Value-at-Risk analysis of cryptocurrency investing
Individual investors who hold cryptocurrencies rarely try to think about their risks in a quantitative way. The institutional investors, on the other hand, have long been using a standard metric called Value-at-Risk (VaR) to get some numerical understanding of what kind of losses they may be looking at on a bad day or a string of bad days.
You can read more about VaR in other places, but the basic idea is that you construct many scenarios of what may happen to your investment tomorrow, or in a few days. Usually you do that using historical track record of prices of whatever you are invested in. Once you have enough history, you can use it to tell you what kind of losses could happen to you once a week, or once a year. Of course, future may bring a day that is much worse than anything in the past history, but some numbers are still better than no numbers.

Below I present VaR numbers for a hypothetical 100$ investment in Bitcoin. Bitcoin has experienced a meteoric rise over the last few years, and if you invested a while ago, you have done really well for yourself. However, as you will see, even if you did bet on a winning horse you had plenty of instances where you had to deal with some steep losses over a short period of time. That is exactly what makes VaR so useful - it helps you understand what kind of losses you should be prepared to ride out, and how often the losses of such magnitude can be expected to occur.

Here is how you read the tables below. Investment horizon tells you what period of time we are considering. 1 day means we are estimating how much of your 100$ can be lost tomorrow, and 10 day is the same but for 10 days from now. Loss frequency refers to the rarity of the losses. For example, 1 in 30 means we are considering only 3% worst days of the price history - in another words, what is the worst day of a month, on average. On 97% of days you will lose less money (or you gain money). VaR (Value-at-Risk) and ES (Expected Shortfall) tell you what happens on those 3% bad days. VaR is the smallest amount you lose on those days - in other words, on the 97% of days which have been good (or at least have not been that bad), your losses were smaller than the VaR number. Expected Shortfall tells you the average losses in all of those bad days. Naturally it will be larger than VaR. One could say, that this is the loss you must be prepared to deal with at least a couple times a month. This is particularly important if you are planning to trade on margin. If you are leveraged, even a small movement in prices can be amplified into a huge loss.
When you are looking at 1-in-300 loss frequency, that means we are using 99.7% percentile of the loss distribution - the meaning of numbers is still the same, but these are now the losses that you must be willing to face at least once or twice a year (if all goes as well as it has gone in the past!) Finally, I also show the worst case scenario, which is the single worst day in the price history used for analysis. Since it is just one scenario, VaR and ES are the same.

Well, let us see the numbers! First let's use only 2 most recent years of price history, and then we will also show the number when the entire history is used going back to 2010.

Bitcoin risks based on 100$ holding, using 2 years of history
Investment Horizon Loss frequency VaR ES
1 day 1-in-30 7.0$9.7$
1 day 1-in-300 14.2$15.4$
1 day Worst case 16.5$16.5$
10 day 1-in-30 15.6$19.7$
10 day 1-in-300 26.0$26.8$
10 day Worst case 27.5$27.5$
Bitcoin risks based on 100$ holding, using full history
Investment Horizon Loss frequency VaR ES
1 day 1-in-30 8.5$14.0$
1 day 1-in-300 21.9$27.4$
1 day Worst case 38.8$38.8$
10 day 1-in-30 22.0$28.8$
10 day 1-in-300 42.1$45.7$
10 day Worst case 52.1$52.1$
This shows that the last couple years have been kind to Bitcoin investors, and bad days were not quite as bad as in more distant past.

And let us see the same calculation done for Ethereum:
Ethereum risks based on 100$ holding
Investment Horizon Loss frequency VaR ES
1 day 1-in-30 13.5$18.5$
1 day 1-in-300 24.8$25.8$
1 day Worst case 26.7$26.7$
10 day 1-in-30 24.2$30.0$
10 day 1-in-300 41.5$42.0$
10 day Worst case 42.4$42.4$


I hope this helps you prepare for and weather the inevitable bad days in your investing adventures. Remember that Bitcoin was the proverbial winning horse, and yet delivered so many bad days. Be prudent and don't gamble more than you can afford, and don't leverage so much that you can't ride out a twice-a-year loss event!



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