Congratulations on your $500,000 car

If you came here for pictures of nice cars, I’ll have to disappoint you: This is a follow-up on an investment post about an engineer’s view of how to see the stock market as an investment.

First, a correction

When presenting the data on the S&P500 corrected by inflation, I didn’t account for dividend re-investment. The difference is quite tremendous and is something not very well pointed out throughout the investment internet. Dividend re-investment, as a first order approximation, negates or alleviates the inflationary effects, which allows the real gains to compound effectively in the long term. In this chart below, I’m showing the mean gain (thick black line) of the S&P 500 from data between 1950 and 2020; across multiple time windows, statistics drawn from any rolling period within the data. The shaded regions correspond to the 1 standard deviation (67% of the cases) and 1-99 percentile (98% of the cases); again all from data. The difference between this curve and the curve posted on the previous post is that here I’m including automatic dividend reinvestment. This means, as the companies pay dividend you automatically purchase more shares on the S&P500 index. On the left, we see a long-term view (from 2 days to 40 years), and on the right we see a zoomed-in version from 2 days to only 1 year.

It is clear that the curve goes up really fast at the longer time windows. For time spans longer than 20 years, there’s literally no scenario that involves you losing money in the market if you re-invest the dividends. That sounds like a decent bet on my future!

Now to the auto loans

I’ve seen some of Dave Ramsey radio shows where he says that “your most powerful wealth building tool is your income” – which is taken away if you start getting engaged in debt (such as auto loan debt). He’s great at putting the qualitative aspects of saving into perspective and making some sort of “mantra” or “religion” out of it. That’s great and it works for everyday people who don’t want to see the math (I guess?), but rational engineers just want more data to make their decisions.

According to Credit Karma, the average auto loan payment in America is $568 for new cars and $397 for used cars. So I put together a Monte-Carlo simulation to understand the impact of auto loan debt over long periods of time. But before checking out the Monte-Carlo results, let’s just do some simple math:

According to the data presented in the previous section, the average dividend-reinvested yearly return of the S&P500 is r=8.6\%/yr, or r_{monthly}=0.689\%/mo. Remember, this is already inflation-corrected. Thus, if we saved the monthly auto loan payment, we would expect, on average:

S=\sum_{n=1}^{N} P (1+r_{monthly})^{N-n}

Where S is the saved amount over N months, and P is the monthly payment; compounded monthly. Thus, having the average car loan payment on your budget for extended periods of time is going to prevent you from accummulating; on average; this amount of wealth over the following time spans:

Time span$400 loan$570 loan
5 years$29 596$42 175
10 years$74 282$105 852
15 years$141 749$201 993
20 years$243 611$347 146
30 years$629 600$897 180
Amount you’re preventing yourself to save by having a car payment, over different time spans.

The amounts over a short period of 5 years are of the order of the car’s price tag, as expected. But over the time-span of a career, like 20-30 years, the potential savings, compounded with the interest, is mind-boggling. For the $400 loan with 30 years, only $144 000 come from your “deposits”. The remainder ($485 600) comes from interest. I can’t stress this enough – these numbers are inflation corrected as of 2021 – You lose about $500 000 over the course of your whole career by having a car payment. Using the famigerate 4% rule, you would be able to buy a $40 000 car every two years with that money!

“But, Fernando, there’s no 30-year car loans! The loan periods are at most 7 years, right?” Well – if you’re used to having the loan on your budget, you’ll always have it. It’s a cultural and psychological aspect. The marketing they make is very convincing. The western culture has this aspect of “But I deserve it, I worked so hard!”.

Well, I’m not saying you don’t deserve a nice car, but you have to understand the trade-off. If $500 000 (in 2021 money) is not much for you to have added to your portfolio 30 years from now, then good for you! Just make sure you’re actually making that decision – and it’s not being made for you, by the financial industry.

Monte carlo simulations

I have an issue with “average” statistics. They are not very useful in assessing the variability of the outcomes, and they don’t take into account that you might go through a bad decade for the market towards the end of your savings period. To get a better view of how the outcomes change with the “certain uncertainty” of the stock market, we can run what’s called a Monte Carlo Simulation.

The simulation I set up is as follows: I’m assuming you’re depositing the auto loan payment P into a S&P500 index fund (say, VOO) every month over the course of 30 years. For every month period, I randomly pick a start date and an end date 1 month apart in the S&P500 time series from 1950 to 2020. I’m assuming that you’re re-investing dividends and I correct the S&P500 time series from inflation effects prior to picking the random returns. There are 17843 rolling 1-month periods within this time span. So I pick one of these, and make this the outcome for that month. I run 1 million of these “scenarios”, each one containing randomly chosen 1-month periods over the course of 360 months (30 years). For each scenario, I get a whole time series of outcomes that looks something like this:

50 sample outcomes from a Monte Carlo simulation for a $400/mo savings to an S&P500 index

As can be seen, the outcomes vary wildly. There’s outcomes that are “lucky strikes”, where the portfolio value accumulated all the way to $2M, and there are unlucky outcomes where the portfolio drops to $150k just as you’re about to “retire”, say.

The chart above is interesting but the power of Monte Carlo simulations is the sheer amount of statistical data you can generate. After running 1 million scenarios, there’s a pretty clear distribution of outcomes, as can be seen in the charts below:

For the used auto loan ($400/mo), we are saving a total of $140k over the period of 30 years, which invested become, again – in 2021 money – $570k; as a median outcome. The percentile 5 outcome (i.e., 5% of the outcomes are worse than this) is $220k; and the percentile 95 outcome (i.e., 5% of the outcomes are better than this) is $1.59M. In other words, it’s rather likely (90% likely) that if you save $400/mo in an index fund for 30 years, you’ll get anywhere between $220k and $1.59M in retirement wealth. Or, conversely, by constantly contracting a $400/mo debt you’re foregoing between $220k and $1.59M in retirement wealth.

Which is a lot. It’s even worse for new car loans – between $310k and $2.28M. Even the worst outcomes still result in some capital gains. So ask yourself next time you go to a car dealership: Is this car really worth $500 000? I would say, probably not.


P.S.: This post is just to put things into perspective. When I did the calculations I was baffled. It’s not about not wanting to have nice things. It’s about whether you really want to pay that premium. Because used cars are so much cheaper, it’s likely you can buy one with cash – and keep on buying them with cash. This way, the impact in your long term wealth will be rather negligible.

Hope you found this useful!