## Pages

### 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.

### The MER of a VBAL-like portfolio constructed from VBAL constituents

You can construct your own DIY portfolio by sticking to the same underlying ETFs (and allocations) used by the Vanguard Balanced ETF Portfolio (VBAL). At the time of writing the MER of this portfolio that uses VBAL as a template is 0.05% cheaper than VBAL itself.

The spreadsheet below calculates the MER of the VBAL like portfolio by using data contained in the factsheets of VBAL and its underlying funds.  For more details refer to How to calculate the MER of an investment portfolio constructed from individual funds?

If you invest \$100 for 20 years this extra cost (0.05%) means you are forgoing \$1 in returns for the whole two decades period. This is not bad at all considering that having one found that rebalances itself (as opposed to 7 individual funds) will save you money in trading commissions. Not to mention that it will simplify considerably your investment process.

I would stick with VBAL unless the size of your portfolio is large enough so that the gross impact of that 0.05% can be felt. Also, as your portfolio grows you might want to diversify to other asset classes beyond the basic constituents of VBAL. With a large portfolio you might want to take control of the rebalancing process in the hope of limiting The Luck of the Rebalance Timing. You might prefer your own portfolio in the hope of making it more tax efficient than VBAL; but again, this makes more sense with larger portfolios.

As conclusion: VBAL is a simple and inexpensive option to implement a globally diversified and balanced portfolio with a 60/40 split between stocks and bonds. The 0.05% that you can save by implementing your own portfolio (using VBAL as template) can be thought as the cost for having automatic rebalancing and limiting the trade activity.