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)

  • 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.

Dual Momentum on Steroids

Dual Momentum is a simple investing strategy that has historically beaten the S&P 500 while providing exceptional downside protection. It was published by Gary Antonacci in his book Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk.

I began my do-it-yourself (DIY) investing journey by investing in couch potato portfolios with a 60% exposure to global equities and 40% fixed income; this portfolio is commonly known as a balanced portfolio. To this day most of my liquid assets are held in this kind of portfolios. 

Then I met Dual Momentum and I felt in love with the strategy. The things I like the most about it are:
  • It is simple, simpler to implement than a couch potato portfolio. Anyone can do it. Chapter 8 of the book explains how to implement it; but I will go over it briefly later.
  • It has delivered great returns historically. Consider this table put together by Gary. The column "GEM Annual" shows the historical annual returns since 1950. GEM stands for Global Equities Momentum which is just an implementation of Dual Momentum.
  • It offers great downside protection when sh__ is hitting the fan. Consider the first chart in this link and draw your own conclusions.
  • This strategy is backed by lots of research and back-testing; not just from Gary but from many others. Hell, you can back test it yourself with sites like Portfolio Visualizer.
  • The strategy requires very little trading activity. It could potentially save you some trading fees.
  • The strategy is somewhat tax efficient (in non-registered accounts) because it generally triggers capital losses when transitioning to bonds in a downturn and it lets the money grow without triggering capital gains in an up trending market. 
In the book Gary covers a variant of the strategy where a 1.30x leverage is used. I decided to implement a similar approach given that the downside protection works pretty well even with leverage and the returns are goosed up by ~3% annually (historically).

For this purpose I decided to use PortfolioPlus ETFs PPLC, PPDM and PPEM offering a 135% daily market exposure to the S&P 500, Developed International Markets and Emerging Markets respectively. I am Canadian and these ETFs trade on the US Market; so I converted cheaply some of my loonies to greenbacks with Norbert’s Gambit.

Dual Momentum (DM) dictates that at any given time all the money in your portfolio should be invested in one (and only one) of these: American Equities, Internal Equities (75% Developed Markets ex US plus 25% Emerging Markets) or US Treasury Bills (you can use US Aggregate Bonds as well).  

At the end of each month I use PerfChart to evaluate the DM signal. I use VOO, ACWX and BIL as proxies for US Equities, International Markets and US Treasury Bills respectively. The look-back period I use is 253 days (1 year). Notice that I don’t trade VOO, ACWX and BIL; these are only used to determine the DM signal. From those ETFs the one with the highest total return in the last 253 days will determine where the money will be allocated.

If VOO wins, the money will be allocated into US equities. If ACWX wins, the money goes to International Stocks (both developed and emerging markets). If BIL wins, the money goes to US bonds. Given that I am using a leveraged implementation of DM, then the above translates as:

If VOO wins, 100% of the portfolio is invested in PPLC. If ACWX wins, the portfolio is invested in a 75% PPDM and 25% PPEM split. If BIL wins, 100% of the money is invested in SCHZ.

Dual Momentum is a great strategy for DIY investors. For those looking to juice up the returns while accepting some added risk (but not much) the use of leverage is at hand. For risk adverse investors there are other ways in which DM can be implemented. For instance, in the book Gary describes GEM 70: an implementation of DM where 30% is always allocated to an US Aggregate Bond ETF while the remaining 70% is allocated to equities as per the rules of DM.

(Disclaimer: I am an amateur DIY investor. What I say here should not be considered investment advice. Investing on the stock market comes with risks and you can lose money.)

The cost of converting Canadian Dollars to American Dollars with Norbert's Gambit

On Feb 26th, 2019, I initiated my first Norbert's Gambit at National Bank Direct Brokerage (NBDB).  The purpose was to exchange over 55k worth of Canadian Dollars (CAD) to American Dollars (USD) within my RRSP account. (Side story: I used the greenbacks to invest in a leveraged implementation of Dual Momentum)

My RRSP account at NBDB is segregated into two sub-accounts: a Canadian Dollar RRSP sub-account and a US Dollar RRSP sub-account.

The original funds were in my Canadian Dollar RRSP. There I bought 4,274 shares of DLR at $13.290 CAD; for a grand total of $56,801.46 CAD. 

I waited until the day after my trade settled (March 1st, 2019) and called NBDB requesting to transfer all 4,274 shares of DLR from my Canadian Dollar RRSP to the  US Dollar RRSP (resulting in 4,274 shares of DLR.U being transferred into the a US Dollar RRSP). I also asked them to include a note in the system so that I could sell all the 4,274 shares of DLR.U that same day. 

Shorty after the call I sold the 4,274 shares of DLR.U at $10.06491 USD for a grand total of $43,017.43 USD.

In summary, I got $43,017.43 USD for my original $56,801.46 CAD.

There were no transaction costs because trading more than a 100 shares of any ETF is free at NBDB.

The bid/ask spread when I bought DLR.TO was $0.01 CAD; incurring in a cost of $42.74 CAD because I bought at the ask price. 

The bid/ask spread when I sold DLR.U.TO was $0.01 USD; incurring in a cost of $42.74 USD because I sold at the bid price. Converted to CAD using the Bank of Canada (BoC) rate on March 1st ($1 CAD -> $0.7541 USD) this cost rounds to $56.68 CAD.

The MER of these ETFs is 0.56% annually; which translates to a cost of 0.0046% (3 * 0.56% / 365) of the market value for holding it 3 days.  For simplification let’s say we apply this tiny percentage to the initial dollar CAD amount: 0.0046% x $56,801.46 CAD = $2.61 CAD.

If the ETF was trading at a premium; then there would be a cost associated with such premium. I honestly don’t know whether the ETFs were trading for a premium or at a discount at the time I executed my trades.  If you execute Norbert's Gambit many times over your life as an investor; then this cost would probably balance itself.  So, I will assume this cost to be zero given that sometimes you would buy at a premium incurring in a cost or buy at a discount pocketing a gain.

Beyond the “typical” costs we need consider the capital gain or loss incurred by holding the ETFs for 3 days (the Forex market keeps moving). Here again I would simplify things by assuming that either the CAD/USD pair did not move significantly during these 3 days or that over a lifetime of executions of Norbert's Gambits the capital gains and losses would balance themselves.

So far the “approximate” “theoretical” cost of my Norbert's Gambit comes to $102.03 for exchanging 56,801.46 CAD. In percentage this cost rounds to 0.18% of the amount I exchanged.

That’s the theory, but what about in practice?

The BoC CAD/USD rate on Feb 26 was 0.7579 ($1 CAD -> $0.7579 USD). If we use this rate for our estimation, then we could have converted $56,801.46 CAD into $43,049.83 USD on Feb 26. This number is very close to the real amount of dollars I ultimately got converted ($43,017.43 USD). The difference is minus $32.40 USD; which could be interpreted as a “cost” of $32.40 USD ($42.97 CAD if we use the BoC exchange rate of March 1st). In percentage this cost rounds to 0.08% ($42.97 CAD / $56,801.46 CAD) of the amount I exchanged.

There are lots of simplifications and assumptions in the math above; but they are not outrageously out of place. My goal was not to calculate the cost of the Norbert's Gambit with scientific precision; but to show that it is a very cheap strategy to convert CAD to USD dollars and vice versa.

How to deposit US cash into Tangerine’s USD Savings Account?

This can only be done indirectly as far as I know.  I opened an RBC U.S. High Interest eSavings account and deposited the American dollars into it by visiting an RBC branch (the teller would do this for you)

I already had a USD Savings Account with Tangerine. In the past I had funded this account via cheques that I received. This time I had some leftover USD cash from a vacation and I wanted to deposit that back into Tangerine (and collect some interest until my next vacation). The problem though is that Tangerine does not have physical branches and so I was stuck with the cash. 

I figured that I could transfer the money from the RBC U.S. High Interest eSavings account into the Tangerine’s USD Savings Account. To achieve this you need to add the RBC U.S. High Interest eSavings account as an external account in Tangerine. This is the link where you can do that: (you will need to log in with your credentials)

As part of the process Tangerine would make two small deposits into the RBC U.S. High Interest eSavings account and you’ll need to type those numbers into the linked-to-be external account in Tangerine. Be careful to enter the right numbers (do not make a typo) and a second later you would have added/linked the RBC account as an external account in Tangerine.

After this simply “Move Money” from the RBC U.S. High Interest eSavings account into the Tangerine’s USD Savings Account. It should take a few days for the money to be transferred from one institution to the other.

I know this works, because I did it myself a week ago. 

Why did I bother? Well the RBC U.S. High Interest eSavings account has an interest rate of 0.25% while the Tangerine’s USD Savings Account offers at this time 0.80%. Also, Tangerine offers US Dollar Guaranteed Investment (US$ GIC) that I wanted to use. I actually locked the cash for 6 months at an interest rate of 1.75%. I know I won’t need this cash for at least another 6 months; so that’s why I picked the 6 month term. Not sure why Tangerine does not publicly posts the rates of the US$ GICs under one year; but Tangerine offers those as well. 

They had as of today:
  • 90 days US$ GIC   – 1.00%
  • 180 days US$ GIC – 1.75%
  • 270 days US$ GIC – 2.00%
All other terms and interests rates can be found here:

If you do not have a Tangerine account and want to open one please consider using my Orange Key: 40030923S1. We could both be rewarded with some signing bonus cash if you do that. Click here to start the process of opening a Tangerine account.