How to calculate the MER of an investment portfolio constructed from individual funds?

A portfolio can be put together by aggregating various independent funds, each of which carries its own fees.

These fees are expressed as an annual percentage of the value of the fund. Exchange Traded Funds (ETFs) and Mutual Funds normally use the term Management Expense Ratio (MER) to refer to these fees. Funds accessible via Group Plans might refer to them as Fund Management Fees (FMF) or Investment Management Fee (IMF).

Moving forward in this article I will be using the term MER when referring to either of them. This is just a simplification and the reader must infer that the right terminology depends on the type of fund.

The MER of a portfolio can be calculated by knowing the MERs and allocation percentages of the underlying funds. The formula below can be used for such purpose:

MER(P)  = MER(F1) * A (F1) + MER(F2) * A (F2) + … MER(Fn) * A (Fn)


Where:

• P is the portfolio.
• F1, F2, …Fn are the underlying funds of the portfolio; for a total of n underlying funds.
• MER(P) is the MER of the portfolio.
• MER(Fn) is the MER of fund Fn; with n =1, 2…, n.
• A(Fn) is the allocation target (in percentage) of fund Fn; with n =1, 2…, n. The sum of all allocation targets should be 100%. In other words, A (F1) + A (F2) + …+ A (Fn) = 100%.

For example:

Let’s consider a portfolio containing 7 underlying funds as in the table below:

Symbol	Allocation	MER
VUN	23.70%	0.16%
VAB	23.60%	0.13%
VCN	18.20%	0.06%
VIU	13.80%	0.23%
VBG	9.20%	0.38%
VBU	7.20%	0.22%
VEE	4.30%	0.24%

MER(P) = MER(VUN) * A(VUN) +  MER(VAB) * A(VAB) +  MER(VCN) * A(VCN) +  MER(VIU) * A(VIU) +  MER(VBG) * A(VBG) +  MER(VBU) * A(VBU) +  MER(VEE) * A(VEE)

MER(P) = 0.16%*23.70% + 0.13% * 23.60% + 0.06% * 18.20% + 0.23%*13.80% + 0.38% * 9.20% + 0.22% * 7.20% + 0.24% * 4.30%

MER(P) = 3.792%% + 3.068%% + 1.092%% + 3.174%% + 3.496%% + 1.584%% + 1.032%%

MER(P) = 17.238%%

MER(P) = 17.238 / 100 %

MER(P) = 0.17238%

MER(P) = ~0.17%


The MER of the portfolio above is approximately 0.17%. It resembles the underlying composition and allocation targets used in VBAL.

Conclusion: the MER of a portfolio as a whole can be calculated by applying a simple formula that takes the MERs and allocation targets of each underlying fund as input. This calculation provides DYI investors with a way to assess how expensive a portfolio is.

How to calculate the weightings of VSB and VSC given a desired allocation of government and corporate bonds?

Let’s say I want to allocate 10% of my investment portfolio in government bonds and 5% in corporate bonds. For that I want to use short-term bonds ETFs.

After some research, I narrowed my choices of ETFs to these:

• Vanguard Canadian Short-Term Bond Index ETF (Ticker symbol: VSB)
• Vanguard Canadian Short-Term Corporate Bond Index ETF (Ticker symbol: VSC)

VSB is composed approximately of 72% government bonds and of 28% corporate bonds. On the other hand, VSC is composed roughly of 8% government bonds and of 92% corporate bonds.

Question: given the description above, what would be the percentages of VSB and VSC in our portfolio?

At this point, I am going to throw a couple of formulas at you. You can use them to calculate the weightings of VSB and VSC. I came up with these formulas by myself. I can share the algebraic demonstration…If you want it, drop a comment below. 

% VSC = S * [ ( X - Y*R ) / ( Z*R – Y*R + X – W )  ]
% VSB = S * [ (Z*R - W) / (Z*R – Y*R + X - W)  ]

Where:

• X is the percentage of VSB dedicated to government bonds; in our example would be 72.
• Y is the percentage of VSB dedicated to corporate bonds; in our example would be 28.
• W is the percentage of VSC dedicated to government bonds; in our example would be 8.
• Z is the percentage of VSC dedicated to corporate bonds; in our example would be 92.
• S is the sum of the weightings of government and corporate bonds in our portfolio; in our example S would be 15 (10 + 5), because we want to have 10% in government bonds and 5% in corporate.
• R is the ratio of government bonds to corporate bonds; in our example R would be 2 (10 / 5).

Finally, let’s evaluate each formula:

% VSC = 15 * [ ( 72 - 28*2 ) / ( 92*2 – 28*2 + 72 – 8 )  ] = 1.25%
% VSB = 15 * [ (92*2 - 8) / (92*2 – 28*2 + 72 – 8)  ] = 13.75%

Answer: if we want to hold 10% in government bonds and 5% in corporate bonds; then 1.25% of our portfolio should be allocated in VSC and 13.75% should be allocated in VSB.

The usefulness of the formulas lies in the ability to change your target weightings for government and corporate bonds. This will of course result in new values for R and S that can be used to revaluate the formulas, allowing you to calculate the new percentages for VSB and VSC.

Finally, notice that the values of X, Y, Z and W do not change often. They represent the weighting of the different bonds within these ETFs. Refer to “Sector weighting (% of net asset value)” within the corresponding ETFs fact sheets if you want to determine these values yourself.

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VSB fact sheet:

https://www.vanguardcanada.ca/individual/mvc/loadImage?country=CAN&docId=249

VSC fact sheet: 

https://www.vanguardcanada.ca/advisors/mvc/loadImage?country=CAN&docId=552

An ETF based Balanced Portfolio for Canadians

I decided to build my own balanced portfolio to grow my hard earned money. No more mutual funds with expensive MERs neither miserable GICs nor saving deposits. For my portfolio I will be using ETFs, which have very low MERs and offer a degree of diversification.

I based my portfolio on the Millennial Portfolio presented by Garth Turner. Below I am listing the different weights per asset classes of the portfolio (taken as a quote from Garth’s blog post).

Canadian bond index ETF

20%

Preferred share index ETF

20%

Canadian equity index (large cap) ETF

15%

US equity index (large cap) ETF

20%

International equity index (large cap) ETF

20%

REIT index (Canadian) ETF

5%

So, what now? The next step is finding the corresponding ETFs for the different classes of assets. I researched a little bit about what ETFs to use and I selected the following ones:

Fixed income portion of the portfolio (40% in total):

• Government and Corporate bonds: VSB – 16.5%
• High Yield Bonds: CHB – 3.5%
• Preferreds: XPF – 20%

Growth portion of the portfolio (60% in total):

• Canadian Equity: XIC – 15%
• American Equity: VSP – 20 %
• International Equity (developed nations): XEF – 15%
• Emerging Markets: XEC – 5%
• Canadian REITs: VRE – 5%

I decided to use only large cap equity ETFs at the moment. I am building this initial portfolio with about $25k CAD, which is not too much. As the portfolio grows, I will consider more diversification by adding also medium and small caps into the mix.

I also decided not to add real return bonds to my portfolio at this moment (I will probably do so in the future). The reason for not adding real return bonds is that the FED is very likely to start rising the interest rate this month. If that happens, the long term bonds will be nailed. As it so happens, the real return bonds ETFs that I have found so far have very long terms. 

OK, now what? The broker of course. I decided to use Questrade. 

Questrade does not charge you when buying ETFs (well, ECN fees might still apply but that is not in their hands). It will charge you though when you sell ETFs (min. $4.95 / max. $9.95). You most likely will have to sell some ETF shares when rebalancing your portfolio, but that should not happen very often: maybe once or twice a year. 

As far as I can tell Questrade has the lowest commissions in Canada when trading ETFs. If you know of a better broker, please let me know with a comment below.

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The same goes for the selection of ETFs I made. If you think my selection sucks and have in mind some better alternatives, please, let me know as well. Your comments are very welcome.

Remember, I am an amateur investor and these are my first trades. So, everything that you read here, is to be used at your own risk.  I am neither a financial advisor nor an expert on this subject. I am a merely a rookie investor and I want to share my investing experiences on this blog.

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Happy investing!