Since last year I’ve been gradually buying Nikkei-related OTC funds, and on-exchange I’ve also been watching the Nikkei ETF (SH:513520) fund: back when I was backtesting with Backtrader, this was the fund I backtested most, so I also made some technical statistics for it.
The analysis results are merely a technical observation; they cannot predict future trends and don’t guarantee profits from buying. If you think technical analysis alone can guarantee never losing money, I’d probably think you’re not suited to stock trading — nor to being my reader.
To view some of the code and more elegant chart interaction, open the Google Colab link.
Loss and Profit Distribution
Same-Day vs Previous-Day Profit/Loss
The computation is based on the probabilities of different profit/loss scenarios of intraday prices relative to the previous day’s high and low. For example, on the x-axis:
- 0.05 means today’s low fell more than 5% below yesterday’s close
- -0.05 means today’s high rose more than 5% above yesterday’s close
I originally wanted to fit with a normal distribution, but when I pasted the data to ChatGPT, it ran fitting analyses for several different distributions and found the distribution below fits the Lorentzian distribution better:
| Characteristic | Description |
|---|---|
| Fat tails | “heavier” tails than the Gaussian, meaning a higher probability of extreme values |
| Undefined mean and variance | theoretically the mean and variance both don’t exist, because the integrals diverge |
| Sharp center | the peak region is sharper than the Gaussian’s, changing rapidly |
| Symmetric peak | symmetric about the center |
| Common in physical processes | e.g. resonance peaks, spectral line broadening, response functions in Fourier transforms |
Consecutive Profits or Losses
The x-axis shows consecutive days: 5 means five consecutive profitable days, -5 means 5 consecutive losing days This chart’s statistics show the probability of 3+ consecutive profitable or losing days is under 10%; for 5+ consecutive days it’s only 1%
Return Expectation Management
Returns After a Stock Price Drop
Explanation of the computed chart content here:
- The Expected Return number means the expected profit is 4%
- Take x-axis 3 as an example: it means the day’s stock is more than 3% below the previous day’s high
- The y-axis shows reaching the expected return; taking the 14-day line as an example, it means that in the next 14 trading days, the probability of achieving a 4% return is close to 60%
Using a simpler example:
- Day 0, high: 1.0 (highest price)
- Day 1: low: 0.97 (a price exists that is 3% below the previous day)
- Day 2: ….
- Day 3: ….
- Day 14: the probability that a price greater than 0.97 * 1.04 exists is close to 60%
You can see that with our patient waiting — from 7 days, 14 days, to 21 and 30 days — the profit probability actually rises progressively.
Returns After a Price Drop - 3D
I also tried making a 3D surface with plotly; it may not be so smooth, but it looks sufficient just for querying.
Average Days Trapped
My definition of average trapped days here: when you buy at some price, e.g. 1 yuan, and want to sell at 1.025 times that price, the distribution of time needed. From the chart data, buying in the 1.41-to-1.48 range has the shortest average time — roughly a 2.5% return within 21 trading days
Data Analysis and Discussion
The views below are personal only, and only about the Nikkei ETF. I take no responsibility for any reader’s choices. Profits and losses have nothing to do with me.
Intuitive Conclusions
- The probabilities of consecutive rises and consecutive falls decrease rapidly as the days increase
- A single stock’s rises and falls basically follow a normal distribution, though what I fitted here is a Cauchy distribution (Lorentz distribution)
- Buying at a suitable price basically means you won’t get trapped, but you won’t make big money either
Possible Strategies
Assume roughly 240 trading days per year.
- Based on the profit/loss distribution
When the same-day drop exceeds 4%, consider buying and holding 15-30 trading days; buying opportunities in a year are roughly 240 days * 2% ≈ 5 trading days
Because each trade has a 70%+ probability of a 4% return, the expected annual return is roughly 4% * 0.7 * 5 ≈ 14%
- Based on the average trapped time
In the Nikkei data, the 1.41-to-1.48 range has the shortest average break-even time — roughly a 2.5% return within 21 trading days. The average trading cycle is 21 days.
Assuming you can always buy between 1.41 and 1.48, your annual trade count would be 240/21 = 10 times, so the annualized return could reach 10 * 2.5% = 25%