RSI Analysis - Part 2

This is Part 2 of mt RSI Analysis.  Here is my intro from first post:

On Ed's Talking Stock, the moderator (Ed) publishes the RSI index everyday.  Now I would not know the RSI Index (Relative strength index) from a wind chill index.  But it is a technical indicator that is supposed to give some guidance on whether the market is overbought or oversold (or neutral).

One of the contributors on ETS pulled RSI data all the way back to 1970.  I thought it would be interesting to do a little statistical analysis on the data to see what the predictive power is.  Here are some items I'd like to test:

1. Does an overbought (greater than 70) or oversold (less than 30) act as a predictor on where the market will be in 1 day, 5 days, 20 days and 50 days?
2. Are the 70 and 30 day cut offs optimal?  Maybe there is a better cut of overbought and oversold?
3. Has the predictive ability (assuming there is some) changed over time?  Meaning is it as effective in 2012-2013 as it was in 1978?
4. What is the overall correlation between the index and the 1/5/20/50 movements? So not just looking at whether flag is overbought or oversold.

I looked at #1 and #3 to some extent.  Let us now look at Correlation.  For those of you who are not statisticians, correlation is the statistical measure of the relationship between two (or more) variables.  An example might be number of years of education and salary.  You would generally expect those to be positively correlated, meaning the more years of experience you have, the more likely it is that your salary is higher.  We calculate a correlation coefficient that runs between 1 and -1.  A 1 means two items are perfectly correlated. A -1 means they are perfectly inversely correlated (when one goes up, the other goes down. a 0 would mean there is no correlation whatsoever.  You never (in the real world) get -1,0, or 1, but anything beyond say .6 would suggest a decent correlation.

Days	Correlation Coefficient
1	-0.00325
3	-0.02404
5	-0.02871
20	-0.02464
50	-0.01840

Wow. Might as well be zero!  Let us try since 2000.  Maybe that will help!

Days	Correlation Coefficient
1	-0.03808
3	-0.03426
5	-0.03380
20	-0.01528
50	0.01098

Hmmm, did not seem to matter.  Still, pretty much what one would call a random walk.

Why 30 and 70?

30 and 70 are the cut off points for overbought and oversold.  I am not very hopeful, but let us see what happens if we ratchet them up or down 5 points.  I will use the high level table for comparison.  First here is the original high level table:

RSI Status	1 Day Change	5 Day Change	20 Day Change	50 Day Change
neutral	0.03%	0.15%	0.59%	1.55%
Overbought	0.03%	0.15%	1.02%	1.92%
Oversold	0.12%	0.55%	1.50%	3.15%
Grand Total	0.03%	0.17%	0.65%	1.63%

Recall, this is where we first noticed that overbought was a weak predictor, but oversold did provide some lift and that lift seems to have increased past 15 years.

What happens when we go 25 and 75?

RSI Status	Number of Days	Pct Days
neutral	10,684	96%
Overbought	332	3%
Oversold	114	1%
Grand Total	11,130	100%

As one might expect, it becomes a much less common occurrence.

RSI Status	1 Day Change	5 Day Change	20 Day Change	50 Day Change
neutral	0.03%	0.16%	0.63%	1.62%
Overbought	-0.02%	0.05%	0.93%	1.62%
Oversold	0.20%	1.00%	1.65%	2.68%
Grand Total	0.03%	0.17%	0.65%	1.63%

Overbought does work a bit better at the higher threshold, at least for the 1 and 5 day movements.  Still, the differential is so small - I would not chase it.  It also seems to make the oversold lift a bit stronger, again especially at the 1 and 5 days points.  But practically this is not useful.  There are many years where you are never oversold or overbought:

Year	Neutral	Overbought	Oversold	Grand Total
1970-1974	1,124	75	49	1,248
1971 - 1975	1,165	66	31	1,262
1972 - 1976	1,207	36	19	1,262
1973 - 1977	1,223	18	22	1,263
1974 - 1978	1,210	31	22	1,263
1975 - 1979	1,200	46	17	1,263
1976 - 1980	1,202	45	16	1,263
1977 - 1981	1,208	35	20	1,263
1978 - 1982	1,202	41	21	1,264
1979 - 1983	1,220	28	17	1,265
1980 - 1984	1,232	17	16	1,265
1981 - 1985	1,218	34	12	1,264
1982 - 1986	1,211	45	8	1,264
1983 - 1987	1,202	55	7	1,264
1984 - 1988	1,202	55	7	1,264
1985 - 1989	1,198	61	4	1,263
1986 - 1990	1,212	43	9	1,264
1987 - 1991	1,212	43	9	1,264
1988 - 1992	1,223	36	6	1,265
1989 - 1993	1,222	37	6	1,265
1990 - 1994	1,228	28	9	1,265
1991 - 1995	1,199	62	3	1,264
1992 - 1996	1,186	74	5	1,265
1993 - 1997	1,188	71	5	1,264
1994 - 1998	1,176	81	6	1,263
1995 - 1999	1,180	80	3	1,263
1996 - 2000	1,219	40	4	1,263
1997 - 2001	1,232	17	8	1,257
1998 - 2002	1,234	11	11	1,256
1999 - 2003	1,246	-	10	1,256
2000 - 2004	1,239	7	10	1,256
2001 - 2005	1,240	7	9	1,256
2002 - 2006	1,245	11	3	1,259
2003 - 2007	1,247	11	-	1,258
2004 - 2008	1,246	11	2	1,259
2005 - 2009	1,251	6	2	1,259
2006 - 2010	1,245	12	2	1,259
2007 - 2011	1,242	13	5	1,260
2008 - 2012	1,239	14	6	1,259
2009 - 2013	1,240	14	4	1,258
2010 - 2014	1,013	12	4	1,029
Grand Total	10,665	332	114	11,111

From this table, you can see 5 year stretches without a single day.  And even when you get that one day, I am not sure it is that powerful a predictor.  

Finally let us make the cut offs 35 and 65.

 

RSI Status	Number of Days	Pct Days
neutral	8,241	74%
Overbought	2,015	18%
Oversold	874	8%
Grand Total	11,130	100%

It certainly gets us more days in the non-neutral buckets.

RSI Status	1 Day Change	5 Day Change	20 Day Change	50 Day Change
neutral	0.02%	0.14%	0.57%	1.51%
Overbought	0.04%	0.16%	0.77%	1.63%
Oversold	0.09%	0.42%	1.18%	2.80%
Grand Total	0.03%	0.17%	0.65%	1.63%

Seems to be similar for the Oversold on 30/70. Let us look at the chart.

Pretty good lift across all years.  Even more consistent than the 30 cutoff point. Could be more data points smoothed out the trend and made it more noticeable. 

Conclusion

I think I have talked RSI to death.  End of the day, on average the signal tells you very little.  The overbought signal is a weak predictor at best.  The oversold signal, starting at 35 and lower does seem to have some usefulness in a good time to buy.  Final table (promise): here is correlation of RSI and market returns using the subset when RSI is under 35:

Days	Correlation Coefficient
1	-0.03534
3	-0.06273
5	-0.06534
20	-0.05627
50	-0.02265

So directionally they are correct - the lower the RSI, the higher the expected return (thus the negative or inverse correlation). But they are all extremely close to 0.  So having an RSI that is 76 does not tell you much more than an RSI of 66.

Hope people find this useful.  I plan to continue to ignore it, especially the over-bought.  Explains a lot on the dangers of shorting when you get that signal.