Dwarves pay the price (Impact of fees on cost averaging profits)

In our world of dwarves, fees matter.

While the industrious mining dwarves are busy mining, the blacksmiths are forging and the brewers brew their great pixie stout, the dwindex dwarves are making their living by charging fees of the other dwarves. They charge these fees each time other dwarves, like our friend Hulrum Gravelgleam, want to invest their ickles into the dwock market. In exchange, they ensure that the dwock market keeps running and provide some useful solutions, like for investing in the whole dwindex instead of, say, only the blacksmith (risky stuff).

There is a large dwock market cave with mighty columns where these little business-minded fellows charge two types of fees:

First, they charge a one-time fee per share purchase, called commission. In this dwarf world, this is a constant percentage, say 0.5 % of each share purchase. So, if Hulrum invests 200 ickles, he has to pay one ickle on top of his investment to the dwindex dwarves (200 ickles plus 0.5 % x 200 ickles = 201 ickles in this example).

Second, if Hulrum wants to invest in the whole dwindex (remember, this represents the whole dwarf economy — larger businesses, like the brewery, also take up a larger portion of this dwindex) and hold this investment for a longer time, he also has to pay an annual fee to the dwindex dwarves. This serves to pay them for their studious calculation of the dwindex itself. The fee is calculated as a percentage of the total invested amount and is deducted automatically. Each month, 1/12 (yes, dwarves also have 12 months in a year) of the annual percentage is deducted. Note that in a human world, this is more complicated, there are also some non-fixed components like the tracking error — but humans are more complicated in many respects, anyway.

Hulrum does not like to cope with this stuff all day long, as he greatly prefers digging for his beloved, (gravel-)gleaming gold. And so, he opened the tunnel to our world once again, asking the author about the impact of these fees on his bottom line. And dwarves like bottom lines if only they lead them to new riches.

Disclaimer: the following content is for informational purposes only and does not constitute financial advice. Do not take any decisions based solely on my writing.

Dear Hulrum,

Fees matter in both worlds. As your previous strategy consisted of monthly investments in the dwindex (so-called cost averaging), I will assume that your fee question relates to this kind of strategy. And I will only show one scenario now, the upwards scenario.

(Grumbling in the tunnel, something about know-it-all)

Erm… (don’t make dwarves angry!) anyway, let’s see what we can do in this analysis:

I will vary the one-time fee percentage from 0 % to 4 % and see what happens to your return after some time. We will look at percentage returns at the end (not annually), defined by return = what comes out (total end value of portfolio, i.e., dwindex shares value) divided by what you put in (cash in ickles), minus one. So, if you invested 100 ickles and obtain 153 ickles in the end — for example, you withdraw in order to buy a nice dwarf mansion — your return will be 153/100–1 = 53 %.

For the two fee types, let me explain:

One-time fees (commission in a human world) will increase your “what-you-put-in” — because you paid fees on top. For example, if you bought dwindex shares for 20 ickles, five times (5 x 20 = 100), and had a one-time fee percentage of 2 %, your total invested ickles would be 102 ickles (fees paid: 5 x 2 % x 20 ickles = 5 x 0.4 ickles = 2 ickles). But you only get 100 ickles worth of dwindex shares, of course. Let us assume you can pay the one-time fees in cash so these will not reduce your invested monthly — and thus overall — amount.

Annual fees (expense ratio in a human world), on the other hand, will reduce your portfolio value. Let’s assume you have 100 ickles in dwindex shares at the beginning of the first year. If these go up in value by 10 % in the first year, you will have a portfolio value of 110 ickles at the end of that year. Now, if the annual fee is 0.5 %, your portfolio will be reduced by 0.5 % and thus your return after fees is just 9.5 %. As I said, this might be a bit simplified compared to our world, where fees are deducted monthly. I will include this “monthly” factor in the following simulations. In general, if you have more ickles invested, you will also pay more fees (in absolute, i.e., ickle terms).

(Grumble)

OK, let’s see what happens when fees increase.

Let’s first increase the one-time fees (for each dwindex share investment) from 0 % to 4 %. We will compare the overall return at the end of the investment period of about 10 years in these cases.

Not much happening here, right, Hulrum? Obviously, the paid commissions reduce our annual return, but not by much (about 6 percentage points from 74 to 68 percent if we compare 0 % and 4 % commission, which corresponds to -9 % difference in return). And 4 % commission is a lot, you should actually negotiate with these greedy dwindex dwarves in this case. As for sure, there will be less pixie stouts and cage furniture that you can buy. The return decreases in a linear fashion: each increase in commission percentage reduces the return equally, no matter if it is 0 to 1 % or 1 to 2 %.

This is how your portfolio looks if you invest 500 ickles each month:

Each month, at 2 % commission, you’ll pay 2 % x 500 ickles = 10 ickles to the clever dwindex dwarves, or 120 ickles per year. This does not change over time; it stays the same, independent of your portfolio overall value.

But now, let’s see what happens if your clever dwindex dwarves increase the annual fee in the same manner (0 % to 4 %).

Holy shovel, that is quite a difference. Your return is decreased by -55 % (41 percentage points)! What about all these nice things you wanted to buy? What happened here? The gnomy problem is the annual fee — each year, your return is decreased. The fee affects your whole portfolio value! So, after three years or so, your portfolio might be worth 20,000 ickles and you’ll pay, say, 2 % in fees, this results in a deduction of 400 ickles of your portfolio value. If, after 10 years, it is around 100,000 ickles, again 2 % fees: this will result in 2000 ickles of fees. Happy dwindex dwarves — but you are not happy at all. We humans say, this impacts “compounding”.

Let’s see what a 2 % annual fee does to your portfolio value.

In this blueish gray you see the portfolio value if you pay 2 % commission (same amount each month, repeated from above). If you compare this to the curve with a 2 % annual fee, paying a fixed commission within certain bounds allows for much better portfolio returns. The difference in return is astounding: 36 % difference (19 percentage points). Note that the commission needs a bit more ickles during the years, which is why the blueish gray ickle line is positioned slightly higher. So, dear little friend, be careful about fees in general; and especially annual fees!

Dear human friend,

Thank you. This will save me a lot of ickles, as I look forward to negotiating with the dwindex dwarves. I will be especially cautious concerning the annual fees!

You might be getting closer to your wish becoming reality.

Yours gleamingly

Hulrum

For curious dwarves who want to dig deeper:

• The return reduction caused by annual fees on the overall portfolio is not linear, in contrast to the discussed commission scheme. It follows a hyperbolic curve. Expressed in a more applicable way, each annual fee percentage point counts, even more so within the first few percentage points than later on. Keep annual fees low, my dear Hulrum!
• Obviously, 2 % commission vs. 2 % annual fee are not the same, as the first is based on dwindex share purchases (one-time fee, making investments more expensive), the second is applied to the whole portfolio value annually (reducing compounding effects). The impact on compounding leads to the strong decrease in return due to annual fees.
• In our dwarves’ world, we will omit inflation for now. But it is important and might be discussed in later articles.
• For more on cost averaging with and without variable size, see the previous Hulrum stories (here and here). There you’ll also find more information on how these financial time series are constructed (random walk / not a normal distribution).

Coding dwarf’s acknowledgements: Studies were carried out using backtrader (https://www.backtrader.com/) in Python within the PyCharm IDE (https://www.jetbrains.com/pycharm/), among other libraries. Thank you to the developers for providing such great user-friendly and reliable tools.

DISCLAIMER: This article presents my own learnings based on studies generated on synthesized (random, i.e., artificial) data which is statistically similar to real-world time series, and personal experience. The content is, thus, purely educational. Past performance is not reliable indicator of future results. The article should not be considered Financial or Legal Advice. Consult a financial professional before making any major financial decisions.