I Calculated the Most Realstic Return of an Index Fund

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I Calculated the Most Realstic Return of an Index Fund

February 26, 2023

I’ve calculated the most realistic return of an index fund so we can have an accurate projection of our portfolio value over time following the most common investment advice.

But before we get straight into the numbers, we need to unravel the complication and nuances of solving this problem. If you have any free time in your busy life, I recommend you watch Jack Bogle’s interview (video link) on YouTube. At around 19 minutes mark in the video, Jack Bogle questions the based on a true story:

Jack B. Bogle: “A lawyer for our underwriters when initiating Vanguard Fund invested 1000 shares ($15,000) into the Vanguard Index Fund Trust in 1976. He didn’t sell a single share ever since. How much is his investment worth today (2016)?”

Interviewer (Tom Gardner): “$106,000?”

Jack B. Bogle: “What a great guess! It’s worth $903,000 now.”

Interviewer (Tom Gardner): “I knew I was wrong!”

Jack B. Bogle: “That’s the best guess I’ve ever heard.” (Laughter)

This looks like a heartful conversation to watch. It also teaches you to stay invested in the market and never sell out of it. Which is Jack Bogle’s investment philosophy.

However, here is the plot twist:

What if I say that Tom Gardner, the interviewer and the CEO of Motley Fool, has actually made the greatest guess in the century?

Would you believe it? Let’s dig in a little deeper.

Investment Returns are like Pineapples

Before I go and explain why Tom Gardner has made the best guess in history, we need to understand a simple concept about real investment return. Think of your investment return as a pineapple. The entire pineapple is what you have at the start. As you probably know what I will say next, the problem is that you cannot eat the whole pineapple. And that’s the same in Investment return. The investment return you see on your brokerage account is an uncut pineapple. To find your actual in-pocket return, realistic return, or whatever you want to call it, we will also need to cut out the heads, skins, and cores, which are the constituents of the return that will not go into our digestive system.

But, unlike pineapples, the expenses of the investment return are more complex. It’s invisible, intangible, indirect, and personified. This complexity is why we never hear anyone talking about the in-pocket return you can use when you go out with friends. Most people will go to the Vanguard website, type in Vanguard 500 Index fund, go to return and performance, and present to the audience that Vanguard has returned 10,99% in annual returns since inception. But I want to know the real benefit and utility I can gain from this investment. So I would like to carry out this calculation with the most negligible variance. We will use the pineapple analogy again; we will find the performance return first, then shred out some significant costs that will equalize the returns to the in-pocket return. In other words, the most realistic return of an index fund.

Settings

Since I also want to show that Tom Gardner’s guess was the best in the century, I want to conduct this calculation by replicating the settings used in this interview. Which is

$15,000 of starting capital
All starting capital has been invested since the inception of the first publicly available index fund VFINX.
The final value of the investment will be as of August 2016, I want to know the exact day of this interview, but I couldn’t find it, so that I will choose the 40-years investment horizon.
We will reinvest the dividends, which are only reinvested at the end of the calendar year. I’m going to explain this later.
We will assume that we will sell the investment entirely after 40 years.
We will assume that the investor lives in the US and they use US dollars as a primary currency.

Ok, first, we will need to explain why we are reinvesting the dividends in this calculation. Can’t we receive the dividends in cash and use it for living expenses? Well, the goat would say that is not happening. With one of the many excellent investment research he’s done before, he also calculated that during the 81 years to 2007, reinvested dividend income accounted for approximately 95% of the long-term compound return earned by the companies in the S&P 500. Meaning that the reinvestment of dividends accounted for almost all of the stock’s long-term total return.

Ok, in case you still need help understanding what I just mentioned, I will simplify it. Reinvested dividends are the most powerful driver of the return that you will receive from an index fund. So that’s why I’m this feature into the calculation subjectively. Jack Bogle did not mention dividend reinvestment in this case. However, it is unlikely that the GOATed index fund manager would overlook the most significant driver of historical returns.

Ok, so finally, let’s get into the calculation!

The steps we are going to take in this calculation goes like this:

Pure price performance- dividends not reinvested
Dividends reinvested performance
First cut – Inflation
Second cut – Taxes (Dividends)
Final cut – Taxes (withdrawals)
In-Pocket return

Step 1: Pure Price Performance + Dividend Reinvested

Ok, this is probably the part of this article where you gain the most happiness and excitement from investing. This is a must-read part if you’re a motivated investor who wants to ignore reality and focus on their unpredictable craft. Just watch this part, and you will have it. In this section, we will calculate the pure price performance, and the dividends reinvested performance. Your purchasing power remains unchanged in a world where the tax doesn’t exist.

The pricing of a trust is typically priced with NAV per unit. NAV stands for net asset value, which is what Vanguard 500 index fund has left over in its fund after subtracting all the liabilities from its total assets. The fund will divide the NAV by the total number of units issued, and you will have the price that you will pay to invest in the vanguard index fund. The management fee that Vanguard will charge isn’t directly assigned to you; what they will do is they will take a certain percentage of the fee out of the NAV, which will consequently reduce all unit holders’ value by that percentage.

After manually entering the start and final price of the NAV each year, the $15,000 invested in 1976 will be $223,198 by 2016. When the dividend is reinvested, this number becomes a whopping $639,541 !

Here is the link to the workbook. The Dividend every year looks so little relative to the invested amount, but notice how it gets bigger and bigger. This is because the amount of dividends you will receive will increase every year. People call this compounding. But this autocatalysis-like cycle will only occur if the fund pays out a stable distribution every year and if you have the balls to reinvest your dividends every year and avoid the temptation to fund Jeff Bezos’s steroids by going to amazon and shopping.

Step 2: The First Cut – Inflation

Inflation, yes, the “price growth of general goods” that will erode our purchasing power. If we want to calculate the In-Pocket return, it’s an essential cut that we need to make on our gross returns. But how are we going to measure this highly controversial number? I have an undergraduate degree in economics, so I’m vaguely aware that Consumer Price Index (CPI) isn’t the best measure of inflation.

CPI only measures the price increase of the “fixed basket of goods,” meaning that if the price of goods not included in this fixed basket skyrockets, the overall CPI will not budge. However, inflation itself is necessary for our calculation.

Why? Just imagine living in Zimbabwe back in 2007-2008.

In June 2008, the annual rate of price growth reached 11.2 million percent. Yes, 11.2 million percent. And in this article, we are only talking about a 5-10% return per year. That is a crazy world to live in; that delicious Z$1 (Zimbabwean dollar) coffee that you were drinking over a year ago was now Z$112,000. You could’ve bought a Tesla a year ago, and now you’re buying a coffee with the same money because you put that money into the index fund and didn’t do anything. So yeah, we are going to include inflation in the calculation.

After manually entering the annual inflation rate from 1976-2016, the lawyer’s $15,000 invested in 1976 is now down to $142,781

That is a massive cut!! Just including the inflation has shrunk, the lawyers return by 77.7%. Now you understand why people go crazy when talking about inflationary pressures. They literally take the wealth away from you without realizing it.

Step 3: The Second Cut – Taxes on Dividends

Regardless of what you do with the dividends that a mutual fund pays to you, it is taxable at your marginal tax rate (excluding imputation credits in some countries). In this case, the lawyer receives dividends from VFINX every quarter, so he must pay tax on the distribution. Given that the lawyer is around the income bracket of $41,676 to $459,750, I’ve set the tax rate for the dividend to a fixed 15%.

Since the distribution gets taxed by 15%, the lawyer can reinvest fewer units of VFINX each year. This has a considerable effect on compounding over time. The unit amount held at the end of 2016 without paying tax on dividends was 3,096 units compared to 2,637 units if paying tax.

Hence after the lawyer gets taxed on the dividend, the lawyer’s $15,000 invested in 1976 is now down to $122,135.

Step 4: The Final Cut – Capital Gains Tax

In this part, we assume that the lawyer is in a retirement phase and he is now happy with withdrawing all his money from the index fund. He will be able to finally put his hard-working money back in his pocket and say goodbye to his client (Jack Bogle) who made him wealthier. When you withdraw the money out of the index fund, your unrealized gain becomes a realized gain and you will be subject to capital gains tax. And this tax is going to be the final cut that we need to bite in order to enjoy our retirement.

These are the two assumptions that we are going to make before the calculation:

The lawyer is going to make a full lumpsum withdrawal all at once
We assume that the lawyer is within the income bracket between $40,401 to $445,850 which makes him subject to a 15% CGT

Following the two assumptions above, the total unrealized gains that he will be subject to CGT is $419,673 (this value excludes the inflation cut), which incurs a $62,950.89 in capital gains tax payable. The total gain of the $15,000 investment that the lawyer made is $356,722, however, if we bring back the inflation cut the real dollar gain goes down to $70,845.

So now we sliced all the skins and head of the pineapple.

The lawyer’s $15,000 investment in 1976 became $85,845 in 2016, after including capital appreciation, dividend reinvestment, dividend tax, inflation, and capital gains tax.

This corresponds to $5.09% in annualized return for 40 years. And that is the most realistic annualized return that you will get from an index fund in my opinion.

Don’t get me wrong, my calculation is full of flaws. I only used VFINX as a sample for an index fund, CPI isn’t the greatest measure, income tax brackets vary and not all people make full withdrawals. But I tried my best, and this is the “in-pocket return” that I came up with.

What do you think about this rate? Some of you might think it’s actually a decent rate, and some of you might not.

Regardless of what you think, my new findings for this calculation were that I found the genius that was hiding from the crowd.

It’s this guy.

His guess ($106,000) was really close to the realistic account value that I came up with ($85,845). If we assume that the lawyer is fully retired and doesn’t have any taxable income, his account value would be $109,097 which is only $3,097 off from his guess!!!!

I can’t believe how he came up with this precise answer in such a short amount of time. It’s mind-boggling.

Anyways, I really appreciate that you actually put in the effort to read this funky article til this point. If your dad asks you what you learned from spending 5 minutes reading this article, say two things.