Crash probability after all-time high

[Grog]

Hi everyone
I hope someone could help me find the relevant information, maybe in some blog I couldn't find. I was curious about the crash probability after an all-time high, specifically:

1) Has there ever been an all-time high (let's pretend a random proxy market index was at an all-time high 10'000 in 1992) that was the bottom of the stock market too? In my example would mean that this index after 1992 NEVER EVER went down under 10'000 again. How common is this? I presume it will be common if we found ourselves in a bull market rising to new highs every day, but over a period of 5-10-20-50 years?

2) If a "crash" happened, (also the stock market went below the past all time high), after how many years in average could you say that you are "safe" (that means that the probability that the index fall down to where it was is very small, like a crash of 80-90%)?

I'm trying to build my arguments portfolio for discussions about long term horizon and what can be considered truly long term. Thanks for any help! Are there tools somewhere that could help me?
NB the starting point would be investing in a new "all-time" high, so not many starting points are available statistically....

[Jack]

1) Has there ever been an all-time high (let's pretend a random proxy market index was at an all-time high 10'000 in 1992) that was the bottom of the stock market too? In my example would mean that this index after 1992 NEVER EVER went down under 10'000 again. How common is this? I presume it will be common if we found ourselves in a bull market rising to new highs every day, but over a period of 5-10-20-50 years?

Yes. You could identify them by looking at a chart of the index's historical returns and identifying values on the Y-axis that the line only crosses once.

Of course, if you build a little wiggle room into your analysis -- say, discounting drops of less than X%, where X∈(0, 5] -- then it happens a lot more often.

[Grog]

Yes. You could identify them by looking at a chart of the index's historical returns and identifying values on the Y-axis that the line only crosses once.

While what you are saying is technically true, is very difficult to count the exact numbers of days where it happened. Do you maybe have the whole Dow Jones historical data so that I could try myself ? The second problem is that I wouldn't know how to calculate the distribution of years after the peak where it crashed, also coming up with a sentence like "95% of the time after an all time high there was a depression, but after 37.5 years in average your investment would be 'safely' above the purchase price." I want to believe someone out there has surely already calculated something like this....

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[Tjat]

Yahoo finance has daily price charts: https://finance.yahoo.com/q/hp?s=%5EDJI+Historical+Prices

I fail to see the relevance of this study though. If you go back far enough to find examples, the data because less and less meaningful for today's investor. If you go a short time period back , your observations lack credibility of being historically tested. If I'm foreseeing your point, I'd focus more on something like, "if you construct a rolling 20 year CAGR going back 100 years, you'll make money in 98% of scenarios.