Dwarves Digging For Riches (Cost Averaging In A Fun-Sized World)

Believe it or not — there is a world of dwarves. And they’re digging for riches.

In this world far away from ours, these little fellows work hard every day, be it as miners, brewers, even smaller dwarves’ teachers, and blacksmiths, among others. And they are excellent, one might even say full-sized, businessmen and businesswomen. To grow their businesses by raising capital, they issue and trade shares of their led-with-love businesses, which they call “dwocks”. If a dwarf needs capital, he issues dwocks and receives dwarf money (“ickles”) for these; the buyer, in turn, receives a part of his business, which they politely negotiate about (these itsy-bitsy fellows are mostly polite, as it happens). Thus, the new business part owner also receives part of the profits later. If some dwarf has dwocks but needs ickles as she is about to run low on vital dwarf equipment, she can also resell her dwocks. Both takes place on the dwock exchange, a huge cave with mighty columns in which they shout prices at each other and, occasionally, have a nice pint of their favorite pixie stout.

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.

Some very clever dwarves one day decided to calculate a certain number from these dwocks, which they call the “dwindex”, so they can see how the whole economy is going. Therefore, they take all of the businesses — the blacksmiths, the brewers, the miners — and calculate each of their businesses’ market capitalizations by multiplying the number of their issued dwocks with their current dwock price (blacksmith 100000 dwocks, 50 ickles each = 5 million ickles market capitalization, etc.). After that, they average these values over the full number of all issued dwocks. Larger businesses thus play a bigger role in the dwindex (e.g., the brewery) than small ones (the clothes store, as dwarves like to wear their stuff for a long time). They even allow their companions to invest in the dwindex by buying a respectable looking document, so that each dwarf does not have to take the risk of only owning the blacksmiths when there’s enough shovels for everyone (which obviously would make his dwock go down as the blacksmiths’ profits fall).

Hulrum Gravelgleam, a particularly hardworking miner dwarf, is interested in this dwindex to grow his wealth, as he presumes that the dwarf economy as a whole will rise over the decades. He wants to know what happens if he puts a fixed amount of his salary in the dwindex each month. Somehow, he managed to open a tunnel to our world (dwarves are good with tunnels, as you might know) and contacted the author to help him understand what will happen with his invested ickles, in three cases: (1) The small-sized, but full-fledged dwarf economy grows as expected, because dwarves are industrious; (2) It does not grow, but rather goes sideways, maybe sometimes up or down, as the dwarves begin to embrace their already gained riches and preserve the beautiful mountain environment; (3) The economy is going down (i.e., more pixie pints, less digging). The author willingly agreed, as hell hath no fury like a dwarf scorned. And, maybe, the author gets a wish granted, if lucky.

So, the author launched his calculating machine using a homemade elaborate statistical slide rule which is able to emulate our world’s dwocks, um, stocks and indices with their return distributions (how much they make each day, basically). But keep in mind, dear dwarf, and reader, that this is not financial advice, and it uses not real, but diligently synthesized data. In this statistical regard, dwarves and humans are hopefully the same, although empirical dwarves’ data has yet to be shown. The dwarf, getting a bit impatient (yet polite, as we know), asked for less background. Thus, the inclined reader is referred to the last paragraph if he or she has the desire to dig deeper.

Here are the results, which the author tunneled back to our industrious fellow.

Dear Hulrum, if you invested 500 ickles each month in an overall uptrending dwindex until the end of 2033, it would look like this. (Do you actually have the same calendar? Well, never mind.)

The muddy black full line is a possible outcome of the dwindex in the future (close prices at the end of each day). The golden scatter points demark the dwindex price each month when you are buying (I suppose you’ll be doing so every 20 workdays). The dashed line shows your overall average buying price of all of your dwindex shares, which rises if you buy more expensively and vice versa. Thus, your dwocks are worth more than you bought, overall, when the muddy line is above the dashed line.

If you buy 500 ickles each month, you will have invested 76500 ickles at the end. But these clever dwindex dwarves are tricky — they want 1 % of your freshly invested ickles each month as a fee for buying (or selling). So, it is actually 765 ickles less. (In a real dwarves’ world, there is also some effect as you can only buy at the open — candle bars not depicted above for simplicity — so you’d have invested 76610 ickles and paid 766.10 ickles in fees in this case). As I said, if your average price of dwindex shares is below the current dwindex price, you profit — which you do heavily, especially in later years, as your average price is still quite low but the dwindex is rising beautifully. You might be able to buy a lot of tasty pixie stouts with your profit of 41000 ickles, my dear fellow. (Except that inflation will eat, um, drink away some these if pixie stout gets more expensive.) Plus, there will be hardly any time during which you suffer large temporary losses. Don’t sell in these times, Hulrum. And you may understand that, had you invested more ickles earlier on , you would have a much larger gain now as your overall average price would have been much lower. Of course, this only holds in a growth scenario.

Right, but what about less favorable times?

That’s not nice, as the final dwindex value is below your average price. (However, maybe at least the environment is more beautiful as there are less holes in the mountains.)

As before, you would have invested 76500 ickles. When you sell your dwocks in 2034, you would receive around 60000 ickles and thus you lost around 16500 ickles. Be aware, dear dwarf, that this kind of investing, which we humans call cost averaging, is not the remedy for everything, but rather functions gnometastically when there’s growth, overall. See the first half of this scenario.

And what about really bad times?

Obviously, my dear Hulrum, you will not like this outcome. The dwindex stands much lower at the end of your investing period. You would lose about -27 %. That hampers your pixie buying power even more.

Of your 76500 ickles, about 55000 would be left, leaving you with a loss of 21000 ickles. But mind, dear fearless fellow, that your loss would be much smaller than the overall dwindex loss over these years, which would be -38 %. Cost averaging has a kind of dampening effect here — similarly on the upside (first scenario), where total profits were smaller than a one-time purchase of the dwindex at the beginning (and selling at the end).

So overall, you will need busy dwarves and more digging for this idea to work well. However, also in slow or even bad times, at least your idea dampens your losses a bit.

Thank you, dear human friend.

• This cost averaging-thing seems to work well in times when we’re successfully digging.
• In times when our blacksmiths and mines are not doing much, my put-in-every-month-idea might still be bearable, but not favorable. Perhaps you could tell me about some alternatives one day.
• In bad times I won’t feel good and will have some more pixie stouts regardless of the dwindex. But at least there’s some dampening. I will go on digging now, thanks.

Yours gleamingly

Hulrum

P.S.: About your wish, our respected dwarves’ laws do not allow prompt grants. But we’ll see in the future.

For dwarves who want to dig deeper:

As dwarves slightly seem to show human traits (our digging dwarves are more amicable and happier, though), their dwindex, somehow, statistically resembles percentage return distributions of a human-made index. For those inclined: real-world distribution is not normal. Mind the fat tails, and I mean, not those of the dwarves. The author, as the dwarves’ observer, obtained this kind of open-high-low-close data using random walks “picking” from the original real-hunan-world return distribution. However, dwarves rather take random walks sometimes to relax in their vast forests… Furthermore, the monthly dwindex purchases are simulated as being carried out at the marked open — as it is not possible to buy right after close — at a four-week interval (about once a month).

Coding human’s acknowledgements: Studies were carried out using backtrader (https://www.backtrader.com/) within the PyCharm IDE (https://www.jetbrains.com/pycharm/), among other libraries, especially plotly https://github.com/plotly/plotly.py. A big thank you to the developers for providing such great user-friendly and reliable tools. And thanks to www.mypetsname.com for the great dwarf’s name generator.

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 a 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.