Refuting "Feasibility Test of Bitcoin Fixed Investment"

(Picture from the Internet)

Yesterday, No Bit in Hand published an article titled "A Feasibility Test of Bitcoin Fixed Investment". In the supplementary explanation paragraph at the end of the article, No Bit in Hand simulated the linear increase of the coin price from 1 yuan to 10 yuan and concluded that

The fixed investment cost is only 3.41 yuan, which is much lower than the average coin price of 5.50 yuan.

The conclusion was then extended to

(Fixed investment) The returns in a bull market are higher than the average, but the losses in a bear market are lower than the average

I dare to bet with AMS... there is at least a 65% chance of winning if you invest regularly

These theories are very tempting at first glance. Just by using mathematical techniques and making some adjustments in fund allocation, the winning rate can be changed. Isn't it easy to make money lying down every day? I don't know if the sales staff of fund companies outside have been using these theories to deceive customers. These theories are so convincing that they are easy to be recognized by customers. There are two rules in the capital market, one is the balance of profit and loss, and the other is that risk is proportional to return. The several theories in my hand are inconsistent with common sense, so I spent some time looking for bugs at that time, hoping to find out the problem, and finally found it.

Continuing with the simulation data without bits in hand, in the first table, that is, the case where the currency price rose linearly from 1 yuan to 10 yuan, the fixed investment calculated without bits in hand finally bought 29.2897 bitcoins.

There are 10 buying points in the table. If a random shuttle is used, it means that each buying point has a 10% chance of hitting the target. The following is a calculation of each possibility:

Buy for 1 yuan, get 100 coins
Buy for 2 yuan, get 50 coins
Buy it for 3 yuan, get 33.333 coins
Buy it for 4 yuan and get 25 coins
Buy for 5 yuan, get 20 coins
Buy it for 6 yuan, get 16.667 coins
Buy it for 7 yuan, get 14.286 coins
Buy it for 8 yuan, get 12.5 coins
Buy it for 9 yuan, get 11.111 coins
Buy for 10 yuan, get 10 coins

The expected coins for random shuttle are (100+50+33.333+25+20+16.667+14.286+12.5+11.111+10)*10%=29.2897. This result is exactly the same as the coins bought by fixed investment. The difference is that fixed investment gets a fixed 29.2897 coins, while the result of stud varies from 10 coins to 100 coins, with great fluctuations. The 5.5 cost price calculated by No Bit before is the arithmetic average rather than the weighted average, so there is a strange phenomenon that "the return in the bull market (fixed investment) is higher than the average, but the loss in the bear market will be lower than the average". The same is true for the linear decline, index rise and fall, and first fall and then rise simulated in the article later. After weighted average, the expected returns of fixed investment and stud are the same.

The expected return of Solitaire is not as stable as that of regular investment. Does this prove that Solitaire is inferior to regular investment? Not necessarily. This question depends on the investment style of the investor (aggressive? moderate?). Regular investment provides relatively stable fund volatility, but the cost is the loss of the possibility of obtaining high returns. Solitaire is the opposite. It's like working and starting a business. Can you tell which one is better?

PS: The pictures in the article represent my favorite style (not my personal experience)

Text/ams
Source: Babbitt Information
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