## The back storyI'm not a hardcore Bitcoin investor. Back in 2017, I put some toy money in on the exponential peak and tripled my investment to a grand total of 100 EUR. Then I figured the hype was over, everyone found out the metaphorical tulip bulbs were worthless, and I didn't look back. Fast forward to 2020, and the money printers have pumped basically all asset prices to the moon. Bitcoin is above the 2017-2018 peak so this got me wondering whether it is truly here to stay, as a very volatile but in the long run appreciating asset class. Well, I might as well take the gamble and put some toy money on it. But then the eternal question: when to invest? How much? What are the risks? The opportunities? Yes, you should sell high and buy low. But when is low, and when is high? Crypto and equity markets are second order chaotic systems: prices influence participants and in turn participants influence the prices in a recursive feedback loop. They are also zero-sum games – your win is another's loss and vice versa. For these reasons it is mathematically impossible to devise an investing strategy that will continue to win in the long run, since other participants will devise strategies to counter yours. You can only make gains by exploiting the inefficiencies and mistakes of others. You may think you are smart and you see things, and sometimes you may get lucky, but in the long run you will lose to participants with vast computational resources, human capital, and lightning fast data streams: the institutional players. Enter dollar cost averaging. If we operate under The power of DCA is well known for equity investing, but what would happen if we apply it to the short history of Bitcoin? In the very simple DCA strategy there are still four degrees of freedom: when did you start investing, with which frequency did you invest, how much did you invest each time, and when did you cash out? I wanted to explore the effect of these parameters on the returns realized on cash out date. ## The resultsLet's first look at frequency and amount invested. All currency amounts are in USD because that happened to be the denomination of the BTC price data. If you invest more frequently with smaller amounts, you will lose a larger proportion to transaction fees. I took the transaction fees from coinbase to estimate the ratio of fees to gain (expressed in percent), if you invested using DCA in Bitcoin from 1/1/2018 – 1/1/2021. The result is shown in the color plot below: A remark on how you should interpret the graph: say you are at 300 USD invested per month on the x-axis and on 3 times per month on the y-axis, this means you invest 100 USD on average 3 times per month. Note also that these are the buy fees only; the sell fee you would have to pay at the end if you want to cash out is not included. Generally with investments, you don't want to be paying over 2% in costs. Everything above 2% in the plot is yellow. You can see that it basically isn't worth it to invest less than 50 USD at a higher frequency than once a month. Note also that these are low estimates for fees due to the high valuation of bitcoin on 1/1/2021. If you cash out at a lower price point, the ratio of fees to gain will be higher. If we look purely at the absolute gain for DCA over this same period, frequency has limited influence on the return, and is basically a linear function of the amount invested per month. So if you consistently invested 500 every month from the peak of 1/1/2018 to 1/1/2021, you would have made about 50000 of pure profit, evaluated on 1/1/2021. In relative terms, that's about 80-90% per year (This is just the total relative gain divided by number of years, not compounded. Should have taken a root. Whatever.). You see below that the percentage you gain is only slightly influenced by transaction fees. The "stepped" transaction fee function is reflected in the 4 slanted lines. The horizontal lines are an effect of market timing, and they become more pronounced near lower investing frequencies. Obviously if you invest big a few times, you could potentially make more, but you could also lose more. So what about market timing? It's harder to study or visualize this systematically, but I thought I would show two examples. Suppose you gave up on BTC and cashed out on 1/1/2019. What is your gain depending on the time you started DCA? The figure below shows the total return (in percent) you would have made as a function of trading frequency and starting date (investing amount is 500/month to ignore effect of fees). Superimposed is the daily BTC price. Well, even if you started at the beginning of the rally, in say 07/2017, you would have made significant losses, because the bulk of your investments would have been made at a time when the price was higher than on cash-out day. Only if you made a big play in early 2017 and did not invest significantly into the peak would you have made big gains. Basically if you stepped on the hype train too late, and you did not get off until 2019, you would have lost. If we now change the cash-out date to 1/1/2020, If you stayed consistent for another year, even if you started investing on the big peak, you would have gained 10-30 percent, which is totally not bad at all for 2 years of investing. Of course if you started investing before the peak you would have monstrous returns. Only if you waited to start investing in the second peak of 2019 would you have incurred losses. Hindsight is 2020, and this is a nice illustration that "time in the market beats timing the market". A final picture to illustrate the effect of investing frequency. The reality is that you have totally no idea which date to start investing. Then any pick of date is just as good as the next. So let's say we pick random days to start investing on the interval 1/1/2017 – 1/1/2021. What is our expected return on cash-out date 1/1/2021? Below I plotted the maximum, minimum, mean, average and standard deviation of total return when picking a random start date, as a function of investing frequency. If you made a few big plays and tried to time the market, the potential pay off is huge, but you also risked not gaining very much at all. In this case, because the price on cash-out date is so huge it looks like things can't "go tits up", but if you would make a plot for another cash out time, the same principles apply and you could have made huge losses. In general, the graphs smooth out when investing at a frequency higher than once per month. There is still a huge spread on profitability at all frequencies, which reflects the inherent volatility. ## ConclusionIf Bitcoin is an appreciating asset, it can make sense to invest in it using dollar cost averaging. Due to the super freaky volatility, you can still make some pretty good returns using such a basic strategy. If you would have started investing on the peak of 2018 and stayed consistent until 2020, you would have come out with a pretty good return, and obviously by now your investment would be huge. Lower investing frequencies lead to potentially higher pay offs but also much higher uncertainty and potential losses. A frequency of 1 time per month or once per 2 months seems to be a decent balance between stability of returns and minimization of fees. Of course if Bitcoin ever becomes irrelevant, you lose everything. submitted by /u/HarvestingPineapple |