If you buy a stock at random,
are your odds fifty-fifty?
Pick no particular stock. Pick no particular day. Just buy something, at random. Intuition says the odds of going up or down should be even. I checked every single day of 2,580 Korean stocks to find out.
01A note on the market, and on the method
Korea has two main stock markets. KOSPI holds the large, established companies — Samsung Electronics, Hyundai, the big banks. KOSDAQ is the smaller, more speculative board, closer in spirit to the Nasdaq of the 1990s: many small technology and biotech names, and far more volatility. Together they list roughly 2,600 companies. Regular trading runs 09:00 to 15:30 local time, so each daily bar is a six-and-a-half hour session.
Now the method. The usual way to test "buying at random" is to sample a few hundred dates and see what happened. The answer then depends on which dates you happened to draw.
So I did not sample. I calculated every possible case. 2,580 stocks × every trading day since listing = 6.15 million starting points. For each one I asked whether the price was higher N days later. That is not a sample; it is the whole population.
I split it two ways. First, literally any stock (all 2,580). Second, only companies of reasonable size — market capitalisation above 100 billion won (about US$70 million) and daily turnover above 500 million won (about US$350,000). That leaves 796 stocks.
02The result — 50% never showed up
| Holding period | Any stock | Larger stocks only |
|---|---|---|
| 1 day | 43.97% | 45.09% |
| 1 week | 45.23% | 47.03% |
| 1 month | 44.97% | 47.65% |
| 6 months | 43.65% | 48.85% |
| 1 year | 42.64% | 49.32% |
| 2 years | 42.04% | 51.30% |
Buy anything at random and you come out ahead a little over four times in ten. Holding longer does not help. If anything it drifts slightly worse.
Restricting to companies of real size changes the picture. Now longer holding does help, and at two years you finally clear half, at 51.3%. The gap between "anything" and "larger names only" is 6.7 percentage points at one year. Simply filtering by size — before any analysis of the business — is worth that much.
03Why it is not fifty-fifty
This is not about Korea. It is arithmetic.
Prices move by multiplication, not addition. That single fact does the damage.
- It rises 10% → $110
- It falls 10% → 110 × 0.9 = $99
Up then down, and you are not back to even. You are down 1%. Reversing the order changes nothing.
Even if up moves and down moves are exactly equally likely, living through both leaves you below where you started. This is called volatility drag, and the more a stock swings, the more it costs you.
The consequence is that the person in the middle — the median — loses money. Buy any stock at random and hold a year and the median outcome is −5.5%. Hold two years and it is −8.9%.
Again, this is not a Korean problem. It happens in every asset whose price compounds, in every market.
04And yet the average is strongly positive
Here is where it gets confusing. Look at the right-hand chart above. The median keeps falling while the mean keeps rising.
| Holding period | Ended in profit | Mean | Median |
|---|---|---|---|
| 1 month | 44.97% | +0.84% | −0.70% |
| 1 year | 42.64% | +11.97% | −5.47% |
| 2 years | 42.04% | +38.34% | −8.91% |
Hold for two years and six people in ten lose money while the average gains 38%. That looks like a contradiction. It is not.
Losers lose modestly; a handful of winners win enormously. A stock can only fall 100%, but it can rise 500%. A small number of large successes drags the average up on its own.
"Average return" and "my chance of making money" are different questions. A +38% average does not mean you are likely to profit.
05Zoom into a single day and it looks the same
Perhaps this is an artefact of long holding periods. It is not. I counted all 6.15 million daily bars and compared each day's open to its close.
| Share | |
|---|---|
| Closed above the open | 42.96% |
| Closed below the open | 50.32% |
| Closed exactly at the open | 6.71% |
Only 43% of sessions finished above where they opened. Even after removing the flat days, the up-days are still only 46.1%.
And the same asymmetry appears here. Up days gain 2.29% on average; down days lose 2.08% on average. Fewer days go up, but the ones that do go up a little further.
That is where "odds below half, average above zero" is manufactured. It is not a property of long holding periods. It is already there inside a single trading day.
06These numbers are flattering
How much lower, this data cannot tell me. The direction, though, is not in doubt. Treat 42% as the generous end of the range.
These figures are also before commissions and taxes. Real buying and selling pushes them down further.
07What I take from this
- Random buying gives you roughly four in ten, not five. Holding longer does not fix it.
- Filtering helps. Size alone is worth 6.7 percentage points at the one-year mark.
- Do not confuse the average with your odds. A +38% average still leaves six in ten losing.
When I build a trading strategy, these numbers are the line it has to clear. A strategy with a 45% win rate has done nothing that random buying would not have done. Even a win rate above 50% is not yet evidence of anything if the median trade still loses money.
A return figure with nothing to compare it against tells you nothing. Doing nothing and buying at random is what you compare it against.
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