# Does selling index fund shares for the same amount the account grew by reduce the account's value?

I've been thinking about what retirement looks like, and I'm trying to figure something out. Let's say I have a sum invested (\$Y) in an index fund that grew by 60k in 12 months, for a total value of \$X. If I sell shares to a value of 60k, bringing my balance back to \$Y, and the growth rate remains the same for the next year, am I correct in assuming that 12 months later the account will once again be worth \$X?

Would I be able to sustain a personal income of 60k a year like that indefinitely, given a constant growth rate? Like, would I eventually run out of shares to sell, or would each share be increasing in value each year enough for those transactions to remain viable?

This seems like a dumb question, since the math seems to side with me on a basic level; eg, Y +60k = X, X-60k = Y, Y +60k = X, and so on forever. However, my experience with investment is nonexistent, so I'm having trouble understanding if there being a specific number of shares representing my balance would change this situation.

This hypothetical is purposefully ignoring the fact that index funds don't normally have a fixed constant growth rate to address the question of whether I'd run out of money by always selling equal or less than the amount by which the account grew each year.

This hypothetical is purposefully ignoring the fact that index funds don't normally have a fixed constant growth rate to address the question of whether I'd run out of money by always selling equal or less than the amount by which the account grew each year.

That's a pretty important fact to ignore, but let's roll with it.

IF the investment had a constant growth rate, then yes your math is correct, but only "risk-free" investments like US government bonds have constant growth rates, and that growth rate is probably not enough to sustain you in retirement. It would mean that you have about 50 times your required income in t-bonds, in which case you can almost certainly afford to take more risk.

If the investment can vary in how much it grows (or loses), and you take out 100% of the growth each year, then you would gradually run out of money due to the years that the investment loses value.

Say you started with \$1,000, removed profits from year 1 to get back to \$1,000, but in year 2 the investment lost 10% (\$100). Then you'd have \$900 at the end of year 2. From there, you could either just reset your base investment (continuing to take 100% of profits) or replenish the \$100 in years that the investment made money.

A more practical plan would be to determine how much you need to withdraw each year. If the investment makes more than that, you keep the excess in the investment to compound returns. If it makes less, then you would still make the necessary withdrawal, hopefully making up for the loss in years where the investment made more.

Depending on how much you need to withdraw, you would then choose an investment portfolio that is expected to make MORE that that with the minimum amount of risk. That way, you have more certainty that the bad years won't be as bad and you will have less catching up to do in the good years. That is easy to say and very hard to do (which is why financial advisors are valuable).

• Thank you for this answer. Yeah, I understand that index funds are volatile, I mostly just wanted to confirm my suspicion about not running out of shares under those conditions. I'll seek a financial advisor for the actual investment plan, for sure. I just wanted to get a better baseline understanding of how to "pay myself" from an investment portfolio. – Will J Sep 5 '18 at 17:04

Your account value is simply the number of shares you own, multiplied by their price, plus any cash in the account.

It's a simple consequence of mathematics that if the share price is increasing, but you are holding the account value constant by withdrawing gains, the number of shares you own must decrease.

It also follows that you would not "run out of shares" unless you owned zero shares, and thus had no remaining value except maybe cash. Either because you liquidated the account, or the value of the fund collapsed for some reason, like all the holdings of the fund went bankrupt.

When dealing in individual stocks or ETFs, trades must be made in whole shares. But for a reasonable retirement account balance which is at least hundreds of thousands of dollars, in almost all cases a single share is such a small fraction of the account value this isn't of much consequence. Companies typically issue stock splits to keep their prices accessible. Even Berkshire Hathaway (BRK) which famously has an obscene stock price for class A shares (\$319,920 currently) because they refuse to split the stock, introduced class B shares which trade at a much more reasonable \$212.

Mutual funds usually trade in fractional shares, so transactions of even a penny are possible.

"Would I be able to sustain a personal income of 60k a year like that indefinitely, given a constant growth rate?"

Please note that even if you received the constant growth rate, the 60k in the first year will be worth much more than the 60k in the 20th or 30th year. The value of your money will decrease due to inflation (and likely also tax increases).

The \$Y and \$X must increase some to retain the same buying power that they had initially.

So "am I correct in assuming that 12 months later the account will once again be worth \$X?"

is a little misleading as a question. The number of dollars will still be the same number, but the value of those dollars will be less because those \$X will buy fewer gallons of milk, gasoline, etc.

So normally people should plan to allow some of the early gains to remain in the account to provide more dollars in future years. One typically the rule of thumb is to withdraw about 4% initially per year if you want to maintain the initial principal in the account and ensure you can increase the levels of withdrawals later.

Yes, you would eventually run out of money because you are selling shares every year. However, the number of years that it would take to deplete your assets would depend on the size of the 'constant' Growth Rate (GR).

As you noted, X + 60k = Y

To achieve \$60k of growth per year, you need a starting amount of (60k / GR) - this is the value of X. The Depletion Rate (DR) is the percent of shares that you will have to sell each year and it equals (60k / Y) or ((60k / (X + 60k))

1) With a growth rate of 1% a year, you need to start with 6 million and the DR will be .99% (60k / 6.06 million)

2) With a growth rate of 5% a year, you need to start with 1.2 million and the DR will be 4.76% (60k / 1,26 million)

3) With a growth rate of 10% a year, you need to start with 600k and the DR will be 9.09% (60k / 660k)

4) With a growth rate of 20% a year, you need to start with 300k and the DR will be 16.67% (60k / 360k)

So the higher the growth rate, the higher the replenishment rate as well as the greater the number of shares you'll have to sell each year. A 10% growth rate will take 100+ years to deplete whereas a 20% growth rate will take 50+ years to deplete. For a better answer, someone with more elegant math skills than me will have to craft some equations that offer a more precise number.

• If this is a traditional mutual fund, they can sell fractional shares and never run out. (Assuming the fund never loses value, as stated in the op) – The Photon Sep 5 '18 at 23:42
• Also of course assuming no inflation adjustments. – The Photon Sep 5 '18 at 23:45
• If you are constantly selling shares, ultimately the number of shares remaining ascentotically approaches zero and that means that you run out of money. – Bob Baerker Sep 6 '18 at 1:45
• Say I have \$10k of a \$100 fund The fund goes up 50%, so I have \$15k. Now I take out \$5k, so I only have 66.6667 shares. Now the fund splits 3:2. Now I have 100 shares of the fund, worth \$10k, plus the \$5k in cash that I took out selling the appreciated shares. If the fund is obliging enough to keep increasing in value predictably, and splitting as needed, this can go on indefinitely. – The Photon Sep 6 '18 at 3:01
• OP never said they'd take out a % equal to the percent appreciation. They said the investment value increased by \$60k and they take out \$60k. – The Photon Sep 6 '18 at 3:03