Is It More Important to Save or Grow?

Everyone is obsessed with return.

We’ve all seen the compounding charts that show your bank balance magically growing exponentially due to compounding returns. The end value result seems to explode as you increase the rate of return. “If I could just increase my return from 5% to 10%, look how much extra cash I’ll have when I’m 50!” you say.

Everyone seems to have forgotten that are two ways to grow the amount in that account: adding more and applying a larger growth rate. Professional money managers are – rightly – mostly concerned with the rate of return because they can’t easily add more money outside of raising rounds of funding and/or getting new clients. You, however, are your own client. You can add money to your account whenever you want.

Your savings rate is as important, if not more, that your growth rate.

Comparing Paths

Let’s compare the differences to the account value of David, a 30-year-old law associate (specialising in commercial property) earning £100,000 annually, after taxes (lucky bugger). When fixing his savings rate at 5% (£5,000 a year for those of you severely mathematically challenged), we can compare the value of his bank account with three different rates of return:

Value of the bank account vs. years. Savings rate fixed at 5%.

Similarly, we can fix his growth rate at 5% and compare the value of the same bank account with three different savings rates:

Value of the bank account vs. years. Growth rate fixed at 5%.

The first thing to note here is that the middle scenario is identical in each chart (both savings and growth rate are 5%). The lower scenario, too, seems to generate a similar path. The high-growth scenario generates a higher terminal value but this account balance only starts to become greater than the high-savings scenario after around 30 years or so. Note the differences between the terminal values: in the variable growth scenario, the differences are increasing but in the variable savings rate scenario they are constant. Why is this the case?

Terminal Values

To compare the terminal values of David’s bank account in different scenarios we need a quick sprinkling of maths. Here’s one I made earlier:

There, that wasn’t so painful, was it? This gives us a formula for calculating the bank account value at any time n.

Savings rate

Let’s fix growth rate at 5% and see the effect of incrementally increasing in the savings rate vr on the value of David’s bank account at time n. Here we use n = 30 (years) – when the poor bastard is 50 and, he hopes, now a partner at his law firm.

As we see below, the final value of the bank account goes up linearly as the savings rate increases up to 20%. This just means that an increase in the savings rate can be thought of as adding a fixed amount to the final value of the bank account, regardless of what savings rate you started with. If the growth rate is constant, our equation reduces to bn = vr * C, where C is some constant. This is why this line is straight – we are adding more and more C. 

Savings rate vs. terminal value. 30-year investment horizon.

The rate of increase for the three different growth rates is different. Think of it like a ladder leaning against a wall where the goal is to reach a certain height. How quickly we do so will be determined by the angle that the ladder is placed at and how quickly we step up the ladder. The growth rate can be likened to the angle: a larger angle (higher growth rate) will mean fewer steps (savings rate) required to get to the top. But, at the end of the day, you still have to take steps up the ladder (increase your savings rate) to get to some height (reach some terminal value). I feel like that analogy was confusing but fuck it, we’ll roll with it.

Growth rate

Now let’s fix the savings rate at 5% and see the effect of incrementally increasing in the growth rate (by increasing CAGR) on the value of David’s bank account, under the same conditions. This line is not so linear: the same increases in the growth rate lead to progressively larger increases in the terminal value. This is known as convexity

Growth rate vs. terminal value. 30-year investment horizon.

Considering different savings rates, we see the contrast in linearity and non-linearity again. As we increase the savings rate, the terminal values increase by the same amount (see the differences between the lines). But if we increase the growth rate, the terminal values increase by increasing amounts (see the difference by moving up one of the lines). 

Direct Comparison

Now let’s compare different combinations of growth and savings rates on the same chart:

Investment horizon vs. terminal value.

As you can see, there is no out-and-out obvious winner. What does seem to be true is that the effects of the growth rate dominate as the time horizon (n) is extended. The curve becomes more curved as we trade off savings rate for growth rate, hence lower at the beginning but higher at the end. 

These lines are (roughly) the same length.

Now let’s introduce two new characters who both have the same net income (£100,000, remember?) but very different savings and growth rates.

Trading212 Tom is a software engineer who works at an anonymous large tech company who used to be exclusively in the book business but have since diversified. He’s obsessed with r/WallStreetBets and has 25% of his net worth in crypto. The other 75%, however, he puts to work and by hook or by crook manages to generate a whopping 10% per year of real returns. Hats off to you, Tom. But Tom only manages to save 5% a year to go into his investment account (takeaways 3 times a day, buying literally all the latest tech, renting a studio apartment in London, etc. are not cheap).

Sensible Susan, a senior research associate for an anonymous big 4 accounting firm with only four letters in its name, wouldn’t dream of investing in anything not recommended to her by her financial adviser, who she emails at least once a week. In fact, she has to cover her ears whenever she hears the words “crypto”, “bitcoin”, or “blockchain” to prevent herself from having an anxiety-induced panic attack. Naturally, she is cautious with her investments: she manages just 2% real return per year. However, she is frugal, spending in a calculated and only-when-necessary-and-if-it-fits-the-budget-that-I-have-in-excel fashion. She doubles Tom’s rate of saving (10%). Bang.

Investment horizon vs. terminal value.

Even though Tom crushes Susan’s rate of return (and posts about it on Reddit), he doesn’t actually start to have more money in the bank until year 17. Turns out saving is fairly important.

Better option

This scenario encapsulated the problem with obsessing over returns: it’s not very effective. Even if you’re able to generate pretty remarkable returns for a sustained period of time (very, very unlikely), it doesn’t matter if you’ve got nothing substantial to grow. Imagine a garden that has perfect conditions but the owner can’t be bothered to plant many seeds vs. one with average conditions but the owner (a bored middle-aged person) is obsessed with generating as much output as possible. Who will have more product when it’s time to harvest? My money’s on the later.

Another problem with growth is the other costs associated with higher rates. Firstly, there is the extra time commitment. If I want a return of 0%, there is no time commitment. I just have to stuff pink £50 notes under my mattress. If I want 10%, however, it’s more work. At the very minimum, I have to conduct due diligence on asset managers (and that probably won’t work). Generating 10% by yourself is a full-time job and, spoiler alert, one that will be extremely stressful and you probably won’t succeed at. Higher returns have higher psychological cost, too. If you’re comfortable with the risks, fine. If not it can be mentally exhausting.

It’s simply far easier to increase s than to increase r. People literally get paid billions of pounds to go from a rate of return of 5% to 10%. And they still fail, most of the time. Going from a savings rate of 5% to 10% requires some minor lifestyle adjustments. What’s more, s is composed of both savings rate (vr) and income (i). Increasing either of these will increase s. To increase r, you must increase CAGR.

Most of all, obsessing over growth rate is a fundamental violation of principles:

  1. Think long-term. Fails if obsessing over your annual growth rate. Passes if obsessing over long-term CAGR.
  2. Risk-focus. Fails. Risk management flies out the window when you’re chasing 15% returns.
  3. Limit downside. Fails. Big downside part of the game.
  4. Consider the big picture. Fails. Investing is about improving your life. Spending all that mental energy trying to get 5% extra return is a waste (unless you love it).

One does not invest to make wealth. If you want to make wealth, there are plenty of other ways to do it. Invest to preserve/nurture wealth, not create it. 


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