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### 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.