After talking about Cash flow vs Savings rate in a recent post, it’s time to look at Savings rate vs market returns.

In the Lazy FI family’s October 2021 results post, someone asked me what market return I assume in my models. Funny enough, my brother asked me the exact same question this week so I thought I’d dedicate a post to it.

I’d like to break it down into 2 parts: The first part will be about how savings rate and market returns work together (or take turns). The second part will be savings rate vs market returns- which one’s more important?

## Savings rate and market returns working together

If I had to sum the concept of savings rate and market returns into one sentence it would go like this:

In the beginning, it’s all about the savings rate. As you progress, it becomes more and more about the market returns.

I can write a long explanation about this but I’d rather let the numbers do the talking.

### Assumptions and how to read the results

- In the Lazy FI family, we have a long term target of a 40% savings rate so we’ll assume that savings rate.

- Let’s assume we earn £10,000 a year and save £4,000 (40% * 10,000). That means our annual expenses are £6,000.

Based on the 4% rule, that means we would need to reach £150,000 to achieve FI.

- Let’s also assume we have no debts or assets so our net value is zero.

- I assumed a 4% annual real return (after inflation), that’s the equivalent (roughly) of a 6% nominal return and a 2% inflation or… a 7% nominal return and 3% inflation and so on. This is also the rate I use in my models. It’s considered very conservative but:

- I prefer planning for low returns and being positively surprised.
- The return doesn’t matter that much, will discuss this in the 2nd part of this post.

- I also assumed the £4,000 is invested in one go at the
**END**of each year for simplicity.

### The results

### What can we learn from this table?

I want you to look at some interesting things:

First of all, assuming a 4% annual return and 40% savings rate, it will take someone 23.36 years to reach FI. Not too bad but still seems a long time. In the second part of this post, you’ll see how a change in savings rate or market returns can affect the length of your FI journey.

#### Handing over the power to Mr Market

Second, in the first few years, Mr Market isn’t really pulling his weight. It takes him 7 years to equal (only) a quarter of the savings that Lazy FI person’s making. It takes Mr Market another 5 years (12 in total) to get to 50% of the savings Lazy FI person makes each year. The next step, 75% is after another 4 years (16 in total). Then, finally, after another 3 years (19 in total), Mr Market takes the lead and increases Lazy FI person’s net value more than Lazy FI Person himself!

Kitces.com called this “The portfolio size effect” in a post, he explains: “the impact of a portfolio’s returns is dependent on the portfolio’s size.” I mentioned this phenomenon in several monthly results posts. As we get closer to financial independence, we become more and more dependent on market returns. That’s because when our portfolio is big enough, market returns have a bigger impact than our contributions.

#### Compound intererst

Third, notice how each 25% increment took less and less time as you go along? that’s the power of compound interest.

As time goes by, the net value increases and so do the market returns (in £). It works the same with the net value by the way: the first £50,000 took 10-11 years but the second £50,000 take only 7-8 years, you can see that in the “Net Value a year-end” column in the table. Then, the next £50,000 take only 6 years! The good news about that is that if you reached 50% (or any other percentage) of your FI number, you’re more than 50% (in time perspective) into your journey because the next 50% will take less time, now that Mr Market is pulling his weight.

That’s the beauty of the savings rate and market returns working together.

#### Do it yourself

If you want to change the data and see the results, here is the link to the file. The first tab, called “FI journey”, has the model for you to play around with. It has 2 more tabs, which I’ll introduce shortly.

Important notice: The file is not editable straight from Google drive so please download a copy to your computer and edit it on there.

## Savings rate vs market returns- which one’s more important?

Ok, after we saw that they work nicely together, let’s see who’s more important.

I must admit I got the idea for this post from ERN’s amazing post titled “The Shockingly Simple/Complicated/Random Math Behind Saving For Early Retirement”.

There was one quote from his post that blew my mind and made me run to my Excel:

*“It’s tempting to get lazy with the savings rate and hope to compensate for that with better investment results. Don’t delude yourself! Imagine person A plans for a 5% return and a 60% savings rate. The path to FI would take 12.2 years. If person B’s savings rate is 55%, even with an 8% annual return, the path to FI would take 12.3 years. Three full percentage points are not enough to overcome just a 5% difference in the savings rate!”*

That quote is amazing and not just because of the word “lazy”.

In this post, big ERN created a table that shows how long will it take a person to reach FI using only his savings rate and the real return. He used monthly contributions, which I like. I recreated his work in 2 tabs (in the same file as before, available here). One tab uses monthly contributions (“Time to FI- Monthly contrib” tab) and one tab uses annual contributions (“Time to FI- Annual contrib” tab).

### Assumptions and how to read the results

- Both models assume the contributions are made at the end of the period (month/year).
- Both models assume you start with 0 net value.

- The annual market returns are all in row 14 (each column represents a different market return). I used 0%-10% with 1% increments
- The monthly return was calculated using this formula:

(1+annual return)^(1/12)-1

In my opinion, this is a bit more accurate than using annual return/12 because it assumes compound interest. - The results in both tables are presented in years.
- How to read this table, example:

In the monthly contributions table, someone with a 30% savings rate and 9% annual return will need 20.9 years to reach FI.

### Savings rate vs market returns- The results

### What can we learn from these tables?

We can learn a lot from these tables.

First, for every single scenario (except 0% market return), the journey to FI is shorter using monthly contributions. That’s not surprising because if you invest each month instead of each year, the money has more time to be invested. As we assume positive returns, it’s more time for Mr Market to do his thing. For example, someone with a 40% savings rate and 4% annual return would need 23.4 years to reach FI if contributing at the end of each year. The same person would need 23.1 years to reach FI if they contribute at the end of each month.

Second, In the lower savings rates, every increase in savings means more. The reason is that going from 5% to 10% doubles your savings rate. However, going from 50% to 55% only increases your savings rate by 10% (5/50). for example, looking at the monthly contributions at 4% return, moving from 5% to 10% reduces your journey by 17.6 years (from 75.9 to 58.3). Moving from 50% to 55% “only” reduces your journey by 2.4 years (from 17.4 to 15).

Third, The market returns mean a lot **less** when your savings rate is high. Let’s look at an example:

A person starts with a 4% return and a 50% savings rate. He will need 17.4 years to reach FI. That person has 2 ways to reduce his journey to 12.8 years. He can either increase his savings rate to 60%, or he can increase his annual returns from 4% to 10%.

I’ll leave it with you to decide what’s easier- increasing your savings rate from 50% to 60% or increasing your annual return from 4% to 10%. Regardless of which answer you chose- which one is more under your own control?

#### My conclusions

I would focus on savings rate for 3 reasons:

- If you’re just starting your FI journey and have a low savings rate, every increase means a lot so I would focus on that.
- If you’re a high saver (50% or more), you’ll reach FI very quickly so the money will have less time to earn those returns, that’s why returns are less meaningful when you save a lot.
- It is much easier to control your savings rate than it is to control Mr Market.

#### Do it yourself

Want to see the results if you don’t start with 0 net value?

Want to input your own data that might have a savings rate that doesn’t divide by 5?

Go to the file on Google Drive by clicking here, download it and play with it yourself 🙂

## Conclusion

In the first part, we saw that it takes time until Mr Market starts pulling his weight. In the second part, we saw what effect a change in the savings rate and the market return has on our FI journey.

Notes:

I know the markets won’t return 4% every year. There will be crashes and years better than 4%, I assume a flat 4% for simplicity and because I don’t attempt to predict market returns.

Some of you have asked to see the actual Excel models. I listened to you and now you have access to these files. I hope this improves your experience.

When I refer to a random person as “he”, “his” etc. it is because in Hebrew (my first language) a non-defined person is referred to as a male so it feels weird to say “their”, “they” (in plural) for a single person. Math doesn’t discriminate between sexes/genders. I promise you the same numbers apply to men and women in the same way.

First of all, I really appreciate what you did in your post! I was familiar with post of Mr. Money Mustache on this topic but you discovered some more helpful thoughts about importance of saving rates vs. market returns. Thank you! I’m following you on Twitter too. Please continue with your posts, it’s very interesting to learn about your journey to FI.

Thank you for your kind words, I really appreciate it.

Yes, the title ERN gave his post was a parody of this famous post by MMM.

For anyone reading this and thinking “what on earth are they talking about?” here’s the link:

https://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/