Index fund stocks and compound interest examples

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anroy
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Index fund stocks and compound interest examples

Post by anroy »

Almost anything you read about investing (at least at my n00b level) invariably contains an example of how compound interest works wonders.

For example (based on momentary googling): And of course many more.

They always make it sound very easy and passive. However when we invest in the financial markets, it's not really that passive and easy is it? The point of compound interest is that your interest earnings are being re-invested and you are increasing your principle.

For example, I mainly just buy index fund ETFs. To replicate the results in these ubiquitous compound interest examples, I'd need to continue actively playing the stock market, selling when high and buying when low to increase the principle.

Is this the assumption being made, in these compound interest examples?
Or am I misunderstanding something?
TokyoBoglehead
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Re: Index fund stocks and compound interest examples

Post by TokyoBoglehead »

anroy wrote: Mon Oct 24, 2022 9:00 am Almost anything you read about investing (at least at my n00b level) invariably contains an example of how compound interest works wonders.

For example (based on momentary googling): And of course many more.

They always make it sound very easy and passive. However when we invest in the financial markets, it's not really that passive and easy is it? The point of compound interest is that your interest earnings are being re-invested and you are increasing your principle.

For example, I mainly just buy index fund ETFs. To replicate the results in these ubiquitous compound interest examples, I'd need to continue actively playing the stock market, selling when high and buying when low to increase the principle.

Is this the assumption being made, in these compound interest examples?
Or am I misunderstanding something?
Passive investing can be easy. The longer your timeline the lower the risk. Look at a long-term chart for the S&P500.

They key is to buy diversified, low-cost funds and hold them for a long time.

Remember stocks make money in two ways

Growth, as in stocks increasing in value
Dividends, quarterly payments received for holding shares.

Dividends can be reinvested and allow you to buy more shares. Japanese trusts do this automatically.
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RetireJapan
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Re: Index fund stocks and compound interest examples

Post by RetireJapan »

anroy wrote: Mon Oct 24, 2022 9:00 am For example, I mainly just buy index fund ETFs. To replicate the results in these ubiquitous compound interest examples, I'd need to continue actively playing the stock market, selling when high and buying when low to increase the principle.
Not necessarily. The compound interest comes from 1) companies investing profits back into the company and increasing the share value, and 2) dividends being reinvested into the fund

You do not need to put more money in to benefit from compound interest, although doing so increases the amount you have invested, which is normally a good thing.
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Tkydon
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Re: Index fund stocks and compound interest examples

Post by Tkydon »

anroy wrote: Mon Oct 24, 2022 9:00 am Almost anything you read about investing (at least at my n00b level) invariably contains an example of how compound interest works wonders.

For example (based on momentary googling): And of course many more.

They always make it sound very easy and passive. However when we invest in the financial markets, it's not really that passive and easy is it? The point of compound interest is that your interest earnings are being re-invested and you are increasing your principle.

For example, I mainly just buy index fund ETFs. To replicate the results in these ubiquitous compound interest examples, I'd need to continue actively playing the stock market, selling when high and buying when low to increase the principle.

Is this the assumption being made, in these compound interest examples?
Or am I misunderstanding something?

The Compound Interest calculation is not really directly appropriate for Stocks / Equities.
You cannot take the value of your ETF today and reliably calculate the Future Value using the formula at a particular interest rate.
The Dividends payable, and the Equity Growth are not fixed, and the quoted Yield % you see will change as the Market Price changes.
You can use the Compound Interest calculation backwards to work out what Compound Interest rate that would have produced the Final Value from the Starting Value after the fact.

The Compound Interest calculation would be correct for Bonds held to Maturity, but would not be correct if you decided to sell the Bonds before maturity.

The Compound Interest calculation is also used backwards to calculate the Net Present Value of a future Cashflow discounted at a given Compound Interest rate.

Having said that, the principle of Compound Interest is still valid, showing how the value of your investment might be expected to grow over time.

Index Fund ETFs - The ETF Provider buys Equities on your behalf matching the composition of Index that it follows, and if any of those Stocks pays Dividends, then the Dividends are reinvested to continue to grow the value of the ETF Unit.

You can project what you think your ETF might be worth in the future by picking a Compound Interest rate and using the formula. For different Compound Rates you will get different ending values. But this is only an Estimate, and the performance is not guaranteed. You will see different Annual, 5 Year, 10 Year, etc. performance rates achieved in the past.

A simple way of working this out is called 'The Rule of 72'. If you divide 72 by your Interest Rate it will tell you approximately how many years it will take you to double your money;
e.g. If your ETF grows at 10% Per Year, it will take 72/10 = 7.2 years to double in value (approximately). If your ETF grows at 5% Per Year, it will take 72/5 = 14.4 years to double in value (approximately).
Conversely, if your Investment doubled in Value in 4 Years, you can calculate the Compound Interest Rate that would have produced that result as 72/4 = 18 Percent (approximately)...

Dividends are quoted as a % Yield. However, this is only applicable if you buy the Shares at that Current Market Price...
The company does not pay you a fixed % on what you paid for the stock. It pays a (fixed, but changeable...) value in Dollars and Cents, which combined with the Current Market Price (constantly changing..) gives a % Yield at that instant...
Your actual Yield % will be determined by the Purchase Price you actually paid for the stock (fixed) and the Dividend Value (fixed, but changeable...). Once you have bought the stock, you cannot go back and change the Purchase Price you paid...

If you are buying your ETFs on a regular basis, then you are doing what is known as 'Dollar Cost Averaging'. When the price is higher, you buy relatively less units, and when the price is lower, you buy relatively more units, but over a long period, the average price you paid for all the units you have will be somewhat lower than the highest price. And your gain will depend on the current Market Price of the units compared to the average price you paid for the units.

The underlying mechanism is rather complex:
A company (hopefully) generates Earnings, which (hopefully) are greater that the Costs of running the business, which lead (hopefully) to Profits, which are then taxed, (hopefully) leaving Net Free Cashflow.
The company can use Net Free Cashflow in various ways:
- Re-Invest in the company to grow the company and revenues in the future, and therefore the company's future value and (hopefully) Share Price
- Acquisitions of other companies to grow the company and revenues in the future, and therefore the company's future value and (hopefully) Share Price
- Pay Down Debt, reducing the Costs associated with interest payments, which increases Profits and future Net Free Cashflow.
- Buy Back Shares, reducing the number of shareholders across which the Value Increase and Profits have to be distributed
- Pay Out Dividends, distributing some portion of the Net Free Cashflow to the shareholders as Income.

Dividends constitute future cashflows / income to the shareholder so do not contribute to the future growth in value of the company, but are still accounted for in the current share price. The other activities contribute to the future growth in value of the company.
Making lots of assumptions, you would expect the company to grow in value and provide growing dividends in the future, which will (hopefully) lead to a growth in the share price over time.

Then, the price people are willing to pay for the stock will depend on these Fundamantal or Intrinsic Value Factors, along with Future Value Factors such as Interest Rates, Risk Premia and Inflation, and Market Factors such as Psychological, Technical Investing, and Market Manipulation Factors...

Having said all that, future performance is not guaranteed, unlike (hopefully) a bank interest rate on a bank account deposit...
:
:
This Guide to Japanese Taxes, English and Japanese Tai-Yaku 対訳, is now a little dated:

https://zaik.jp/books/472-4

The Publisher is not planning to publish an update for '23 Tax Season.
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