/home/bill/PROJECTS/Investments/References/Howell projections/SP500 Fibonacci mirror comments.txt
www.BillHowell.ca ?date <=06Jun2020? initial
SP500 Fibonacci mirror measurements
http://www.BillHowell.ca//media/bill/SWAPPER/Website/economics, markets/SP500 Fibonacci mirror measurements.ods
/home/bill/PROJECTS/Investments/References/Howell projections/SP500 Fibonacci mirror measurements.ods
07Jun2020 initial - PARTIALLY "translated" from text file to become a "functioning derivation".
Others can easily finish the "translation", and adapt this to their own computer [software, screen, setup, problems, etc]
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TradingView - TSX
see "Howell 2020 Great Crash & depression forecasts.ods"
sheet : "Buy, sell"
Key issue : slope of the 50 year trend line of log(SP500 price) versus year
1970-2020 graph I rotated by -24 degrees :
200606 Fibonacci mirror reflection for a log scale only.xcf
200606 Fibonacci mirror reflection, log scale labels.xcf
Measures for Fibonacci=0 line :
delta x-axis : 2019-1971 = 48 years
delta y-axis : on-screen (23.4 - 8.26) cm on screen / log(5600/28) = 6.5797 cm/log approximately
test screen measure eg 450/45 = 10 or 1 log unit
(16-9.5) cm * 1 log / 6.5797 cm = 0.9879 ~1 (not highly accurate, but some confidence)
50 year slope of log(SP500), measured :
delta y-axis : low point, 1971 = 11.67 cm -> versus 8.26 cm @SP500=28
low = (11.26 - 8.26)cm *
high point, 2019 = 21.61 cm
(21.61-11.67) cm / 6.5797 cm/log = 1.5107 logs
slope : 1.5107 logs / 48 years = 0.0315 (logs of SP500)/year
equation :
log(SP500(year)/SP500(1971))@(Fibonacci=0 line))
= 0.0315 (logs of SP500)/year * (year - 1971)
y-axis@(Fibonacci=0, 1971), 11.67 cm -> versus 8.26 cm @SP500=28
log(SP500(1971)/28) = (11.26 - 8.26)cm / 6.5797 cm/log
SP500(1971) = 10^((11.26 - 8.26)cm / 6.5797 cm/log) * 28 = 80
SP500(2019) = 10^((21.72 - 8.26)cm / 6.5797 cm/log) * 28 = 3110.6 versus ~3,000 eyeball number
therefore :
SP500(year)@(Fibonacci=0 line))
= { 10^[slope(log(SP500)/year) * (year - 1971)] * SP500(1971) }
= 10^[0.0315*(year - 1971)] * 80
check the equation :
SP500(01Jan2019)@(Fibonacci=0 line)
= 10^[0.0315 (logs of SP500)/year * (2019 - 1971)] * 80
= 2,593 versus ~3,000 roughly read off graph
= OOPS?!?!??? - but it's hard to tell without a fine-detailed y-axis scale...
look at the angle of the (Fibonacci=0 line) :
this will make it easier to rotate the "Fibonacci mirror" using gimp (GNU image processor)
arctan(angle of the (Fibonacci=0 line))
= arctan(on-screen measures of axis scales when using gimp!! y-axis is log(SP500))
= arctan( delta y-axis / delta x-axis )
= arctan( (21.75 - 11.71) / 22.46 cm)
= 24 degrees, which is what I got with gimp by eye!!! awesome
look at the "spread" of the "Fibonacci mirror", measured ONLY on the vertical axis (y-axis) :
Note that I set the spread "arbitrarily", looking for a "balanced fit" of trends in the data over time.
It's easiest to measure on-screen verticle cm spread, for 1971 :
Fib_spread
= log(SP500@(Fibonacci=0 line)) - log(SP500@(Fibonacci=1 line))
= (14.08 - 11.26)cm / 6.5797 cm/log
= 0.4286 logs = a multiplicative factor of 2.6828
This is up the vertical axis, not perpendicular to the (Fibonacci=0) line.
/home/bill/PROJECTS/Investments/References/Howell projections/200604 S&P500 1970-2020.png
06Jun2020 Fibonacci mirror 50 year view based on TradingView posts : Lanmar 06Jun; PriceActionNation 03Jun2020
blogRep Lanmar :
Interesting decadal-length perspective. I'm still watching out for that asteroid.
/home/bill/PROJECTS/Investments/References/Howell projections/200604 S&P500 with Fibonacci mirror 1970-2020.jpg
/home/bill/PROJECTS/Investments/References/Howell projections/200604 S&P500 Jan-to-Jun2020.png
/home/bill/PROJECTS/Investments/References/Howell projections/200604 S&P500 Fibonacci mirror reflection 2020 Jan to Jun.png
http://www.BillHowell.ca/economics, markets/200604 S&P500 with Fibonacci mirror 1970-2020.jpg
http://www.billhowell.ca/economics,%20markets/200604%20S&P500%20with%20Fibonacci%20mirror%201970-2020.jpg
MarketWatch posting :
S&P500 - 50 year trend using a "Fibonacci mirror"
Following up on TradingView posts by Lanmar & PriceActionNation, here's a weird plot over the last 50 years that provides an easy visual comparison of market trends during different periods. I'm not convinced that this might be useful, but at least it's colorful. I'm working on another for Jan-Jun2020, using the same "Fibonacci mirror".
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SP500 Fibonacci mirror for Jan-Jun2020
axis measurments on screen :
x-axis : 21.37 cm / 0.5 year
= 42.74 cm / year
y-axis : log(3800 / 2005) / (23.5 - 9.0) cm = 0.01915 log(SP500) / cm
equation for (Fibonacci=0 line) from above :
SP500(year)@(Fibonacci=0 line))
= { 10^[slope(log(SP500)/year) * (year - 1971)] * SP500(1971) }
= 10^[0.0315*(year - 1971)] * 80
slope for 1970-2020 graph above :
= 0.0315 (logs of SP500) / year
This needs to be the same as the slope for Jan-Jun2020 :
0.0315 (logs of SP500) / year
"Physical (cm) slope" :
= y_delta(cm) / x_delta(cm)
just take 0.5 years :
x_delta(cm) = 21.37 cm
y_delta(log(SP500)) for x_delta as per above
= log(2,891 / 2,788)
y_delta(cm)
= y_delta(log(SP500)) / [0.01915 (logs of SP500) / cm]
= log(2,891 / 2,788) (logs of SP500) / [0.01915 (logs of SP500) / cm]
= 0.82273 cm
so "Physical (cm) slope"
= 0.82273 cm / 21.37 cm
arctan(angle of the (Fibonacci=0 line))
= arctan(on-screen measures of axis scales when using gimp!! y-axis is log(SP500))
= arctan( delta y-axis / delta x-axis )
= arctan(0.82273 cm / 21.37 cm)
= 2.2 degrees
Physical, on-screen, positioning of the Fibonacci=0 endpoints :
SP500(2020.0) = 10^[0.0315*(2020.0 - 1971)] * 80 = 2,788
SP500(2020.5) = 10^[0.0315*(2020.5 - 1971)] * 80 = 2,891
Physical distances from SP500 = 2,800 line :
delta_vertical(SP500(2020.0))
= log(2788 / 2,800) / (0.01915 log(SP500) / cm)
=
"spread" of the "Fibonacci mirror", measured ONLY on the vertical axis (y-axis), see above :
= 0.4286 logs = a multiplicative factor of 2.6828
This is up the vertical axis, not perpendicular to the (Fibonacci=0) line.
y_spread(cm from Fibonacci=0 to Fibonacci=1)
= 0.4286 (logs of SP500) / [0.01915 (logs of SP500) / cm]
= 22.38120 cm (2.23812 cm)
The "Fibonacci mirror" initial spread on the screen is : (19.11 - 17.69) cm = 1.42
Therefore, the vertical enlargement of the "Fibonacci mirror" is
= 2.23812 cm / 1.42 cm = 1.5761 or 157.6%
Positioning the "Fibonacci mirror" on the Jan-Jun2020 graph of SP500 :
Both endpoints of Fibonacci=0 ARE on the graph - so put these points on as circles
"Fibonacci mirror" :
vertically expand by 157.6%
rotate by -2.2 degrees
move to connect the endpoints with the Fibonacci=0 line