Visualizing the devastating impact of fees

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Lobster
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Visualizing the devastating impact of fees

Post by Lobster » Wed Apr 19, 2017 11:03 pm

I have been experimenting with ways to better help visualize the real impact of costs over an investors lifetime. For example the chart in this frequently linked vanguard article has compelling data, but I believe the same information might be presented in an easier to understand way.

Here is one attempt, I am interested to hear feedback!
Image

Here is the link to the google doc
Last edited by Lobster on Wed Apr 19, 2017 11:37 pm, edited 1 time in total.
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ofcmetz
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Re: The devastating impact of fees

Post by ofcmetz » Wed Apr 19, 2017 11:27 pm

Nice. I used to be around the 1% amount and am now around 0.25% for total fund ER plus account fees. It's nice to visualize the difference that can make.
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finite_difference
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Re: Visualizing the devastating impact of fees

Post by finite_difference » Wed Apr 19, 2017 11:45 pm

Very nice. I would not have believed that at 2% they would have 50% of your portfolio.

I was then wondering how much more you would need to save %wise to counter 1% in fees.

Does this graphic mean that if you save 10% gross and have 0.1% fees, that would be equivalent to saving 13.3% with 1% fees and saving 20% with 2% fees?
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ram
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Re: Visualizing the devastating impact of fees

Post by ram » Wed Apr 19, 2017 11:59 pm

Excellent work.
Perhaps a similar document can me made to show the ratio of principal and interest for a 5%, 30 year mortgage paid in 5, 10, 15, 20, 25, 30 years.

Then perhaps this data, mortgage interest data and Taylor Larimore's "buy a Toyota Corolla and save" data can all be posted together to show cumulative lifetime savings on these big ticket expenses.
Ram

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celia
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Re: Visualizing the devastating impact of fees

Post by celia » Thu Apr 20, 2017 12:21 am

I don't understand this. Suppose there is an average of 5% growth each year, over the long term. Even if I should lose 2% to fees each year, my account is still growing. This chart looks like it is shrinking. Maybe the chart needs some descriptions/labels on it???

I can see how the chart might look like that if you had a money market account, for example, and there was no inflation, but you had to pay an advisor. But that's not us.

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Re: Visualizing the devastating impact of fees

Post by MotoTrojan » Thu Apr 20, 2017 12:31 am

celia wrote:I don't understand this. Suppose there is an average of 5% growth each year, over the long term. Even if I should lose 2% to fees each year, my account is still growing. This chart looks like it is shrinking. Maybe the chart needs some descriptions/labels on it???

I can see how the chart might look like that if you had a money market account, for example, and there was no inflation, but you had to pay an advisor. But that's not us.
This visualization is just your gains after 40 years, not your principal (or total account value). Over 40 years at 2% is splitting the gains between you and the advisor.

Lobster
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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 12:34 am

celia wrote:I don't understand this. Suppose there is an average of 5% growth each year, over the long term. Even if I should lose 2% to fees each year, my account is still growing. This chart looks like it is shrinking. Maybe the chart needs some descriptions/labels on it???

I can see how the chart might look like that if you had a money market account, for example, and there was no inflation, but you had to pay an advisor. But that's not us.
Thanks for the feedback Celia. The chart shows the final balance of 5 different portfolios after 40 years. Each would have accumulated $1 million before fees. Each bar shows the impact on the final portfolio given the listed fee compounded over the 40 years.

It's tough to come up with concise labels to describe this, please make any suggestions you think might make it clearer!
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Lobster
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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 12:36 am

MotoTrojan wrote:
This visualization is just your gains after 40 years, not your principal (or total account value). Over 40 years at 2% is splitting the gains between you and the advisor.
I like your explanation better :beer
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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 12:39 am

finite_difference wrote: I was then wondering how much more you would need to save %wise to counter 1% in fees.

Does this graphic mean that if you save 10% gross and have 0.1% fees, that would be equivalent to saving 13.3% with 1% fees and saving 20% with 2% fees?
This shows what happens to the investment gains, regardless of the rate of return. If a portfolio is left to grow without ongoing contributions, 2% in fees they result in losing more than half of your returns.

[edit] changed 'regardless of savings rate' to 'regardless of rate of return'. Making contributions throughout the investment period which will be subject to fees for a shorter length of time which will of course change the amount lost to fees (thanks to Kevin M for pointing this out).
Last edited by Lobster on Thu Apr 20, 2017 7:40 pm, edited 2 times in total.
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Lobster
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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 12:44 am

ram wrote:Excellent work.
Perhaps a similar document can me made to show the ratio of principal and interest for a 5%, 30 year mortgage paid in 5, 10, 15, 20, 25, 30 years.

Then perhaps this data, mortgage interest data and Taylor Larimore's "buy a Toyota Corolla and save" data can all be posted together to show cumulative lifetime savings on these big ticket expenses.
Great idea! I've found that the math inclined bhs (myself included) are able to appreciate the impact of these things by reading the numbers. For many, though, visualizing it can go a long ways to appreciating the power of compounding.

I'll look at the total mortgage cost tomorrow, another very practical illustration 8-)
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Re: Visualizing the devastating impact of fees

Post by Theoretical » Thu Apr 20, 2017 7:15 am

This makes 2/20 hedge funds look even more ridiculous as a BAD deal.

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Re: Visualizing the devastating impact of fees

Post by sunnywindy » Thu Apr 20, 2017 7:37 am

Your chart's great and I'm one of the people who likes to post the Vanguard sliding scale chart. The only improvement I could suggest for your chart is to lower the total amount from $1 million to something more in line with what someone might accrue in regular corporate America. Certainly, the chart is more dramatic with a higher denomination, but I think $1 million is too abstract and high of a number for most people to emotionally latch onto. Maybe $250,000 is better? (Not really sure what's a better number.)

This is the chart I usually link: https://personal.vanguard.com/us/insigh ... about-cost
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Re: Visualizing the devastating impact of fees

Post by alrick » Thu Apr 20, 2017 7:44 am

Chart should be retitled "Investment Gains" and noted that if your investments gained $1,000,000 over 40 years, the chart shows what portion of those games go to the investor and what portion go to the advisor.

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Re: Visualizing the devastating impact of fees

Post by Gadget » Thu Apr 20, 2017 8:13 am

It didn't hit home for me until I scheduled a couple initial financial advisor meetings (33 and just starting to get enough invested that this is becoming more real), then started trying to prepare for the meeting. I linked all my accounts to the personal capital website and slid the additional fee slider to 1 percent like most of them were asking for. Then said hell no... Personal capitals site has the same type of stark visual on fees. So much so that I have no idea how they get clients that actually have perused their retirement calculator tools. Even though I really liked the advisor from personal capital that I talked to.

Glad I found this site and the recommended boggleheads guide to investments book. I agree if I saw your chart first it would have also had the same effect. I always assumed paying a financial advisor was like paying someone to mow and fertilize the lawn. Apparently it's more like buying them their very own vacation home on an island somewhere.

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Higman
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Re: Visualizing the devastating impact of fees

Post by Higman » Thu Apr 20, 2017 8:20 am

Nice chart Lobster. The only minor point I have is that your percentage is correct as far as the investor is concerned but the advisor does not get all the rest.

Part of the dark blue area is due to opportunity costs. That is money you could have earned if you reinvested the advisor fees. If the market returned 8% over the 40 years the opportunity costs would be greater than of it had only returned 6%.

A gross estimate of a typical 2% fee (e.g. 1% AUM + 1% mutual fund expense ratio) would be that each year you keep 98% of your portfolio and the fees take the rest (2%). Do that for 40 years and you get to keep .98^40 = 44.57% of what it could have earned without fees.
For more detail see:

http://buyupside.com/calculators/feesdec07.htm

Just enter the 2% under annual operating fee. The actual rate of return is immaterial in calculation the percentage lost due to fees. The rate of return only influences the total ending portfolio value and opportunity lost cost.

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Re: Visualizing the devastating impact of fees

Post by NiceUnparticularMan » Thu Apr 20, 2017 8:30 am

Higman wrote:Nice chart Lobster. The only minor point I have is that your percentage is correct as far as the investor is concerned but the advisor does not get all the rest. Part of the dark blue area is due to opportunity costs. That is money you could have earned if you reinvested the advisor fees.
Just spitballing, but if you imagine the advisor is reinvesting the fees, does it work out as originally stated?

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Re: Visualizing the devastating impact of fees

Post by pshonore » Thu Apr 20, 2017 8:43 am

There is one major distortion in the way this data is presented and labeled in the graph. In a case where 10K was invested at 10% with no advisor, the investor winds up with approx 452K after 40 years. If the advisor got 2%, the investor winds up with 239K and the advisor nets 56K. Still outrageous though.

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Re: Visualizing the devastating impact of fees

Post by NiceUnparticularMan » Thu Apr 20, 2017 8:59 am

pshonore wrote:There is one major distortion in the way this data is presented and labeled in the graph. In a case where 10K was invested at 10% with no advisor, the investor winds up with approx 452K after 40 years. If the advisor got 2%, the investor winds up with 239K and the advisor nets 56K. Still outrageous though.
I have the same question--if you assume the advisor actually re-invests the fees for themselves at 10%, wouldn't that close the gap?

In other words, don't you have to scale up the fees for the time value of money?

At the end of the day it probably shouldn't matter to the hyperrational investor where the missing money goes, but I do think there is something rhetorically significant about emphasizing exactly how valuable these fees are to the advisor.

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Re: Visualizing the devastating impact of fees

Post by pshonore » Thu Apr 20, 2017 9:21 am

NiceUnparticularMan wrote:
pshonore wrote:There is one major distortion in the way this data is presented and labeled in the graph. In a case where 10K was invested at 10% with no advisor, the investor winds up with approx 452K after 40 years. If the advisor got 2%, the investor winds up with 239K and the advisor nets 56K. Still outrageous though.
I have the same question--if you assume the advisor actually re-invests the fees for themselves at 10%, wouldn't that close the gap?

In other words, don't you have to scale up the fees for the time value of money?

At the end of the day it probably shouldn't matter to the hyperrational investor where the missing money goes, but I do think there is something rhetorically significant about emphasizing exactly how valuable these fees are to the advisor.
I believe it would if he reinvested his cut; however the advisor probably bought a yacht with the money somewhere year 10 :D

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Re: Visualizing the devastating impact of fees

Post by NiceUnparticularMan » Thu Apr 20, 2017 9:25 am

pshonore wrote:I believe it would if he reinvested his cut; however the advisor probably bought a yacht with the money somewhere year 10 :D
If he bought instead of chartered, he really isn't worth any fees!

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 9:44 am

sunnywindy wrote:Your chart's great and I'm one of the people who likes to post the Vanguard sliding scale chart. The only improvement I could suggest for your chart is to lower the total amount from $1 million to something more in line with what someone might accrue in regular corporate America. Certainly, the chart is more dramatic with a higher denomination, but I think $1 million is too abstract and high of a number for most people to emotionally latch onto. Maybe $250,000 is better? (Not really sure what's a better number.)

This is the chart I usually link: https://personal.vanguard.com/us/insigh ... about-cost
Thanks! I forgot about that page and I believe it does a much better job demonstrating the impact. I agree $1 million is a bit abstract, I'll try $250k to see how that feels.
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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 9:58 am

Higman wrote:Nice chart Lobster. The only minor point I have is that your percentage is correct as far as the investor is concerned but the advisor does not get all the rest.

Part of the dark blue area is due to opportunity costs. That is money you could have earned if you reinvested the advisor fees. If the market returned 8% over the 40 years the opportunity costs would be greater than of it had only returned 6%.

A gross estimate of a typical 2% fee (e.g. 1% AUM + 1% mutual fund expense ratio) would be that each year you keep 98% of your portfolio and the fees take the rest (2%). Do that for 40 years and you get to keep .98^40 = 44.57% of what it could have earned without fees.
For more detail see:

http://buyupside.com/calculators/feesdec07.htm

Just enter the 2% under annual operating fee. The actual rate of return is immaterial in calculation the percentage lost due to fees. The rate of return only influences the total ending portfolio value and opportunity lost cost.
Thanks for pointing that out Higman, you're right about the rate of return being independent of the percentage lost due to fees. In fact, I notice that changing the rate return on the Vanguard slider impacts the percentage lost to fees, which I don't understand.

Regarding losing it due to opportunity cost (therefore not going directly to the advisor), the assumption is that the investor invested those fees for themselves, (hopefully they use low cost indexes to avoid losing a significant portion of their return :twisted: ). Also the advisor does not collect the mutual fund ER themselves (though they frequently get kickbacks), so it isn't all to the advisor. On the other hand it was the advisor's advice that led the investor down a path to lose all of those returns, so I feel comfortable holding them responsible for the entire amount :wink:
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Re: Visualizing the devastating impact of fees

Post by Vanguard Fan 1367 » Thu Apr 20, 2017 10:15 am

I believe that John Bogle said that he is looking for returns to be in the 4 percent range going ahead. If the advisor takes 2 percent of that then you are looking at half of the increase lost and with compounding that really adds up over the .03 to .05 percent available with some of today's index funds

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 11:36 am

pshonore wrote:There is one major distortion in the way this data is presented and labeled in the graph. In a case where 10K was invested at 10% with no advisor, the investor winds up with approx 452K after 40 years. If the advisor got 2%, the investor winds up with 239K and the advisor nets 56K. Still outrageous though.
As others mention, the assumption is that the advisor will invest the fees he collects for himself. To keep the illustration simple we use the same rate of return for the advisor.
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Re: Visualizing the devastating impact of fees

Post by learning_head » Thu Apr 20, 2017 1:17 pm

Lobster wrote:... I notice that changing the rate return on the Vanguard slider impacts the percentage lost to fees, which I don't understand. ...
In case of Vanguard, their chart shows growth on 10k principal. Consider 2% fee charged and 2 scenarios after year 1:
- 5% return implies $500 growth out of which ~$205(*) is lost to fees ($205 is based on average between starting and ending balances, i.e. 2% off of $10250)
- 10% return implies $1000 growth out of which ~$210 is lost to fees (2% * $10500).
So rate of return clearly matters as far as percentage of growth lost to fees: in first scenario it's a little over 40% and in second a little over 20%.

(*) Minor: Vanguard uses more precise way of evaluating 2% I am guessing, which is why their 2% fee results in 205.88 in first case and 215.69 in second - perhaps they do this based on monthly or even daily balance?

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Re: Visualizing the devastating impact of fees

Post by NiceUnparticularMan » Thu Apr 20, 2017 1:36 pm

learning_head wrote:So rate of return clearly matters as far as percentage of growth lost to fees: in first scenario it's a little over 40% and in second a little over 20%.
That makes sense for a one-year scenario, but I am pretty sure it converges as growth versus initial contribution becomes a more and more dominant portion of the portfolio.

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Re: Visualizing the devastating impact of fees

Post by Kevin M » Thu Apr 20, 2017 2:48 pm

It is a nice chart.
Lobster wrote: This shows what happens to the investment returns, regardless of your savings rate. No matter how much you contribute, at 2% in fees they will keep half of your returns.
I don't think this is quite right, assuming I'm understanding what you mean. Working with the following numbers:

FV = 250,000 with 0% fees/costs
Number of years = 40
Investment return = 7%

If you assume no additional annual investments, your PV to get to $250K at zero cost is 16,695. At 2% annualized fees your annualized return is reduced to 4.90%, and your ending value is 113,223. In this case you keep 45% and advisor gets 55%.

If instead you assume annual investments of $1K, your PV is 3,363, and your ending value after fees is 140,758. In this case you keep 56% and advisor gets 44%.

The intuitive way to understand this is that the impact of fees compounds, so with annual investments more of your money is subject to fees for less time, and the fees have less impact on final value.

Kevin
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Re: Visualizing the devastating impact of fees

Post by celia » Thu Apr 20, 2017 2:51 pm

Lobster wrote:It's tough to come up with concise labels to describe this, please make any suggestions you think might make it clearer!
First, you should say something to the effect that it is based on a $250,000 lump sum invested at the beginning.

Second, you don't say what the investment earns on average. If it is 5%, by the rule of 72, the value doubles in 14.4 years, not counting for fees. So lets say the account value doubles in 15 years. In 30 years, it would have quadrupled (now have $1M), and in 45 years it would have 8-tupled ($2M). So I think I would have a lot more after 40 years.

I think it makes more sense (and probably a convincing argument for the reader) that if you were to suppose the fees were invested by the advisor and they compounded at the same rate your money did, that is the percent of your could-have-kept money that now belongs to her. Why not show the total of them growing over 40 years, with the advisor portion on top of the owner's portion. The total of the two accounts (yours and advisors) would equal the same after 40 years in all cases since the same number of dollars are growing at the same rate. It is only the ownership of those dollars percentage-wise that would be the point of the bar chart. Or is that what you originally tried to do? If so, give us the rate of growth per year. It appears to be very low.

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Re: Visualizing the devastating impact of fees

Post by deltaneutral83 » Thu Apr 20, 2017 2:57 pm

I assume if you're with an AUM guy that he's got you in actively managed funds with 0.6-1.2% ER's so it would be most likely the 2% total fees. I also agree with the others who have pointed out that while it's industry norms to just skim the account for the 1% AUM, you could hypothetically replace what is removed every quarter. But yes, it would be better and more transparent if they sent you a bill.

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Re: Visualizing the devastating impact of fees

Post by willthrill81 » Thu Apr 20, 2017 3:02 pm

Kevin M wrote:It is a nice chart.
Lobster wrote: This shows what happens to the investment returns, regardless of your savings rate. No matter how much you contribute, at 2% in fees they will keep half of your returns.
I don't think this is quite right, assuming I'm understanding what you mean. Working with the following numbers:

FV = 250,000 with 0% fees/costs
Number of years = 40
Investment return = 7%

If you assume no additional annual investments, your PV to get to $250K at zero cost is 16,695. At 2% annualized fees your annualized return is reduced to 4.90%, and your ending value is 113,223. In this case you keep 45% and advisor gets 55%.

If instead you assume annual investments of $1K, your PV is 3,363, and your ending value after fees is 140,758. In this case you keep 56% and advisor gets 44%.

The intuitive way to understand this is that the impact of fees compounds, so with annual investments more of your money is subject to fees for less time, and the fees have less impact on final value.

Kevin
Right. Perhaps a stacked bar chart could illustrate the impact of varying means of investment (lump sum vs. DCA).
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Re: Visualizing the devastating impact of fees

Post by celia » Thu Apr 20, 2017 3:11 pm

I went back to the original Vanguard article you mentioned, to see the point that was being made:
John Ameriks of Vanguard wrote:Expressed this way, the fees seem pretty steep. But you still might get the mistaken sense you’re only losing money/paying fees if there are positive returns to give up. The problem is that reality doesn’t work that way. A provider charging a 1% fee doesn’t levy fees on just the returns. They levy fees on your balance.

So I think about the impact of investment costs more simply: If there are no returns and the provider takes 1% every year for 30 years, that sums to roughly 30% of my wealth (not exactly, because the fee declines slightly each year along with my balance ). In the case where the return is 1% per year and just equals the fee, they would get an amount exactly equal to 30% of my initial deposit.
The underlining is mine.

So, yeah, if the growth rate is 0, of course you are giving away part of your principal to the advisor. But most of us in that situation, after 2 or 3 years, would wake up and do something--change to a different advisor, different investment, put the money in CDs....

The likelihood of this example happening is about as likely as an annual 15% growth every year. Yes, our stock markets could become like Japan's, but in that case, we would change what we do with our money.

I would become an advisor! :beer

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 3:20 pm

celia wrote: The likelihood of this example happening is about as likely as an annual 15% growth every year. Yes, our stock markets could become like Japan's, but in that case, we would change what we do with our money.
The graph illustrates what portion of your portfolio returns will be taken by an advisor. Anyone paying 2% in total costs per year will see more than half of their portfolio returns go to an advisor regardless of percentage return of the portfolio (as mentioned in the article). The illustration accurately shows the percentage of gains lost to an advisor at those costs compounded over 40 years. It does not show what your total portfolio balance will be, which will be determined by contribution rate and return percentage (which can be seen in the vanguard slider link).

My goal is to help people who hear '1%' or '2%' and think that it is not significant. The goal of this chart is to help illustrate that paying such high fees forfeits a tremendous amount of the gains that are available to the investor using a simple, low-cost approach.
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Re: Visualizing the devastating impact of fees

Post by Kevin M » Thu Apr 20, 2017 3:30 pm

celia wrote:
Lobster wrote:It's tough to come up with concise labels to describe this, please make any suggestions you think might make it clearer!
First, you should say something to the effect that it is based on a $250,000 lump sum invested at the beginning.
I didn't get the impression that it was anything like $250K invested at the beginning, but the version of the chart I first saw indicated $250K ending value with 0% costs (I didn't see it with $1M ending value). It was clear to me that the chart was showing only ending values.

I had to play around with different numbers to try and duplicate something close to what is shown in the chart, and then I decided to just start with $250K ending value (FV) at zero cost and work backwards to different scenarios that could generate that. As I mentioned, you do get different answers depending on your investment schedule (all at beginning, or also annual investments), so I agree that it's better to state the assumptions.
Second, you don't say what the investment earns on average.
Yes, another assumption that can change the results somewhat, but only if you make annual investments. If all investment is at the beginning, then the rate of return does not change the result, assuming a fixed terminal value (e.g., $250K). In this case, you end up with 45% regardless of rate of return.

However, if you assume fixed annual investments, then rate of return changes required starting value and ending value after costs to arrive at a fixed ending value before costs. With $500 annual investments, at 10% return you need to start with only 634, and you end up with 137,296 (55%), while at 2% return, you must start with 99,545, and you end up with 119,545 (48%).
I think it makes more sense (and probably a convincing argument for the reader) that if you were to suppose the fees were invested by the advisor and they compounded at the same rate your money did, that is the percent of your could-have-kept money that now belongs to her. Why not show the total of them growing over 40 years, with the advisor portion on top of the owner's portion. The total of the two accounts (yours and advisors) would equal the same after 40 years in all cases since the same number of dollars are growing at the same rate. It is only the ownership of those dollars percentage-wise that would be the point of the bar chart. Or is that what you originally tried to do?
Yes, I think this is what the chart is showing, except that the horizontal axis is not time--it's the fees percentage. Your version would be growth over time at a fixed cost. This version is terminal value at variable costs. I think this version packs more useful information into one chart, but I understood the intent of the chart at first glance; we each grasp visuals differently.

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 3:33 pm

Kevin M wrote:It is a nice chart.
The intuitive way to understand this is that the impact of fees compounds, so with annual investments more of your money is subject to fees for less time, and the fees have less impact on final value.
You're are absolutely right, thanks! I edited my original post to state that the percentage lost to fees is the same regardless of the rate of return, but is dependent on savings rate over time as you describe :beer
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Re: Visualizing the devastating impact of fees

Post by Kevin M » Thu Apr 20, 2017 3:44 pm

Lobster wrote:
Kevin M wrote:It is a nice chart.
The intuitive way to understand this is that the impact of fees compounds, so with annual investments more of your money is subject to fees for less time, and the fees have less impact on final value.
You're are absolutely right, thanks! I edited my original post to state that the percentage lost to fees is the same regardless of the rate of return, but is dependent on savings rate over time as you describe :beer
Still not quite right. Independent of rate of return for a lump sum investment, but not for a given, fixed periodic investment.

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Re: Visualizing the devastating impact of fees

Post by Kevin M » Thu Apr 20, 2017 3:52 pm

celia wrote: So, yeah, if the growth rate is 0, of course you are giving away part of your principal to the advisor. But most of us in that situation, after 2 or 3 years, would wake up and do something--change to a different advisor, different investment, put the money in CDs....

The likelihood of this example happening is about as likely as an annual 15% growth every year. Yes, our stock markets could become like Japan's, but in that case, we would change what we do with our money.
There's a problem here in understanding the parameters of the problem. With a fixed terminal value (e.g., $250K), before costs, and a given number of years (e.g., 40), you can pick any rate of return you want. What changes is the starting value for a given periodic investment.

With a periodic investment of $0, at 0% return you start with $250K, and at 10% return you start with $5,524. Either way, with annual costs of 2%, you end up with $113,223.

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 3:55 pm

Kevin M wrote: Still not quite right. Independent of rate of return for a lump sum investment, but not for a given, fixed periodic investment.
Ah, that is what I meant but I'll try to reword for clarity
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Re: Visualizing the devastating impact of fees

Post by #Cruncher » Thu Apr 20, 2017 4:19 pm

Lobster in original post wrote:... the chart in this frequently linked vanguard article has compelling data, but I believe the same information might be presented in an easier to understand way.
Perhaps. But only if you enter the correct data, Lobster. :( In cells D3 & D4 of your Google Docs spreadsheet you copied the 0.5% and 1% fee numbers for 30 years (13.9% and 25.8%). You should have copied the numbers for 40 years (18.1% and 32.8%) as you did for 0.1%, 2%, and 3% fees.

[The remainder of this post is rather arcane, probably of interest only to number crunching purists like me.]

The referenced Vanguard article, Stopping the silent killer of returns, makes the following assertion which I didn't at first believe:
... what an investment provider gets as a fraction of what you would otherwise have had depends only on their fees, not returns.
But then the author slips up when he continues,
Looked at more precisely, the provider gets a fraction equal to 1–(1+c)^(–T) of what would otherwise be my wealth, given fee c and time horizon T.
Setting aside whether the wording should be "the provider gets" or "the investor loses", this formula is approximately correct. But since the author says "precisely" I feel OK in correcting him. For example with 1% fees over 40 years the author's formula produces 32.8%.

Code: Select all

reduction = 1 - (1 + c) ^ (-T)
    32.8% = 1 -  1.01   ^ -40
But the correct formula produces 33.1%.

Code: Select all

reduction = 1 - (1 - c) ^ T
    33.1% = 1 -  0.99   ^ 40
That the latter formula is correct can be seen from the case where the investment has no growth. In this case every year the advisor will deduct 1% from a steadily declining balance. After 40 years the investment balance would decline to 66.9% of what it initially was (0.669 = 0.99 ^ 40).

With this correction, the author's first statement that the portion lost to fees is independent of growth is precisely correct. The following illustrates this for an initial $1,000 investment growing at a constant annual 0%, 1%, and 2%. In all cases a 1% fee is taken out at the end of each year.

First here is what $1,000 would have grown to if there were no fees. For example 1061.21 = 1000 * 1.02 ^ 3.

Code: Select all

       ------- Annual Growth --------
Year      0%         1%         2%
----   --------   --------   --------
   3   1,000.00   1,030.30   1,061.21
   5   1,000.00   1,051.01   1,104.08
  10   1,000.00   1,104.62   1,218.99
  20   1,000.00   1,220.19   1,485.95
  30   1,000.00   1,347.85   1,811.36
  40   1,000.00   1,488.86   2,208.04
Here is what it would grow (or decline) to after the 1% fee is deducted each year. For example 1029.69 = 1000 * (1.02 * 0.99) ^ 3.

Code: Select all

       ------- Annual Growth --------
Year      0%         1%         2%
----   --------   --------   --------
   3     970.30     999.70   1,029.69
   5     950.99     999.50   1,049.97
  10     904.38     999.00   1,102.44
  20     817.91     998.00   1,215.37
  30     739.70     997.00   1,339.86
  40     668.97     996.01   1,477.12
And lastly here is the portion lost because of fees. For example 2.970% = 1 - 1029.69 / 1061.21.

Code: Select all

       ------- Annual Growth --------
Year      0%         1%         2%
----   --------   --------   --------
   3     2.970%     2.970%     2.970%
   5     4.901%     4.901%     4.901%
  10     9.562%     9.562%     9.562%
  20    18.209%    18.209%    18.209%
  30    26.030%    26.030%    26.030%
  40    33.103%    33.103%    33.103%
Note that the reductions are the same regardless of growth.

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Re: Visualizing the devastating impact of fees

Post by Kevin M » Thu Apr 20, 2017 6:11 pm

Here's the way I worked the problem. I use spreadsheet PV and FV functions, but for the simple case of a lump sum investment at the beginning of the period, we can use the simple TVM equation:

FV = PV * (1+r)^N

In the chart, we're given FV=250,000 (at 0% cost) and N = 40. So first we need a PV value. Solving for PV:

PV = FV / (1+r)^N

Using r = 7%

PV = 250,000 / 1.07^40
PV = 16,695

So 16,695 is the starting value that results in 250K after 40 years at 7%.

I believe the standard way to calculate after-cost return is this formula (the same as adjusting or inflation):

R = (1+r) / (1+c) -1

Plugging in r = 7% and c = 2%:

R = 1.07/1.02 - 1
R = 4.90%

Plugging this into the FV formula:

FV = 16,695 * 1.049^40
FV = 113,137

(Slightly different than the number I shared earlier, due to rounding)

Your share is 113,137/250,000 = 45% (and advisor's share is 55%).

Re-running the numbers with a 1% fee, these calculations give your share as 167,913, which is 67.2%, leaving advisor with 32.8%. So these calculations result in the same number provided by "the author's formula".

#Cruncher?

This result (FV) does not change if you change the rate of return; changing the rate of return changes the amount you start with (PV) to get to $250K.

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 7:41 pm

#Cruncher wrote:Perhaps. But only if you enter the correct data, Lobster. :( In cells D3 & D4 of your Google Docs spreadsheet you copied the 0.5% and 1% fee numbers for 30 years (13.9% and 25.8%). You should have copied the numbers for 40 years (18.1% and 32.8%) as you did for 0.1%, 2%, and 3% fees.
:oops: Corrected, thanks.
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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 7:54 pm

Kevin M wrote: This result (FV) does not change if you change the rate of return; changing the rate of return changes the amount you start with (PV) to get to $250K.
Kevin
I put a concrete $ amount on the Y-axis simply to provide an anchor point to help someone understand the significance of returns lost. It has definitely caused a fair bit of confusion.
#Cruncher wrote:Note that the reductions are the same regardless of growth.
Thanks for crunching the numbers to confirm the author's assertion (as well as correcting his formula).

The two questions I'm pondering:
  • Should the title indicate a lump sum investment?
  • Should the Y-axis be labeled to help reinforce that these are returns (rather than portfolio balance)
  • There is ongoing discussion about whether the advisor keeps all of the returns. My perspective is that they are accountable for the loss of all of those returns, and I think the rhetorical device of labeling all of the lost returns under the advisor is valuable (thanks pshonore for this point). Given a 1% AUM and 1% ER mutual fund (w/ some amount of kickback), perhaps only half of the amount goes to the advisor. I do think it's relevant though to show it sum to the same total ($250k as the current value) to demonstrate that they can put that money to work on their own behalf.
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Re: Visualizing the devastating impact of fees

Post by selftalk » Thu Apr 20, 2017 8:01 pm

I hope John Bogle read this.

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Re: Visualizing the devastating impact of fees

Post by Kevin M » Thu Apr 20, 2017 8:11 pm

Lobster wrote:
Kevin M wrote: This result (FV) does not change if you change the rate of return; changing the rate of return changes the amount you start with (PV) to get to $250K.
Kevin
I put a concrete $ amount on the Y-axis simply to provide an anchor point to help someone understand the significance of returns lost. It has definitely caused a fair bit of confusion.
I think it's fine. Didn't cause me any confusion, but I translate these things into time value of money (TVM) formula elements as I think about them. So I see your chart as providing two of the five TVM formula components:

FV = $250K
N = 40 years
PV = ?
I = ?
PMT = ?

You have to specify two more of these elements to calculate the fifth. Of course I (or r or R) depends on the fees, so there's an extra calculation for that, which of course is fundamental to the point of the chart. And then once you get PV for the zero fees case, you have to calculate the different FVs for different fees.

I thought the chart was fine and very understandable as is, but obviously others didn't. The exact numbers change if you assume PMT <> 0, but the message is the same.

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 8:16 pm

sunnywindy wrote:Your chart's great and I'm one of the people who likes to post the Vanguard sliding scale chart. The only improvement I could suggest for your chart is to lower the total amount from $1 million to something more in line with what someone might accrue in regular corporate America. Certainly, the chart is more dramatic with a higher denomination, but I think $1 million is too abstract and high of a number for most people to emotionally latch onto. Maybe $250,000 is better? (Not really sure what's a better number.)

This is the chart I usually link: https://personal.vanguard.com/us/insigh ... about-cost
I spent a bit more time with the slider page and I think it's great. Actually I believe it could achieve greater impact with some very small adjustments. For example it's unclear why they use .9% as the 'expensive' example in the long term impact chart halfway down. Similarly, I'm not sure why they use 1, 5, and 10 year columns in the sliding chart itself. Not to mention the slider doesn't actually let me select exactly 2% :wink:. Maybe I should write them and suggest a couple of adjustments :happy
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Re: Visualizing the devastating impact of fees

Post by arcticpineapplecorp. » Thu Apr 20, 2017 8:21 pm

selftalk wrote:I hope John Bogle read this.
I think he already knows this. Afterall, one of the things he's now known for (thanks in part to "The Great Retirement Gamble" on pbs) is saying "You put up 100% of the capital and take 100% of the risk, but only get 66% of the returns".

https://www.google.com/search?q=jack+bo ... 8&oe=utf-8

As already mentioned, at https://vanguardblog.com/2011/10/28/sto ... f-returns/ shows a 2.00% return actually costs you MORE than 50% of your returns over 40 years (54.7% to be precise).

Image

The eye opener for me was when Charles Ellis explained it as such: You get an 8% return from the stock market but you pay 1% in fees. That's 1/8 = 12.5%. You've just given your advisor 12.5% of your return. :oops: Redo the math and see that when you instead get 8% but only pay 0.05% in fees that equals .05/8 = only 0.625% of your return is lost in fees. You get to keep 99.375% of your return that way. :moneybag We have Jack Bogle to thank for that.
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Re: Visualizing the devastating impact of fees

Post by htdrag11 » Thu Apr 20, 2017 9:37 pm

arcticpineapplecorp. wrote:
As already mentioned, at https://vanguardblog.com/2011/10/28/sto ... f-returns/ shows a 2.00% return actually costs you MORE than 50% of your returns over 40 years (54.7% to be precise).

Image
This is the best telling chart among all. Thank you for sharing.

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Re: Visualizing the devastating impact of fees

Post by Lobster » Thu Apr 20, 2017 9:55 pm

arcticpineapplecorp. wrote:The eye opener for me was when Charles Ellis explained it as such: You get an 8% return from the stock market but you pay 1% in fees. That's 1/8 = 12.5%. You've just given your advisor 12.5% of your return.
I also very much appreciated Charlie Ellis' explanation in Winning the Loser's Game.

In behavioral science, Loss Aversion is the idea that individuals feel worse about losing $100 than they would feel great about winning $100. There are many classic experiments around this concept. Amazingly, the way in which these various scenarios are presented to people can cause the majority of participants to switch from one answer to the other, despite being mathematically identical.

Board Game Designer Geoff Engelstein gave a fantastic talk at the Game Developer Conference this year (link). Here's one example he used to demonstrate this effect.

You are given two choices:
Choice A:
● Guaranteed to get $3,000

Choice B:
● 80% chance to get $4,000
● 20% chance to get $0
Hint: Expectation value of Choice B is $3,200

Most people will choose A because they feel more comfortable with the guarantee, despite the higher expected value of choice B. Another factor at play, though, is that for most people, $3,000 and $4,000 occupy the same mental space. Meaning that even though $4,000 is 33% larger (which is significant!), most people don't really appreciate that. It's almost as if they interpret the situation as:

Choice A:
● Guaranteed to get $3,000

Choice B:
● 80% chance to get $3,000 (the offer is really for $4,000, but most people just kinda lump numbers together that are kinda sorta similar, despite having a real, tangible, mathematical impact on the final result).
● 20% chance to get $0

If instead you present the scenario as a guaranteed loss of $3,000 vs an 80% chance of losing $4,000 and a 20% chance to lose nothing, most people will switch to taking the 80% chance, despite the fact that they expect to lose more money!

This experience, as well as many others like it, have led me to want to experiment with trying to present the same information as that dense image in a simpler manner that helps really drive home the implications. For example I chose 40 years because the impact is amplified over time. I chose to show the final value of 5 different scenarios rather than the impact over time so that you can visually see, side by side, how much money was lost. I chose to show the impact against the portfolio returns rather than a whole portfolio balance because it can 'hide' the damage by showing the investors savings as part of the dollar amount in each bar.

Anyhow, I'm intrigued based on the dialogue of this thread to explore more, and am hopeful that even small ways of adjusting the presentation of this important information can help the average investor develop some urgency to shed their expensive portfolios.

:sharebeer
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Re: Visualizing the devastating impact of fees

Post by learning_head » Thu Apr 20, 2017 10:00 pm

To summarize: what investor loses
- as percentage of their overall wealth does not depend on market returns
- as percentage of growth *does* depend on market returns

With any reasonable market returns assumptions, the latter is a much larger number over years (e.g. over 50-60% as opposed to "just" ~30% as #Cruncher showed for the former), which makes a bigger impact / more impressive point.

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Re: Visualizing the devastating impact of fees

Post by Nova1967 » Fri Apr 21, 2017 8:43 am

I'm grateful to the BHs and Jack Bogle books helping me to realize the benefits of low fees. When I first started investing in the 80s and 90s it was normal to get a 20% return therefore 1% did not seem to be that much.
Nowadays with 5% the norm its understandable why low fee index funds are so popular

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Re: Visualizing the devastating impact of fees

Post by k66 » Fri Apr 21, 2017 10:28 am

Vanguard wrote:...
In fact, what an investment provider gets as a fraction of what you would otherwise have had depends only on their fees, not returns. Looked at more precisely, the provider gets a fraction equal to 1–(1+c)^(–T) of what would otherwise be my wealth, given fee c and time horizon T.
Is the relationship above just for a single payment invested over period T?

I'm thinking that if there were a series of equal (or unequal) contributions made at intervals over the same period T, that the net effect of the fees would become diluted (as compared to the single longest term in the series). The effect on the investor's portfolio would still be "corrosive" but perhaps not as much as only considering the single longest (highest loss) period.
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