Mutual Fund Transfer to ETF Problem

Patrick Fisher

New member
Joined
Jun 9, 2017
Messages
9
Hi there, this is my first time posting on the forum.

I'm fast approaching 30 years old and have recently been thinking about what will be the most effective way to invest for my retirement. For the sake of this math question I will have only two investment options: I can invest in a mutual fund or an ETF. Let's assume that the stock holdings in both the mutual fund and the ETF are identical. Let's also assume that we know that the value of the stocks held by the mutual fund and ETF will increase in value by 8% annually. I have decided that starting on my 30th birthday I will invest $500 every month until I turn 65.

The advantage of investing in the mutual fund is that I can buy into the fund without having to pay a trading commission. The disadvantage of investing in the mutual fund is that I will have to pay a 1.5% management fee, bringing my effective returns down to 6.5% from 8%

The advantage of investing in the ETF is that the management fee is much lower at 0.06%, bringing my effective returns down to 7.94% from 8%. The disadvantage is that I will have to pay a trading commission of $10 every time I want to buy into the fund.

I've decided that in order to get the best returns on my investment that I should buy into the mutual fund every month, and then transfer the money into an ETF once I have X number of dollars in the mutual fund holdings. How do I calculate the value for X in order to generate the most profit?

Thanks!

note: I know that stock market returns aren't predictable and consistent like I have suggested in the problem, but for the sake of this problem we are going to pretend that they are. I also know that it is risky to put all of your retirement savings into the stock market, but we'll pretend that is my plan for this question.
 
If this is a "real life" question, then you arguably need a financial advisor, not a volunteer math tutor. If this is from a class, please reply showing your work so far. Thank you! ;)
 
If this is a "real life" question, then you arguably need a financial advisor, not a volunteer math tutor. If this is from a class, please reply showing your work so far. Thank you! ;)

Thanks for your reply! This is a theoretical question, but one that is relevant for many investors. I do have a financial advisor and I'm not presently in a math class, just looking to improve my skills for the sake of personal betterment.

Here's what I've got using the online calculator found at: http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php
(note: all the interest rates I've stated are nominal rather than effective rates)

Total after 35 years investing $500 in mutual fund every month: $804,492.28
Total after 35 years investing $500 in ETF every month (and paying $10 fee to make each deposit) $1,114,914.99

It looks like the ETF is clearly on top there, BUT it doesn't make sense to pay $10 each month for each and every deposit.

For example, the results after the first year would be: $6215.50 in mutual fund account, $6139.13 in ETF account

Clearly it would be better to make regular investments into the mutual fund and then transfer that amount into an ETF once you have built up a certain amount of capital, but how do you go about calculating the optimal amount of money to save before transferring?

Thanks
 
I think the answer is to transfer once you have saved somewhere between $8,000 and $11,000 but I'm not sure how to calculate the exact amount
 
Formula

Okay I think I have figured this one out.

Known quantities:
MER a.k.a. Management Expense Ratio a.k.a. annual management fee: 1.5%
Initial investment $0
Monthly contribution to mutual fund account: $500
Trading commission for buying into the ETF: $10
Annual increase in value of all the stocks held by both the ETF and the mutual fund: 8% (obviously I'm making this part up as the market will go up and down every year, but we will pretend this is a constant, known variable for the sake of this model)

Here is my proposed formula for calculating X dollars:

First we have to figure out what the MER works out to in a monthly percentage:
MER = 1.5%
1.5% = 0.015
0.015 per year ÷ 12 months = 0.00125

This would actually work out to an effective monthly rate of 0.00124 when you account for compound interest, but it's close enough that I'm going to stick with 0.00125 for the sake of simplicity.

Next we divide the trading commission of $10 by the monthly MER
$10 ÷ 0.00125 = $8000
X dollars = $8000

And there is our answer! Once I have accumulated $8000 of value in my mutual fund account then it makes sense to sell the mutual funds and use that cash to buy into the ETF.

This should work out to selling the mutual funds approximately once every 15 months in order to buy into the ETF

How do you think I did with this problem? Would you come up with a different solution? Perhaps I have oversimplified this. Also I'm not sure exactly why I picked the monthly MER to make my calculation, but I think that is correct.

Thanks!
 
Anyone here willing to help out? I would like to test my answer using a graph as a model, but am not sure how to graph this properly. I can graph using a single rate of return and a trading commission, but don't know how to make a graph where the funds are changed to a different rate of return once the account hits $8000, along with a $10 trading commission being debited from the account.

I have made an excel workbook to help me with this problem and have uploaded it to a Google Doc here. Feel free to make edits to that doc as I have the original saved on my hard drive.

Thanks!
 
Patrick, I get a headache when I read your problem :rolleyes:

500 * .0006 = 30 cents !
Why use this: insignificant in a "projection"?

Seems to boil down to this:
Mutual:
deposit = 500 monthly, rate 8 - 1.5 = 6.5% cpd. monthly
After 1 year: $6182

ETF:
deposit = 500 - 10 = 490, rate 8% cpd. monthly
After 1 year: $6101

Note:
looking at the $10 commission on each monthly deposit,
why not change to an annual deposit of $6000?

Sorry, that's all I have for you today;
preparing my 2nd coffee...

Hey Denis,

Thanks for helping out. This is a headache for me as well, especially since I haven't studied any math in over a decade!

If you change it to an annual deposit to the ETF then you miss out on the $182 you would have made investing in the mutual fund. That's why I'm trying to find out the ideal time to transfer the money to the ETF from the mutual fund.

What I'm really trying to figure out is how to write an equation that will calculate the ideal time to switch between the two investment types. Then once I have that equation I can use it to find solutions for more than just this one scenario.

The reason to include the 0.0006 is so that once I have an equation figured out then I can change this variable as needed in different scenarios
 
The reason to include the 0.0006 is so that once I have an equation figured out then I can change this variable as needed in different scenarios
That sounds like a parameter.

Parameters are values that are fixed for a particular situation but change when beginning a different situation.

In other words, parameters are variable constants! :cool:
 
That sounds like a parameter.

Parameters are values that are fixed for a particular situation but change when beginning a different situation.

In other words, parameters are variable constants! :cool:

You're right, you'll have to excuse me it's been a while since I last stepped in a math class.

Ok so for my problem:

Parameters:

a = Annual returns = 8% (for the sake of this model)
b = Mutual fund MER (fee) = 1.5%
c = ETF MER (fee) = 0.06%
d = Monthly contribution (investment) = $500
e = Initial investment = $0
f = Trading commission for buying into ETF = $10
g = Trading commission for buying into mutual fund = $0
h = Investment horizon = 420 months

Variables:

X = the number of months at which you must sell your mutual funds and invest in ETFs in order to maximize your return
Y = the amount of money you have invested in mutual funds at the point when you must sell your mutual funds and invest in ETFs in order to maximize your return

How would one go about writing this equation?
 
Fyi, that online calculator results is based on
"immediate annuity" (1st deposit at beginning of month).

If you intended a regular annuity (1st deposit end of mo.)
then the formula is:
f = d[(1 + i)^n - 1] / i where:
f = future value
d = monthly deposit
i = monthly interest rate
n = number of months

Mutual funds: d = 500, i = .065/12, n = 420
so f = 800,158.09

ETF: d = 490, i = .0794/12, n = 420
so f = 1,107,586.46

Not that important in the big picture;
just so you're aware...

Thanks, I did figure that out but wasn't sure what the formula was. I'm going to stick with regular annuity going forward. Knowing that formula is very helpful, cheers!
 
Interesting, I've never heard of a looper program before. Thanks for checking my results. Do you think that my method of dividing the trading commission by the MER was correct then? I suppose to be accurate I should actually be dividing the trading commission by the difference in MER between the two investment types.

Just to "see", I set up a looper program
and got these results:
(when balance hits 4000, do switch: likewise after)
4000: 1,108,565
8000: 1,108,908 : BINGO, you're correct!
12000: 1,108,716
16000: 1,108,090

Still quite meaningless, but could be quite important
under different rates/fees.
 
Top