*This is the second post in a series of three on the factors that determine how much we can expect to make from investing. The previous post covered how our risk tolerance affects our returns, this post explores how our time horizon affects our returns, and the next post covers how the fees we pay affect our returns. It’s the intersection of all three factors that determines our ultimate returns. For an overview of all the posts on this blog, please refer to the guide.*

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Most people haven’t heard of Sylvia Bloom. I certainly hadn’t, until recently.

She managed to amass a $9.2m fortune whilst spending her entire 67 year-long career as a legal secretary. Even her closest friends and relatives had no idea she had amassed such a sum, until, upon her death in 2016, her will provided for $8.2m in donations to various charities for needy children.

But how did she accumulate such a massive pot for someone who never earned more than a secretary’s salary? By all accounts, she was a frugal person, living in a rent-controlled apartment in New York and avoiding all trappings that come with wealth. A colleague of hers for over 35 years said of her, “She never talked money and she didn’t live the high life. She wasn’t showy and didn’t want to call attention to herself”.

But Sylvia’s success is due to more than just a frugal lifestyle. She also had the massive advantage of living to the age of 96, and spending 67 years in employment. Calculations by investment research company Morningstar estimate that, to reach $9.2m in 2016, she would only have needed to contribute $652 a year when she started investing in 1948, increasing every year with inflation. Whilst $652 a year would have been worth much more in 1948 than it would today, it was certainly possible for someone on a modest salary to save.

Sylvia understood that small amounts invested regularly could quickly add up and, if left uninterrupted, could eventually snowball into an enormous portfolio. In short, she understood the power of compounding.

**What is compounding? **

Compounding is growth on growth.

If you put £100 into a bank account earning 5% a year, after one year your balance would grow to £105. After another year, though, your balance would not grow to £110, but £110.25. That extra 25p is earned because the 5% interest rate is applied to the balance of £105, not £100 – the £5 interest earned in your first year has had interest applied to it again in your second year.

Whilst an extra 25p sounds insignificant, this effect slowly snowballs, with more interest being earned every year, producing larger cash balances, which in turn earn more interest. Given enough time, compounding can have an extraordinary effect on wealth.

What the traditional explanation of compounding being “interest on interest” fails to capture, is that compounding doesn’t need reinvested income to work. A gold bar which pays no dividends or interest, but increases in value by 3% every year will also benefit from the effects of compounding, because the 3% growth rate will be applied to an ever-increasing value.

All that compounding needs to work is a positive growth rate, and time.

Whilst the stock market doesn’t pay interest in the same way as a bank, the same principles apply. Returns from the stock market, both through dividends and capital appreciation in stock price, grow a portfolio value, which means the portfolio generates more returns, which grows the portfolio value – and so the cycle continues.

To see the power of compounding in action, you can stick your own numbers into this compound interest calculator (UK).

**The power of compounding**

Compounding becomes more powerful the longer you can harness its benefits for. Warren Buffet’s business partner Charlie Munger noted that “The first rule of compounding is to never interrupt it unnecessarily”. Investing early and keeping the money invested can provide a massive benefit in later life:

In the example above, the initial £1,000 grows to £14,974, through nothing but the power of compounding – that’s 15x the initial investment. The £13,974 in profit requires no effort on the part of the investor, but the ability to stay invested. Nowhere else can money be made as easily as through compounding.

Compounding becomes more powerful the longer it can exert its effect on a portfolio. That means investing early is extremely important in maximising returns from a portfolio.

The chart below shows that someone investing £1,000 per year from age 25-35 (10 years) and then **stopping all contributions** will end up with a larger portfolio by aged 65 years than someone who invests £1,000 per year from ages 35-65 (30 years):

Looked at from another angle, **for every 10 years an investor waits before investing, the final value of their portfolio is halved:**

Having touted the benefits of investing as early as possible, it’s easy to forget the real-world constraints of investing early.

Investing when we’re young means putting money away when we’re the poorest we’ll ever be. Cash becomes more valuable to us the less we have of it, so we’re far more likely to spend it than invest it when we’re younger. Not to mention that necessities like food, heat, and rent consume a larger percentage of our income in the early years, meaning less is left for other uses, including investing.

It’s for this reason that many people decide to delay investing until they can afford to contribute more meaningful chunks of their salary to their pension scheme. But what happens to an investor’s final pot if they decide to wait until they’re earning more money to start saving?

The chart above shows that **if you delay investing by 10 years, then double your contribution to catch up, you still wouldn’t end up with as much as if you started 10 years earlier with half the contributions.** Investing even small amounts early on can still have a huge impact in the future.

Investors who delay contributions are not missing out on the early years of the compounding benefit, but the later years. With the later years providing exponentially larger gains than the early years, investors miss out on the most important and most lucrative part of investing:

Assuming an investment of £1,000, a 70-year time horizon, and a growth rate of 7%, in the first 10 years of compounding, the investor makes £967. In the last 10 years of compounding, the investor makes £59,834. Missing out on the later years of compounding, when your portfolio is at its largest, makes a massive difference.

If we think backwards from the final goal, we can see from a different perspective how important compounding can be. For example, if you wanted to become a millionaire by the time you retire (assumed retirement age is 65), how much would you have to invest?

The chart above shows that by investing early from aged 25, you’d have to invest £4,681 per year. Waiting 30 years until aged 55 before investing means you’d have to increase contributions to £67,643.

**Free money**

Using the example above, of the 25 year old’s final £1m pot, he would have had to make £187,240 in total contributions (40 annual contributions of £4,681). The other £812,760 of the final pot is the effect of compounding. **82% of the final £1,000,000 is growth gained through nothing but market returns from compounding.** This is free money given by the market. Of the 55 year old’s £1m pot, he would have had to contribute £676,430 (10 contributions of £67,643), and only benefitted from £323,570 in growth – a mere **32% of the £1,000,000**. The market gives free money to those who have the patience and time to take it.

**Why does compounding work?**

Compounding is made possible by the fact that markets tend to go up over time.

Looking at a calendar year basis, markets in the past have risen 75% of the time. So the longer you invest for, the more likely you are to benefit from continued positive returns, and so benefit from compounding. The chart below shows the historic probabilities, based on data going back to 1971, of the returns (in sterling terms) on an investment in the MSCI World over 20 years:

The probability of losing money is around 23% after one year (as we’d expect), but there has not been a single historic 12 year period where you would have lost money investing in the MSCI World (assuming no fees were paid). **After investing for 20 years, you had a 46% chance of having made between 2 and 5 times your original investment, and a 38% chance of having made at least 10 times your original investment**. It’s clear that the longer a diversified portfolio is held, the less likely we are to lose money, and the more likely we are to end up with a higher multiple of our original investment.

All this is thanks to simple maths. The power of compounding comes from a small, yet powerful formula: (1+r) ^{n}. The ‘r’ is the rate of return, and ‘n’ is the number of years to compound. Most people focus on the ‘r’ part of the formula – trying everything they can to maximise their rate of return. But the reality is that ‘n’ is far more important, and also happens to be the only part of the formula within our control. Increasing the length of time we invest for has a huge effect on our ending portfolio size.

**Time reduces risk**

Not only does investing for the long-term increase return, it also reduces the risk that returns are much lower than your average expected return.

In the previous post, we discussed how average returns can be misleading, especially when investing in more volatile asset classes like equities. However, the longer a portfolio of equities remains invested, the more likely the long terms returns are to approximate the average return. If we look at the annualised returns for the MSCI World since 1971, we can see that the longer a portfolio is invested in the index, the more likely the portfolio is to converge on its long-term average return of 10%:

Investing can either be very good or very bad in the short term, but the longer the portfolio is invested for, the more likely it is that the portfolio will generate the asset class’ average return. This effect is especially pronounced for volatile asset classes, as they tend to have higher highs and lower lows in the short term. Staying invested in these asset classes can be more difficult in the short term if the investment performs poorly, but staying the course and investing for the long-term can help investors benefit from increased returns and reduce the risk of unexpectedly low returns.

**Why doesn’t everyone do this?**

If compounding is so great, then why doesn’t everyone invest as soon as possible, keep their cash in the market, and end up as millionaires?

Firstly, most people underestimate the power of compounding because nobody teaches us about it. The exponential function is rarely focussed on in schools, and almost never explained in terms of investing. By the end of university, most students will have forgotten their school maths lessons anyway. When we first start employment and are given the option to contribute to a pension scheme, there is often no formal education or training on the benefits of investing, how to invest, risk tolerance, or anything in the way of guidance on what is one of the most important financial decisions of our lives. It is hardly surprising that financial literacy levels in the UK are so low.

In the US, an academic study conducted by researchers at the University of California and New York University questioned both undergraduate students and Fortune 100 company employees on their understanding of compounding. The study showed that:

- The majority of participants expected savings over 40 years to grow linearly rather than exponentially, leading them to grossly underestimate their account balance at retirement.
- This misunderstanding of savings growth led to underestimating the cost of waiting to save, which makes putting off saving more attractive than it should be.
- Highlighting the exponential growth of savings motivated both college students and real employees to save more for retirement.

When we’re young is the most important time for us to understand compounding, yet is the time where it’s least understood. The chart below shows that for an investor starting with nothing, but investing £1,000 per year at 7% return, the final value of his first £1,000 contribution after 40 years will be £14,974. His £1,000 contribution in his 20^{th} year will grow to £4,141, and the £1,000 contribution in his 40^{th} year will grow to £1,070. It is the earliest contributions that contribute the most to the final portfolio value.

A second reason why we don’t fully take advantage of compounding is that it’s not intuitive. Working out 6+6+6+6 in our heads is easy, but 6x6x6x6 is almost impossible. Our brains are naturally wired to think in terms of linear progression, but struggle when confronted with exponential growth. Physicist Albert Bartlett noted that “The greatest shortcoming of the human race is our inability to understand the exponential function.”

To demonstrate, few people realise that 96% of Warren Buffet’s $81bn net worth was accumulated after he qualified for social security in his mid-60s. If he started investing at age 30, rather than aged 11 he’d be worth $1.9bn instead of $81bn. That’s 97.6% lower. As Morgan Housel puts it: ‘*How can most of Buffett’s success be attributed to what he did as a teenager? It’s so crazy, so counterintuitive. And since it’s crazy and counterintuitive we overlook the right lessons. So we write 2,000 books on how Buffett sizes up management teams when the biggest and most practical takeaway from his success is, “Start investing when you’re in third grade.*”’

A third obstacle to compounding is fees. Compounding works in reverse too, and investment fees can have a devastating impact on final wealth. They reduce a portfolio value in two ways: firstly, they reduce the annual rate of return – a 2% fee paid to a third party reduces the portfolio’s future returns by 2%. Secondly, as fees are paid out of the portfolio, every time an investment fee is paid, less is leftover in the portfolio to compound into the future. Higher fees therefore have a double impact: they reduce the value of the portfolio at the moment fees are paid, and they reduce the rate at which the portfolio grows in the future.

Fourthly, compounding is boring. It is especially boring at the start of the process, when it feels like nothing is happening. But it’s at this stage where investing is most important. It’s the compounding effects of the earliest investments that provide the bulk of the later gain – you can’t enjoy the right hand side of the compounding graph without first experiencing the left.

A fifth obstacle is that with so many different products all vying for our attention and cash, it’s much easier to imagine what £1,000 would buy us today or tomorrow, than what it could turn into if we invested it for 20 years. I know that £1,000 could buy me the latest iPhone today (just about), but I’ve got no idea what it could buy me if I invested it and realised the gain at some future point. The ability to avoid temptation and prioritise financial stability in the future over spending today is crucial in maximising the benefits of investing.

Finally, real life often gets in the way. The best time to invest is when we have the least money, so prioritising future goals over more immediate wants and needs can be extremely difficult to do. We’re also our own worst enemies when it comes to investments, and our own behaviour can often get in the way of benefitting from compounding. Compounding is able to run rampant when we invest early and often, and leave the portfolio alone. But markets can make holding on to our portfolios extremely difficult during times of volatility, and it can be incredibly tempting to withdraw cash at exactly the wrong time. As well as market volatility causing us to withdraw cash, unexpected expenses are also excellent at interrupting compounding. We might think our time horizon is 10 years, but when the car breaks down, our dream house comes up for sale, or we get a chance to take that holiday we’ve always wanted, we might find our time horizons shorter than we think. And as far as the portfolio is concerned, the more money we take out, reallocate, and move around, the less is there to compound. A portfolio can be thought of like a bar of soap – the more you touch it, the smaller it gets.

**Conclusion**

The benefits of compounding are hard to overstate, and can be a powerful force in shaping our financial futures. Compounding doesn’t care whether you’re one of the greatest investors of our time, a legal secretary like Sylvia Bloom, a carpenter, a gas station attendant, or a flight attendant – the rewards are there for anyone to enjoy.

Despite its benefits, there are a whole host of obstacles that can prevent us from reaping these rewards. Some are easily remedied through understanding and education, and some are ingrained into our psyche.

Nonetheless, a simple set of rules can help us in maximising our returns. By investing early, investing often, minimising fees, and staying invested, we can maximise our chances of capturing the benefits of compounding that are there for the taking.

*This is the second article in a series of three on the factors that influence our investment returns. Click here for the previous article on risk, and here for the next article on fees.*

Possibly the best I’ve read on compounding. If I was trying to educate a youngster I’d start here.

Thanks Doug!

Is there any chance you could provide some extra clarification as to

howspecifically a portfolio becomes more and more likely to converge on its long-term average return the longer it remains invested for? While I don’t doubt the veracity of the conclusion, I’m genuinely curious to understandhowexactly it works. If you invest in risky assets, isn’t there always a chance you might “cash out” at precisely the wrong moment even after 40 years of continuous investment and ultimately end up having lost money?Maybe I’m thinking too much in binary terms; would be happy if you could point out exactly where my logic is flawed.

Thank you!

Hi Jeko,

That’s a great question.

You’re right, the riskier your investment are, the more likely you are to panic when the market crashes and sell out at the wrong time, which is disastrous for long-term wealth building. That’s why it’s so crucial to figure out your own personal ability and willingness to take risk, to make sure that’s translated into your portfolio, and to stick to your investing plan. Otherwise, as you say, you can end up in a position where you’ve earned high returns for a long period of time, only to lose all your gains as a result of your own behaviour during a crash.

In terms of how that’s factored into the graph you’re referring to, all the returns are based on an initial investment which is bought and held for the whole duration (obviously reality is much more complicated than that, but it’s only meant as an illustration). As time goes on, both the unlucky and the lucky investor’s annualised returns end up looking similar, as the number of periods they’ve been investing for increases. The effects of one excellent year or one disastrous year are diminished as time goes on.

However, you’ve hit on an interesting point here (and one which would result in me editing the post if I ever had the time!). What the similarities in the annualised returns over time obscure is that even very small differences in annualised returns can have a big impact on the terminal distributions of ending portfolio values. For example, if you invest £100 at a market peak, then someone else invests £100 after the market falls 50%, after 50 years of investing both your annualised returns will look extremely similar. But the final value of his £100 will be twice the size of yours, because you’ve both earned the same returns since.

That’s not a good argument for market timing (despite appearing to be), but just shows how much small differences in long-term returns can have a huge impact on your portfolio’s size.

I hope I haven’t confused things, that was a bit of tangent!

All the best,

Occam

Right, I

thinkI understand your point. I’m trying to get there slowly and patiently but can’t say for sure that I fully grasp the mathematics quite yet!For one thing, in asking whether you couldn’t “cash out at the wrong moment” I was thinking less of human behavior and more of the typical fluctuations of a risky portfolio. Apologies in advance for speaking in lay terms but if a high-risk portfolio tends to go deeper down and higher up more regularly than a low-risk one, then don’t those fluctuations remain constant even 40 years into the future? What exactly mitigates those fluctuations; is it the compounding factor? Or something else entirely?

Say it’s been 40 years and I’m 70 (I’m obviously 30 at the moment, lol). I’ve been lucky enough to withstand one-two-three market crashes and have amassed a sizable fortune by a combination of decent luck and excellent behavior. I decide it’s time to liquidate everything. Can’t my portfolio spontaneously drop in value for whatever reason and leave me at net 0 or negative?

I’ve got a pretty strong feeling my struggle mostly has to do with the exponential function right now, haha. As in, I get the base of it but can’t seem to apply it in more complex scenarios (if we

aretalking about exponentiality here and not something else that’s super obvious).On (maybe?) the same note, if we take your example with the £100, even though I get I’m wrong, I always intuitively assume that person B’s returns are just twice as high as person A’s. That’s still me failing to comprehend exponentiality, isn’t it? Or I’m just mixing up different forms of the the term “returns”?

Thank you so much for taking the time to engage, btw; I am super grateful and your website is a godsend.

Ah apologies, I misunderstood your question!

You’re right, those fluctuations are the same no matter whether you’ve invest for one day or one century.

If you’d been investing for 50 years and I’d only invested yesterday, and the market fell 50%, we’d both experience a 50% drop.

What causes your annualised returns to look less risky is that you’ve got 50 years of other returns in the past. If you’ve had 49 years of returns at about 9% every year, for example, then one fall of 50% won’t (on paper) make much of a difference to your long term average, which will now likely be just under 9%. As you’ve correctly intuited though, that 50% still halves your portfolio’s value. So the returns aren’t any less volatile, it’s just that the longer you measure returns over, the closer your average return will be – on paper – to the long-term average. But this isn’t particularly relevant for us investors in the real-world, as, as I mentioned in my previous comment, small differences in annualised returns can make a huge difference to terminal portfolio values. Not only that, but as you’ve rightly stated, the timing of when a crash occurs matters greatly to your ending portfolio value.

You’ve stumbled upon an interesting area of investing known as ‘sequence risk’ (which I touch on in this post), which is all about how the order of your returns matter.

If you’d instead had that 50% drop right at the

startof your investing journey (rather than the end), when you were making small contributions to a brand new pension pot, followed by 49 years of 9% returns a year, then the impact on your final portfolio value of that initial 50% drop would be tiny. The -50% would be being applied to a very small number, and you have 49 years of additional contributions which would compound at 9% per year.There’s a whole branch of investing theory dedicated to how you manage the transition into retirement, as this is when the sequence risk is at its greatest. As you point out, if you’re about to retire and see your portfolio halve, then you’re not going to be a happy bunny.

In terms of your question on your portfolio falling to zero – as long you hold a sensible, risk-appropriate, global, diversified portfolio, then your portfolio will never drop to zero. If it does, it’s time to start hoarding guns and ammo, because it’s either a zombie apocalypse or an alien invasion. In either case, your investment portfolio is the least of your worries.

Hopefully that helps clarify things and I haven’t just added to the confusion!

Awesome, yes, that very much clarifies everything. Thanks for another in-depth reply! It seems my initial impression of the graph was that given enough decades, you are

actuallyreducing your volatility risk and essentially “transforming” your high-risk assets into a sure deal. My intuition was telling me something was off about that and I’m happy to see what the idea was in reality: that your long-term annualized average return may theoretically be a satisfying number but pragmatically you may end up with a relatively unsatisfying terminal return depending on timing.Thanks for the link. Evidently I have tons more reading to do. 🙂

One final question (on this subject anyway!), say my strategy is to invest either a fixed sum per month for the next 40 years or a percentage of my earnings, once again on a monthly basis; either way I’m contributing regularly and maybe even overcontributing during crashes. If I have a stock-heavy portfolio with an annualized average return rate of 10% at the end of said 40 years but suddenly experience a 50% loss, would I still be above or at least near the expected terminal value of a very low-risk portfolio? Am I correct in assuming that a high-risk portfolio is ultimately more lucrative than a low-risk one in the long run (if you survive) even in the worst case scenario?

Great, no problem!

Afraid that’s a difficult one to answer, as it depends on the level of long-term stock returns and exactly how low-risk your comparison portfolio is. In theory, assuming you’re investing in something with a long-term expected return of at least double the low-risk investment then yes you should be OK if you incur a 50% drawdown at the finish line. But that’s not really how you should be deciding on whether to invest in something high risk or not. A more sensible/conventional approach to asset allocation would be to try and figure out your own risk tolerance (see this post), which should help you understand how you’re likely to react to market losses, and therefore inform your asset allocation decision.

Bunging everything into a 100% stock portfolio always looks great in theory (especially in backtests and theoretical scenarios), but different people react to drawdowns in different ways. If you’re a pure equity investor, you can expect your life savings to halve in value every 10 years or so. While this has been the strategy to maximise long-term returns in the past, it’s not for everyone. If it means you’d pull out of the market after a 30% drawdown and go to cash for the next 10 years, then a lower-risk portfolio would have been the better choice for you, as you’d have been able to stay invested and not miss the eventual recovery (which there always is). The best asset allocation is one which you can stick with. For some people that’s 100% equity, but for most it’s not.

All the best,

Occam

Thanks! I did read the post you linked to and realize there are much more factors to determining your risk tolerance than that. I just wanted to get my math straight first so I really appreciate all your feedback. 🙂

Ah good, great stuff! Sounds like you’re on the right track then.

Hey, Occam, me again with a quick question after brushing up on the subject, if that’s okay. 🙂

Strictly mathematically, how is the issue of negative compounding resolved? Is it the fact that markets grow 75% of the time that neutralizes any losses, however magnified by compounding?

Secondly, I came across the subject of “return dispersion” recently. So if I get 10% returns for three straight years, I’d have a compound average return of 10%, but if I get 30% on year 1, then -20% on year 2, then 20% on year 3, I’d have a compound average return of just 7.66%. And the number goes down the higher the variance from year to year despite the “simple average return” of 10% remaining the same. This is something I wasn’t familiar with until now; can you tell me how it fits into the overarching conclusion in this post?

Thanks a million, as always.