Calculating expense ratio with multiple funds

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Gonewiththewind
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Calculating expense ratio with multiple funds

Post by Gonewiththewind »

New to Vanguard and indexing.

My question involves the total expense ratio calculation in a DIY index vs target 2020 .

So if I do a DIY and replicate exactly the 2020 model (VTWNX) and add up the expense ratios for each fund (.05+.07+.14+.07+.1) it comes to 0.43% expense ratio for DIY indexing VS. the VTMX let Vanguard do it expense ratio of 0.16. That difference is so in favor of not doing DIY that I and wondering if I am calculating the DIY expense correctly. Do you just add up the individual expense ratios like I did?

Thank you!
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Aptenodytes
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Re: Calculating expense ratio with multiple funds

Post by Aptenodytes »

You need to summon the power of your middle school algebra training. The ER of your portfolio is a weighted average of the ERs of the funds in your portfolio.

1) For each account, divide the account total but the portfolio total to get a weight for that portfolio.
2) For each account, multiply the ER by the weight.
3) Sum the products of the ERs and the weights.

If you run into trouble try googling "weighted average excel" or something like that.
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LadyGeek
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Re: Calculating expense ratio with multiple funds

Post by LadyGeek »

^^^ We posted at the same time. :) Here's what Aptenodytes means:

Welcome! You need to adjust for the relative weighting for each fund.

Fund A contains $200 with an expense ratio of 10%
Fund B contains $100 with an expense ratio of 5%

Total portfolio: $300 = $200 + $100

Fund A's portion: 6.67% = 10% * 200/300

Fund B's portion: 1.67% = 5% * 100/300

Total expense ratio (rounded): 8.33% = 6.67% + 1.67%

Go back to Vanguard Target Retirement 2020 Fund (VTWNX) and use the same approach with the fund's portfolio composition. Feel free to post your answer (and calculations) here.

The idea is to be sure you understand how to do this for yourself. If you get stuck, just ask for help.
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BL
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Re: Calculating expense ratio with multiple funds

Post by BL »

The portfolio's ER would never be higher than the highest ER (nor lower than the lowest ER).

If you had 50% at .5% and the other 50% was at 1.0%, the ending ER would be .75%.

If more funds at different rates, you need to do the math as illustrated above in this thread.
snarlyjack
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Re: Calculating expense ratio with multiple funds

Post by snarlyjack »

Welcome to how I think :)

ER (Expense ratio's) matter a lot.

If you google "expense fund calculators" & run the
numbers for 20, 30, 40 years. Trust me you will be amazed!
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LadyGeek
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Re: Calculating expense ratio with multiple funds

Post by LadyGeek »

DIY - The wiki has a spreadsheet: Effect of expenses on a portfolio
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EyeDee
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Calculating expense ratio with multiple funds

Post by EyeDee »

.
Vanguard Target Retirement 2020 Fund (VTWNX)

............................................................................ Holding % ..ER%.. Weighted ER%
Total Stock Market Index Fund Investor Shares...................... 35.70% ...0.17%..... 0.0607%
Total Bond Market II Index Fund Investor Shares*................... 28.20% ...0.05%..... 0.0141%
Total International Stock Index Fund Investor Shares............... 23.10% ...0.22%..... 0.0508%
Total International Bond Index Fund Investor Shares................ 12.10% ...0.23%..... 0.0278%
Short-Term Inflation-Protected Securities Index Fund Investor..... 0.90% ...0.17%..... 0.0015%

Total Weighted Expense Ratio ................................................................... 0.1550%

One would need to substitute Admiral Fees to see how much it would be lower if one can qualify for Admiral funds in each case.
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jhfenton
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Re: Calculating expense ratio with multiple funds

Post by jhfenton »

It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
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Aptenodytes
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Re: Calculating expense ratio with multiple funds

Post by Aptenodytes »

jhfenton wrote:It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
You did better in algebra than I did.
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Gonewiththewind
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Re: Calculating expense ratio with multiple funds

Post by Gonewiththewind »

Wow! What a helpful site! Looking forward to learning more!
Thanks for the comments!
hnzw rui
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Re: Calculating expense ratio with multiple funds

Post by hnzw rui »

jhfenton wrote:It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
That only works if each holding is in a separate fund. If you're only holding a single Target Retirement or LifeStrategy fund, the balance of the TR/LS fund is the same as your portfolio value. You need to look at the prospectus to see the breakdown. For example, if you want to compare costs between TR/LS vs DIY Admiral Shares.
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Aptenodytes
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Re: Calculating expense ratio with multiple funds

Post by Aptenodytes »

hnzw rui wrote:
jhfenton wrote:It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
That only works if each holding is in a separate fund. If you're only holding a single Target Retirement or LifeStrategy fund, the balance of the TR/LS fund is the same as your portfolio value. You need to look at the prospectus to see the breakdown. For example, if you want to compare costs between TR/LS vs DIY Admiral Shares.
If your portfolio consists of a single fund, the ER of your portfolio is the ER of that fund. But note that the beauty of math makes the weighted average formula still get you the right answer.

It doesn't matter if the fund is a target date fund or not. There's no need to look under the hood in that case -- in fact I think in many cases you'd get the wrong answer if you tried to estimate the target date fund's ER from the ERs of its constituents.
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jhfenton
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Re: Calculating expense ratio with multiple funds

Post by jhfenton »

Aptenodytes wrote:
hnzw rui wrote:
jhfenton wrote:It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
That only works if each holding is in a separate fund. If you're only holding a single Target Retirement or LifeStrategy fund, the balance of the TR/LS fund is the same as your portfolio value. You need to look at the prospectus to see the breakdown. For example, if you want to compare costs between TR/LS vs DIY Admiral Shares.
If your portfolio consists of a single fund, the ER of your portfolio is the ER of that fund. But note that the beauty of math makes the weighted average formula still get you the right answer.

It doesn't matter if the fund is a target date fund or not. There's no need to look under the hood in that case -- in fact I think in many cases you'd get the wrong answer if you tried to estimate the target date fund's ER from the ERs of its constituents.
You beat me to it, Aptenodytes. Vanguard already gives you the weighted average expense ratio of the target retirement funds, so you just apply that to that holding.
hnzw rui
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Re: Calculating expense ratio with multiple funds

Post by hnzw rui »

Aptenodytes wrote:
hnzw rui wrote:
jhfenton wrote:It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
That only works if each holding is in a separate fund. If you're only holding a single Target Retirement or LifeStrategy fund, the balance of the TR/LS fund is the same as your portfolio value. You need to look at the prospectus to see the breakdown. For example, if you want to compare costs between TR/LS vs DIY Admiral Shares.
If your portfolio consists of a single fund, the ER of your portfolio is the ER of that fund. But note that the beauty of math makes the weighted average formula still get you the right answer.

It doesn't matter if the fund is a target date fund or not. There's no need to look under the hood in that case -- in fact I think in many cases you'd get the wrong answer if you tried to estimate the target date fund's ER from the ERs of its constituents.
Yes, the ER of the single balanced fund is already a given. The goal is trying to discern whether the ER of the balanced fund is comparable to the (weighted) ER of its constituent funds. Useful for example if you were trying to compare ER of the single TR/LS fund versus if you switch to an equivalent 3-5 fund portfolio using Admiral shares.

Besides, while Vanguard does not add extra expenses to their TR/LS funds on top of the underlying fund ER, that may not be true for other fund families.
Last edited by hnzw rui on Sun Jan 31, 2016 4:23 pm, edited 1 time in total.
carolinaman
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Re: Calculating expense ratio with multiple funds

Post by carolinaman »

jhfenton wrote:It's the same process, but I think that calculating the holding weight just adds an unnecessary step.

1. Just multiply the balance in each holding by that holding's ER.
2. Add up the answers.
3. Divide by your total portfolio value.
This is the way I do it. It is simple and easy to understand.
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CABob
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Re: Calculating expense ratio with multiple funds

Post by CABob »

Gonewiththewind wrote:So if I do a DIY and replicate exactly the 2020 model (VTWNX) and add up the expense ratios for each fund (.05+.07+.14+.07+.1) it comes to 0.43% expense ratio for DIY indexing VS. the VTMX let Vanguard do it expense ratio of 0.16.
It appears that you are using the Admiral share class ERs. The Vanguard TR funds use the ERs from the Investor share class of the funds.
The important thing however is that you use the weighted average of the ERs.
Bob
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telemark
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Re: Calculating expense ratio with multiple funds

Post by telemark »

You can also let Morningstar calculate it for you. Go to http://www.morningstar.com/tools.html and near the bottom is Instant X-Ray. You don't need to enter the actual amounts in your portfolio. I usually enter 1000 for 10 percent, 3000 for 30 percent, etc.
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Re: Calculating expense ratio with multiple funds

Post by #Cruncher »

Gonewiththewind in original post wrote:My question involves the total expense ratio calculation in a DIY index vs target 2020. So if I do a DIY and replicate exactly the 2020 model (VTWNX) ...
Here's what I get replicating the Target Retirement 2020 Fund (VTWNX) with individual Vanguard funds, both Investor and Admiral class:

Code: Select all

                                                  2020    Investor Class    Admiral Class	
                                                  Alloc   Symbol Expense    Symbol Expense
                                                  -----   ------ -------    ------ -------
Total Stock Market Index                          35.7%    VTSMX   0.17%     VTSAX   0.05%
Total Bond Market Index                           28.2%    VBMFX   0.20%     VBTLX   0.07%
Total International Stock Index                   23.1%    VGTSX   0.22%     VTIAX   0.14%
Total International Bond Index                    12.1%    VTIBX   0.23%     VTABX   0.19%
Short-Term Inflation-Protected Securities Index    0.9%    VTIPX   0.17%     VTAPX   0.08%
                                                 ------            ------            ------
Total and Weighted Average                       100.0%            0.197%            0.094%
The 0.14% expense of the 2020 target fund falls in between the weighted average of doing-it-yourself with Investor funds (0.20%) and with Admiral funds (0.09%). The weighted average expenses can be computed with the Excel SUMPRODUCT function. For example, if the 2020 allocations are in cells B3:B7 and the Investor and Admiral class expenses in cells D3:D7 and F3:F7, the following formulas will calculate the weighted averages:

Code: Select all

0.197% =SUMPRODUCT($B3:$B7, D3:D7)
0.094% =SUMPRODUCT($B3:$B7, F3:F7)
Sources:
Total Stock Market Index Fund Investor Shares (VTSMX)
Total Bond Market Index Fund Investor Shares (VBMFX)
Total International Stock Index Fund Investor Shares (VGTSX)
Total International Bond Index Fund Investor Shares (VTIBX)
Short-Term Inflation-Protected Securities Index Fund Investor Shares (VTIPX)
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Re: Calculating expense ratio with multiple funds

Post by LadyGeek »

#Cruncher has shown how the expense ratio was calculated (thanks!), but it does not match the fund exactly. Take another look at the Total Bond Market Index fund used in Vanguard Target Retirement 2020 Fund (VTWNX).

Code: Select all

Vanguard Total Bond Market II Index Fund Investor Shares*

*Information on this fund can be found on Vanguard's Institutional Investors site.
Always check the footnotes. This leads to Total Bond Market II Index Fund Institutional Shares (VTBNX)

Expense ratio = 0.10% for investors.

On a related note, always check the date of any financial statement - they are snapshots in time.
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iceport
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Re: Calculating expense ratio with multiple funds

Post by iceport »

There's another potential complication. The target retirement fund might be using more recent expense ratio data than have been reported for the underlying holdings.

For example, the most recent expense ratio for the Total Stock Market Index Fund Investor Shares (VTSMX) is shown in the fine print on Page 4 of the June 30, 2015 semiannual report: as of 6/30/15 it was 0.15% for investor shares.

"The fund expense ratios shown are from the prospectus dated April 28, 2015, and represent estimated costs for the current fiscal year. For the six months ended June 30, 2015, the fund’s annualized expense ratios were 0.15% for Investor Shares..."


That number was available after the 4/28/15 prospectus, so it is not yet officially reported for the Total Stock Market Index Fund Investor Shares (VTSMX). (So far, the official expense ratio is still listed as 0.17%, but that will likely be changed to 0.15% when the next prospectus is published.) However, is it possible Vanguard is using the more recent expense ratio (0.015%) for reporting in the 1/28/16 prospectus for the target date fund?
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Re: Calculating expense ratio with multiple funds

Post by IPer »

I used to do it on a spreadsheet, figured out the math, IMHO kind of a waste of time these days
unless you enjoy that sort of thing. Can plug in here for free: http://personalcapital.com
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Re: Calculating expense ratio with multiple funds

Post by TheQuietMan »

This post is a typical example of the knowledge passed along on this forum. I have a small three fund portfolio in my traditional IRA at Vanguard, and always wondered how to calculate the overall ER. Thanks to the folks on this forum, some valuable pieces are falling into place. This was one of them.
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