Author Topic: Low MER vs. Tax Free Gains  (Read 5714 times)

BigBangWeary

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Low MER vs. Tax Free Gains
« on: February 02, 2016, 12:38:46 AM »
Hypothetical.

Based on a $600,000 account and a 30 year time frame, which of the two scenarios would you choose and why. Assuming the portfolio was held by a couple in their early to mid-30s:

A) Invest in low MER Index funds with a total expense ratio of 0.3% but only be able to shelter the usual amount from tax.

B) Invest in actively traded funds with high MER and a total expense ratio of 2% but never pay any tax on the portfolio before or after needing the funds (ie. tax-free growth)

Which of these portfolios would likely come out a head based on historical norms.  Which would you choose?

I would love to see the Canadian and US investor opinion on this.

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #1 on: February 02, 2016, 03:06:50 AM »
Biggest assumption will be the raw returns prior to the expense ratio.

If we assume the raw returns are identical at 7.3%, with 2% from dividends and 5.3% from growth, then subtract the expense ratio from the growth, we get:
 
Option A
cgt = capital gain tax rate, %15.0%
d = annual dividend rate, %2.0%
g = annual growth excluding dividends, %5.0%
n = years invested, yr30
P = principal invested, $$600,000
t = tax rate on dividends, %15.0%
e = tax-adjusted annual growth, %6.70%
ecgt = tax-adjusted cap. gain tax rate, %11.194%
F = Future, after tax, value $3,795,594

Option B
cgt = capital gain tax rate, %0.0%
d = annual dividend rate, %2.0%
g = annual growth excluding dividends, %3.30%
n = years invested, yr30
P = principal invested, $$600,000
t = tax rate on dividends, %0.0%
e = tax-adjusted annual growth, %5.30%
ecgt = tax-adjusted cap. gain tax rate, %0.0%
F = Future, after tax, value $2,824,895

Option A looks better - with these assumptions.

BigBangWeary

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Re: Low MER vs. Tax Free Gains
« Reply #2 on: February 03, 2016, 07:25:00 AM »
Wow that is incredibly helpful. It goes to show the real drag costs can be. Almost a million dollar difference despite the tax free option.

I don't suppose you can share your calculations? I want to run scenario A with a 0.6 MER.

Either way that is eye opening

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #3 on: February 03, 2016, 07:39:26 AM »
Wow that is incredibly helpful. It goes to show the real drag costs can be. Almost a million dollar difference despite the tax free option.

I don't suppose you can share your calculations? I want to run scenario A with a 0.6 MER.

Either way that is eye opening

Download the spreadsheet from http://forum.mrmoneymustache.com/ask-a-mustachian/how-to-write-a-%27case-study%27-topic/msg274228/#msg274228, go to row 123 on the 'Misc. calcs' tab, and modify as you wish.  Have fun!

BigBangWeary

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Re: Low MER vs. Tax Free Gains
« Reply #4 on: February 03, 2016, 07:27:30 PM »
Thank you MDM!

BigBangWeary

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Re: Low MER vs. Tax Free Gains
« Reply #5 on: February 04, 2016, 07:34:05 PM »
What is the calculation for subtracting the MER from the total? I didn't quite understand that part.

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #6 on: February 04, 2016, 08:52:33 PM »
What is the calculation for subtracting the MER from the total? I didn't quite understand that part.

Yes, it is good to define TLAs (Three Letter Acronyms) when using them because people may assume the TLAs mean different things.

I'll assume MER here is Management Expense Ratio as described in https://en.wikipedia.org/wiki/Expense_ratio.

Ignoring taxes, an investment compounded annually increases by (1 + i)^n, where i = annual investment return and n = number of years.  E.g., after 30 years at 2%/yr, the investment would be worth 1.02^30 = 1.81 times as much as the original amount.

Instead of saying "...increases by (1 + i)^n" we can say "...changes by (1 + x)^n".  Here, n is still years but x can be positive (as in the investment return above) or negative (e.g., a MER).  An investment earning no return but subject to a 2% MER for 30 years would be worth only 0.98^30 = 55% of the original amount.

An investment earning 2%/year and subject to a 2% MER, after any number of years, would be worth (1 + 0.02 - 0.02)^n = 1^n = exactly the original amount.

In other words, the MER gets subtracted from the raw investment return to determine an effective investment return.  Does that make sense?

johnny847

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Re: Low MER vs. Tax Free Gains
« Reply #7 on: February 04, 2016, 09:08:28 PM »
What is the calculation for subtracting the MER from the total? I didn't quite understand that part.

Yes, it is good to define TLAs (Three Letter Acronyms) when using them because people may assume the TLAs mean different things.

I'll assume MER here is Management Expense Ratio as described in https://en.wikipedia.org/wiki/Expense_ratio.

Ignoring taxes, an investment compounded annually increases by (1 + i)^n, where i = annual investment return and n = number of years.  E.g., after 30 years at 2%/yr, the investment would be worth 1.02^30 = 1.81 times as much as the original amount.

Instead of saying "...increases by (1 + i)^n" we can say "...changes by (1 + x)^n".  Here, n is still years but x can be positive (as in the investment return above) or negative (e.g., a MER).  An investment earning no return but subject to a 2% MER for 30 years would be worth only 0.98^30 = 55% of the original amount.

An investment earning 2%/year and subject to a 2% MER, after any number of years, would be worth (1 + 0.02 - 0.02)^n = 1^n = exactly the original amount.

In other words, the MER gets subtracted from the raw investment return to determine an effective investment return.  Does that make sense?

As long as we're actually writing down equations, let's do it correctly.

An investment that earns 2% a year before expenses and costs 2% in management fees doesn't mean you have
(1 + 0.02 - 0.02)^n = 1^n.

It's actually
((1+0.2)*(1-.02))^n = 0.9996^n.

So you're actually very slowly losing money.

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #8 on: February 04, 2016, 09:19:40 PM »
As long as we're actually writing down equations, let's do it correctly.

An investment that earns 2% a year before expenses and costs 2% in management fees doesn't mean you have
(1 + 0.02 - 0.02)^n = 1^n.

It's actually
((1+0.2)*(1-.02))^n = 0.9996^n.

So you're actually very slowly losing money.

Although, it depends on the definition of "correctly." :)  And we'll ignore typos. ;)

If either or both 2% numbers are good to 1 significant figure, (1 + 0.02) * (1 - 0.02) still equals 1.

But yes, if the 2% growth is based on the year's starting amount, while the 2% MER is based on the year end amount after the 2% increase has occurred, the change is indeed as johnny847 implied.

This is similar to the difference between real (ignoring inflation) and nominal (including inflation) growth.  See http://www.investopedia.com/terms/n/nominalinterestrate.asp.

johnny847

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Re: Low MER vs. Tax Free Gains
« Reply #9 on: February 04, 2016, 10:15:27 PM »
As long as we're actually writing down equations, let's do it correctly.

An investment that earns 2% a year before expenses and costs 2% in management fees doesn't mean you have
(1 + 0.02 - 0.02)^n = 1^n.

It's actually
((1+0.2)*(1-.02))^n = 0.9996^n.

So you're actually very slowly losing money.

Although, it depends on the definition of "correctly." :)  And we'll ignore typos. ;)

If either or both 2% numbers are good to 1 significant figure, (1 + 0.02) * (1 - 0.02) still equals 1.

But yes, if the 2% growth is based on the year's starting amount, while the 2% MER is based on the year end amount after the 2% increase has occurred, the change is indeed as johnny847 implied.

This is similar to the difference between real (ignoring inflation) and nominal (including inflation) growth.  See http://www.investopedia.com/terms/n/nominalinterestrate.asp.

I'm not sure what typo you're talking about.

And the order of growth vs when the expenses happen doesn't matter at all, because multiplication is commutative. The 2% fee could be taken at the beginning of the year and you'd still have the same result.

Finally there's is only one definition of correct. It means 100% accurate. Now we can say something is close enough, or approximately true, or within the margin of error if we're lacking significant figures in the numbers (which I don't know why we would, expense ratios are typically written out to two decimal places, and we're not talking about single digit basis point expense ratios here), but your formula is still not correct. I purposely point out this error because while it does not lead to any significant difference in this case, there are other real world cases where it actually can amount to a significant difference.

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #10 on: February 04, 2016, 10:30:59 PM »
I'm not sure what typo you're talking about.
That would be the difference between 0.02 and 0.2.

Quote
And the order of growth vs when the expenses happen doesn't matter at all, because multiplication is commutative. The 2% fee could be taken at the beginning of the year and you'd still have the same result.
You are correct that multiplication is commutative, so 1.02 * 0.98 is the same as 0.98 * 1.02.  But the underlying details of how the investment grows and how the MER is charged do matter.  E.g., if the 2% fee is taken at the end of the year but based on the value at the beginning of the year it really would be a (1 + .02 - .02) situation.

Quote
Finally there's is only one definition of correct. It means 100% accurate. Now we can say something is close enough, or approximately true, or within the margin of error if we're lacking significant figures in the numbers (which I don't know why we would, expense ratios are typically written out to two decimal places, and we're not talking about single digit basis point expense ratios here), but your formula is still not correct. I purposely point out this error because while it does not lead to any significant difference in this case, there are other real world cases where it actually can amount to a significant difference.
Yup. 

There is still something to be said, when explaining new concepts, for keeping things simple and "correct enough".  E.g, one can get a long way in physics by assuming F=MA instead of the details as described in https://en.wikipedia.org/wiki/Relativistic_mechanics.

johnny847

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Re: Low MER vs. Tax Free Gains
« Reply #11 on: February 04, 2016, 11:01:02 PM »
I'm not sure what typo you're talking about.
That would be the difference between 0.02 and 0.2.


Oops.

Quote
And the order of growth vs when the expenses happen doesn't matter at all, because multiplication is commutative. The 2% fee could be taken at the beginning of the year and you'd still have the same result.
You are correct that multiplication is commutative, so 1.02 * 0.98 is the same as 0.98 * 1.02.  But the underlying details of how the investment grows and how the MER is charged do matter.  E.g., if the 2% fee is taken at the end of the year but based on the value at the beginning of the year it really would be a (1 + .02 - .02) situation.

That's not how expense ratios are calculated.
Quote
Prospectus Gross Expense Ratio - Gross Expense Ratio represents the total gross expenses divided by the fund's average net assets. In some instances, a mutual fund might "waive" a portion of its costs. Some fee waivers have an expiration date; other waivers are in place indefinitely. If the gross expense ratio is not equal to the net expense ratio, the gross expense ratio portrays the fund's expenses had the fund not waived a portion, or all, of its fees. Thus, to some degree, it is an indication of fee contracts.
https://www.bogleheads.org/wiki/Expense_ratios
[Emphasis mine]
I just looked this up. So really, not even ((1+.02)(1-.02))^n is correct either. So long as we're assuming constant 2% growth, the expense ratio expressed as a percentage of the starting balance would be slightly higher than 2%.

Quote
Finally there's is only one definition of correct. It means 100% accurate. Now we can say something is close enough, or approximately true, or within the margin of error if we're lacking significant figures in the numbers (which I don't know why we would, expense ratios are typically written out to two decimal places, and we're not talking about single digit basis point expense ratios here), but your formula is still not correct. I purposely point out this error because while it does not lead to any significant difference in this case, there are other real world cases where it actually can amount to a significant difference.
Yup. 

There is still something to be said, when explaining new concepts, for keeping things simple and "correct enough".  E.g, one can get a long way in physics by assuming F=MA instead of the details as described in https://en.wikipedia.org/wiki/Relativistic_mechanics.

Yes there's something to be said for good enough, but there should be a disclaimer along the lines of "this is close enough for this situation, but you should keep in mind this assumption can start to break apart when ...."

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #12 on: February 04, 2016, 11:29:42 PM »
That's not how expense ratios are calculated.
While it may not be true in that case, there are other real world cases (e.g., the AUM fee my mother pays to her adviser) where it is calculated differently.

Quote
Yes there's something to be said for good enough, but there should be a disclaimer along the lines of "this is close enough for this situation, but you should keep in mind this assumption can start to break apart when ...."
Yes, sometimes that is appropriate.  Gets tiresome if one would do that for every possible post.  YMMV.

johnny847

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Re: Low MER vs. Tax Free Gains
« Reply #13 on: February 04, 2016, 11:44:10 PM »
That's not how expense ratios are calculated.
While it may not be true in that case, there are other real world cases (e.g., the AUM fee my mother pays to her adviser) where it is calculated differently.

Sure, but I wasn't talking about the AUM fee you mother pays to her adviser.

Quote
Yes there's something to be said for good enough, but there should be a disclaimer along the lines of "this is close enough for this situation, but you should keep in mind this assumption can start to break apart when ...."
Yes, sometimes that is appropriate.  Gets tiresome if one would do that for every possible post.  YMMV.
Guess we'll have to agree to disagree.

MDM

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Re: Low MER vs. Tax Free Gains
« Reply #14 on: February 05, 2016, 12:00:02 AM »
Sure, but I wasn't talking about the AUM fee you mother pays to her adviser.
Quote
Guess we'll have to agree to disagree.

I can agree with both of those. :)

BigBangWeary

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Re: Low MER vs. Tax Free Gains
« Reply #15 on: February 05, 2016, 07:51:51 PM »
Thank you both. I admit, simple and 'good enough' do have a certain appeal to those less mathematically inclined (ME!). Either way, my question seems to have been answered.

Cheers!

ShoulderThingThatGoesUp

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Re: Low MER vs. Tax Free Gains
« Reply #16 on: February 05, 2016, 08:20:27 PM »
0.3% is pretty high, even.

BigBangWeary

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Re: Low MER vs. Tax Free Gains
« Reply #17 on: February 07, 2016, 12:43:00 AM »
Actually, one more twist on this scenario.

How would these two situations compare once the retiree was ready for the withdrawal/retirement phase? Assuming the same tax situation as in the above.

 Since the person in the tax free situation does not pay any capital gains, etc, would they not come out ahead?


MDM

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Re: Low MER vs. Tax Free Gains
« Reply #18 on: February 07, 2016, 07:28:05 AM »
Actually, one more twist on this scenario.

How would these two situations compare once the retiree was ready for the withdrawal/retirement phase? Assuming the same tax situation as in the above.

 Since the person in the tax free situation does not pay any capital gains, etc, would they not come out ahead?

The calculations in reply #1 include withdrawal and the payment of capital gains tax, if any.  Is that what you have in mind here?