above scenarios is that most people don’t get to start with $100,000. Some may start with $10,000 if they’re lucky but most people would probably start with $1,000.

So there has to be a better way right?

**(b) Increasing the rate of return per annum**

This is the obvious variable to focus on.

Unfortunately, there’s no easy solution to this. In my opinion, there are three ways one could go about doing this.

One, find higher rates of returns. This could be in form of asset classes that do better than market returns although it’s not entirely certain one without the right skills and temperament will do better than the market over time. Or it could be in the form of a highly speculative asset like bitcoin where the price has gone from about USD 1,000 to USD 15,000 (or more, at one point) in one year. Unfortunately, that’s only 15 times or just under 4 doublings. So if you start with $1,000, you only have $15,000. Another 6 more to go. Problem is speculative assets like this are once in a blue moon. That is if you even got invested early enough.

Two, increase your leverage. It’s no secret that being levered increases your rate of return.*** Whether they know it or not, that’s one of the real reason why Singaporeans are obsessed with property. The returns seem paltry on paper but given that no one pays for property in full, the returns are pretty decent.**** Unfortunately, not many people have the gumption for increased leverage, especially in equities. As Lord Keynes remarked, “The market can stay irrational longer than you can stay solvent.”

Another form of leverage is through leveraging the efforts of other people’s labour and capital. This basically refers to setting up a business so that other people’s labour and capital become your returns. I think this depends on person to person. Not everyone is suited to take on the many varied tasks that a business requires.

Three, you can boost your rate of return on the initial sum through a higher savings rate or by adding more money to the pile. I know this sounds like cheating but hear me out. The goal is to get a certain amount of money (e.g. $1,000,000). Adding more money is like adding more seeds to the ground, it increases your chance of getting more crop. The magic of compounding will add a rate of return to ever-increasing sums and that helps you hit the target quicker. It’s just math.

Personally, I’ve only used methods one and three. With number three, there’s no way to lose. I guess the only “loss” would be the utility given up from things I could have bought but hey, I don’t feel it. With number one, I’ve had my fair share of successes and misses. Overall, I’m probably doing slightly better than the market but honestly, not by much.

**Real-world results (sample size n = 1)**

I realise that many people may wonder how all this works in the real world. I’m glad to say that the above has worked pretty well for me. **In the last 10 years, my portfolio has doubled just under 6 times**. Let that sink in. $1,000 would have become $64,000 with that sort of returns.

If you think that I had some magic wand or some incredible investing insight, you’re wrong. Most of it happened because I had a high savings rate. A high savings rate contributes a lot to your portfolio in the beginning as your initial sum is so small that it’s probably a fraction of your annual income once you start working.

That really juices the returns per year in the initial stages. For example, starting with $1,000, saving 20% of the average fresh graduate starting salary of $36,000 per year ($3,000 per month) gives you $7,200 which is a 7.2 times increase in the size of your portfolio. That’s basically three doublings taken care of in one year through savings alone.

Obviously, the same savings rate does little to move the needle as your portfolio gets bigger and that’s where you need the markets to do the heavy lifting. Right now, my savings can still move the needle by a few percentage points a year so saving still works for now. At some point*****, I’m probably going to have to find returns either through better investing or leverage. That’s no two ways about it.

Many others have started on this path and have shown similar success. Just take Mr. 15HWW or Kyith over at Investment Moats for example. They have 6-figure portfolios but don’t for a moment think that that’s due to investment returns alone. My guess is that a fair percentage came from a high savings rate. There are too many newbies out there promising to teach you something about investing when the simplest thing they should be starting with is how to save lots of money.

Notes:

*Or as Monish says, for easy math, round it down to a thousand.

**You should see the problem with this. For one, 90 years is more than an average person’s lifetime even for a developed country like Singapore. Second, I’m not sure it’ll mean much to be a millionaire, in nominal terms, 90 years from today.

***Kyith from Investment Moats has a great article on this.

****side note: I had an interesting exchange with my boss where he said that many people in Asia invest in property because that’s how lots of tycoons in Asia (e.g. Ng Teng Fong’s family, Li Ka Shing etc.) made their money. I then pointed out the irony that these guys all developed and SOLD property to retail investors. Basically, mom-and-pop property investors hoping to be the next Li Ka Shing is on the other end of the deal from him.

*****Probably when the same level of savings moves the needle by less than 1%.