We are hearing a lot of chatter about RSI and rightfully so - the move underway is remarkable. But how rare? Let's look at charts.
I'm going to keep to SPX and NDX, though a full study would use the Dow and go back further in time.
Sum
In both Q and M charts, above 70 is a sign of strength. This is exactly what happens in bull runs. It is not that terribly uncommon. What you don't want to see is:
1) A move that stops at 70 cold and turns lower. A few of many examples: SPX 2007 Q chart, SPX 1994 M, NDX 2011 M.
2) A move than returns back under 70 after a long stretch above. Some of these can come back (1998), but negative examples are SPX Q chart in 2000 and both SPX and NDX M charts in 2015.
3) A parabolic move that has RSI values above 85 with price outside the Bollinger bands - risk at this point for a fast drop is significant. Obviously referring to the generational NDX 2000 top here. SPX M chart also reached 85 in 1997 and was outside the band, then spent about 4 months going sideways before another launch.
Where indexes are now (values not final until quarterly and monthly closes):
SPX Q 77.4, strong and can go higher. Currently not showing divergence.
NDX Q 80.7, strong and near area of 2015 high at 81.4.
SPX M 71.6, better to close above 70 and stay outside of BB than to drop back under and fall back near 70 for the close.
NDX M 71.5, ditto.
As it turns out, weekly and daily chart RSIs are also above 70 here. It would take a better data provider to run the stats on the line up of Q, M, W and D charts with RSIs all above 70. I just don't have that right now. It would be on the lower side of total percentile events, but everything depends on environment selection. If you measured all trading quarters, months, weeks and days from 1980 then you might come up with something that appears statistically significant. But if you kept to bull markets when indexes are above all moving averages with rising slopes, then this is what happens a decent amount of the time. Mostly, no. Often enough, yes. An exit signal? No, not the incidence itself. A sell short signal? Definitely not.
SPX Q
RSI currently 77.4 looks strong as it is above the 2015 peak of 75.8. Quarter is only halfway through, and this value won't be 'on the books' until close. But look at 1980s and 1990s; quarterly chart RSI above 70 is what happens in real bull markets and one cannot say it is uncommon. While we are at it, just look at the 10MA and it has held on Q close since 2011 Q4.
The danger in SPX Q RSI was falling back under 70 after a long stretch of above. This happened in 2000 Q4 which also coincided with a close under its 10MA, the first since 1990. This didn't nail the top but did keep you long term invested for an amazing stretch. Realize the difference at the 2007 top - SPX was overbought for only 2 quarters and then clearly rejected in 2007 Q4, falling to 66. 2008 Q1 closed under its 10MA and from there trend was down until its 100MA a year later.
NDX Q
We're not in the 1990s yet with quarterly chart RSI at 80.7 compared to 96 then but hey, NDX Q RSI totally overbought from July 2013 on. Bullish, and yet not too bullish. When NDX reached the heights of the 2000 top it did have a faster drop, going from outside the BB to under 10MA in 3 quarters. RSI was a still healthy 76.9 in 2000 Q3, then fell to 57 in Q4. That was quite a walloping for the latecomers, basically 1999 Q4 to 2000 Q1.
SPX M, 2000+
Looking at this chart you might be more concerned, as only a handful of monthly bars are above 70. Even so, above 70 is better than stopping cold at 70 and turning lower.
SPX M 1980-2000
But 1983-1987 had frequent moves into overbought territory. 10/1987 did come out of the blue from RSI perspective. SPX monthly chart entirely overbought from 5/1995 to 8/1998. The next phase up in 1999 and 2000 the chart showed very clear divergence, with RSI highs getting lower and lower over more than a year before the big rollover down.
NDX M 2000+
NDX monthly chart RSI above 70 less common from 2000 on, but not unheard of per the 8/2013 - 7/2015 run.
NDX M 1995+
Showing the chart this way to keep consistent with SPX periods. This did bounce around having moves from above 70 to below several times 1997-1998. From there purely overbought with RSI highs at 88, with a huge wick on the monthly chart before the walloping.