The weighted average expense ratio of your portfolio is an important number to know. Most people know that expenses have a huge impact on your portfolio over time since they are a drag on investment returns.
If your portfolio returns 11% during a particular year before adjusting for expenses, and your portfolio has a weighted expense ratio of 1%, your portfolio returns after adjusting for expenses will be 10%.
Lets assume you have a portfolio of $10,000 invested in the following Fidelity index funds:
Fund
Ticker
Balance
Fidelity S&P 500 Index Fund
FXAIX
$ 5,000.00
Fidelity Large Cap Value Enhanced Index
FLVEX
$ 2,500.00
Fidelity Large Cap Growth Index
FSPGX
$ 2,500.00
hypothetical portfolio allocations
The expense ratios associated with each of the funds are as follows:
Fund
Exp Ratio
Fidelity S&P 500 Index Fund
0.015%
Fidelity Large Cap Value Enhanced Index
0.390%
Fidelity Large Cap Growth Index
0.035%
expense ratios
Adding the expense ratios together and dividing by three would yield an arithmetic average of 0.147%; however, that is not the actual average of the portfolio itself since there are different dollar amounts in each fund.
In order to calculate the weighted average, we need to multiply the dollar amount in each fund by that specific fund’s expense ratio:
Fund
Balance
Exp Ratio
Dollar Exp
Fidelity S&P 500 Index Fund
$ 5,000.00
0.015%
$ 0.75
Fidelity Large Cap Value Enhanced Index
$ 2,500.00
0.390%
$ 9.75
Fidelity Large Cap Growth Index
$ 2,500.00
0.035%
$ 0.88
TOTALS
$ 10,000.00
$ 11.38
fund expenses
Based on the table above, the Fidelity Large Cap Value Enhanced Index contributes $9.75 in total portfolio expenses on a weighted basis. This amount is calculated by multiplying $2,500 by the expense ratio of 0.39%.
Calculating the dollar contribution of expenses for every fund in the portfolio and summing them together gives you a total dollar expense of $11.38 on a weighted basis. This total dollar expense is divided by the total portfolio value of $10,000 to calculate the weighted average of 0.1138% which is less than the arithmetic average of 0.147%.
Fund
Balance
Exp Ratio
Dollar Exp
Weighted Avg
Fidelity S&P 500 Index Fund
$ 5,000.00
0.015%
$ 0.75
Fidelity Large Cap Value Enhanced Index
$ 2,500.00
0.390%
$ 9.75
Fidelity Large Cap Growth Index
$ 2,500.00
0.035%
$ 0.88
TOTALS
$ 10,000.00
$ 11.38
0.1138%
weighted average table
In this hypothetical scenario, the weighted average is actually lower than the arithmetic average; however, that may not always be the case. Depending on the expense ratios and dollar allocations in your portfolio, it is possible that the weighted average could be higher than the arithmetic average.
If you have a portfolio that includes both active and passive management, calculating the weighted average expense ratio will provide you with a clearer understanding of the impact investment costs may have on the future value of your portfolio over longer periods of time.
Many people are familiar with the different tax treatment between Traditional IRAs and Roth IRAs; unfortunately, often times most individuals are not sure which contribution type is right for them.
Typically, advocates for either type of IRA tend to elect 100% of their annual contribution limits towards their IRA flavor of choice.
Ultimately, if taxes never changed then mathematically it makes zero difference if you elected Traditional IRA or Roth IRA contributions, the ending balances would be the same.
Where: FV = Future Value PV = Present Value r = rate n = period
In order to determine the after-tax value of a Traditional IRA or a Roth IRA, a new quantity for taxes is added. The key difference is the order that the taxes are taken out, which becomes clearer when comparing the two formulas. Here is the formula for the after-tax value of a Traditional IRA:
Notice how the quantity (1 – t) is moved to the front of the equation, which makes sense given that Roth IRA contributions are taxed up front, and the remaining amount is invested. Since multiplication is cumulative, then the ending balances after paying taxes should be identical between both accounts.
Let’s assume that you invest $1,000 in a Traditional IRA growing at a rate of 7.00% for 10 years, when you retire your marginal tax bracket is 30%. Plugging those values into the formula for a Traditional IRA would yield the following:
where; PV = $1,000, rate = 0.07, n = 10, t = 30%
Your initial $1,000 contribution grew tax free for 10 years, and after paying a 30% tax in the tenth year you are left with $1,377.01. The table below illustrates the tax free growth for 10 years, the tax paid, and the net after-tax future value:
Traditional IRA
Year
PV
Rate
FV
Tax (30%)
1
$ 1,000.00
7.00%
$ 1,070.00
2
$ 1,070.00
7.00%
$ 1,144.90
3
$ 1,144.90
7.00%
$ 1,225.04
4
$ 1,225.04
7.00%
$ 1,310.80
5
$ 1,310.80
7.00%
$ 1,402.55
6
$ 1,402.55
7.00%
$ 1,500.73
7
$ 1,500.73
7.00%
$ 1,605.78
8
$ 1,605.78
7.00%
$ 1,718.19
9
$ 1,718.19
7.00%
$ 1,838.46
10
$ 1,838.46
7.00%
$ 1,967.15
TAX
$ 590.15
Net ATFV
$ 1,377.01
traditional IRA table
We can represent the data above in the following chart:
traditional IRA ATFV
Let’s plug the same values into the Roth IRA formula to prove that they are identical:
where; PV = $1,000, rate = 0.07, n = 10, t = 30%
Despite starting with a lower initial investment since the tax with Roth IRA contributions are paid up front, the ending value is still identical to the Traditional IRA account:
Roth IRA
Year
PV
Rate
FV
Tax (30%)
1
$ 700.00
7.00%
$ 749.00
2
$ 749.00
7.00%
$ 801.43
3
$ 801.43
7.00%
$ 857.53
4
$ 857.53
7.00%
$ 917.56
5
$ 917.56
7.00%
$ 981.79
6
$ 981.79
7.00%
$ 1,050.51
7
$ 1,050.51
7.00%
$ 1,124.05
8
$ 1,124.05
7.00%
$ 1,202.73
9
$ 1,202.73
7.00%
$ 1,286.92
10
$ 1,286.92
7.00%
$ 1,377.01
TAX
$ –
Net ATFV
$ 1,377.01
roth IRA table
roth IRA ATFV
To reiterate, if your marginal tax bracket in the future is identical to your marginal tax bracket today, there is zero difference between a Traditional IRA and a Roth IRA (there may be a perceived difference due to emotional or cognitive biases).
Obviously, the future state of taxation is a huge assumption to make and the world is not that simple. There are a multitude of additional variables and factors that need to be taken into account in order to determine what blend between Traditional IRA or Roth IRA contributions makes the most financial sense for you.
Since there are exactly zero people on the planet who can accurately predict what the marginal tax brackets will look like when you retire (I’d be skeptical of anyone claiming that they can), having money in both account types will provide you with the maximum flexibility in determining your actual tax bracket when you retire.
Remember that the next time anyone says, “Roth IRAs are better than Traditional IRAs so I put 100% of my annual contribution limits into my Roth IRA”, or vice versa. Generalized advice, generally has good intentions, but produces generally bad outcomes, generally speaking.
Taxes aren’t the only variable that should be taken into account when determining the optimal Traditional IRA and Roth IRA blend. One should also consider the following:
what will your burn rate be when you retire
what will your projected federal tax bracket be
do you pay state income taxes
will you move to a state that has no income taxes
will you move to a state that does have an income tax
what is your current blend of qualified vs non-qualified assets
what proportion of your employer matching contributions into any qualified plans is made on your behalf
The list above, while somewhat lengthy, is nowhere near exhaustive despite the potential to get exhausted while thinking about it.
All of the concepts above are also applicable to the world of 401(k)s. From a taxation standpoint, Traditional IRAs (which are a type of qualified accounts) are taxed identically to Traditional 401(k) contributions. Similarly, Roth IRAs are taxed identically to Roth 401(k) contributions.
Other important subtleties that you should be aware of for Roth IRAs and Roth 401(k)s are the lack of required minimum distributions. RMDs do not apply to Roth IRAs or Roth 401(k)s which make them an extremely potent estate planning wealth transfer tool.
In my opinion, the best kept secret about Roth 401(k) contributions are the fact that the income limitations that apply to Roth IRAs, do not apply to Roth 401(k) contributions. You could make $1mm dollars a year and still contribute the IRS maximum into a Roth 401(k).
If you don’t have a Traditional IRA or a Roth IRA you can open one at Charles Schwab for commission free trading with an initial funding bonus of up to $500 by clicking here.
