Education
How To Keep Up With Theoretical Compounding
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# How To Keep Up With Theoretical Compounding

June 13, 2018

It’s FOMC Wednesday and that means today’s session is officially hosed. In order to keep everyone focused and on mission I decided to repost some educational highlights of years past. I’m sure are familiar with the concept of compounding and how it can affect your system’s P&L over time. What you may not know however is that keeping up with theoretical compounding over time is actually a tad tricky, for various reasons outlined below. Enjoy!

A few days ago I accidentally ran into a white paper by a certain Christian B. Smart, PhD thatÂ hadÂ mysteriouslyÂ made its wayÂ into my dropbox. It immediately grabbed my attention for several reasons. For oneÂ you simply cannot pass up a paper authored by someone with that name, although it may just be a pen name. More importantlyÂ it not only highlights aÂ major flaw inÂ fixed fractional position sizing, a methodÂ we use religiously here at Evil Speculator, but also promisesÂ to fix the problem. How could I resist? Of course, nothing in life is free and ifÂ you suspect that there may beÂ a price to be paid for keeping up with theoretical compounding then I promise that you won’t be disappointed. More on that further below.

Now after familiarizing myself with the mathÂ I spent a bit of time running the numbers. The aim of this post is not to regurgitateÂ Dr. Smart’sÂ white paperÂ but to share some rather interesting findingsÂ on how his approach affects a variety of trading systems. Before you continue reading I strongly recommend you read hisÂ paperÂ first. No worries, it’s pretty light on the mathÂ and you’ll get away with basic algebra. But just to set the stage here’s the skinny:

• Fixed fractional position sizing is a popular and time tested method for money management. In the strategy a fixed percentage of equity (e.g. 1%) is risked per trade. We call that ‘R’ here at Evil Speculator and it refers to a unit of risk per campaign.
• Fixed-fractional money management is an intuitive method in which bet size increases when equity increases and bet size decreases when equity decreases. This form of money management is conservative in that it dramatically decreases risk of ruin.
• A concept related to money management is system expectancy. A systemâ€™s expectancy is the average, or expected, amount of money an investor expects to make per dollar risked. For example, a trading system with a winning percentage of 40%, whose average win is equal to twice the average loss, has an expectancy approximately equal to 0.40 * 2 â€“ 0.60 = 0.80 â€“ 0.60 = 0.20.
• Another key concept related to money management is that of compounding. Dr. Smith actually does not make mention of theÂ word which surprised me a bit as the entire aim of his paper revolves around permitting effectiveÂ compounding. If you’re unfamiliar with the concept of compounding then Google will be your best friend.
• With fixed fractional position sizing, anyÂ system does not achieve itsÂ expectancy (and thus its theoretical compounding) in the long run, but an amount less than the system expectancy.Â With a progressive betting system like fixed fractional sizing, in which returns are reinvested, the total return is the product of a series of numbers.
• The underperformance of fixed fractional position sizing has a basis in mathematics. The system expectancy is the systemâ€™s arithmetic mean. The average amount made per trade with fixed fractional position sizing is the systemâ€™s geometric mean. A well known inequality in mathematics states that the geometric mean is always less than or equal to its arithmetic mean. So in the long run, fixed fractional position sizing will never achieve system expectancy but will underperform.

So in a nutshell – in reality trading systems will always lag behind their theoretical expectancy. Over time the difference actually adds to quite a bit of lost profits:

This graph is taken off the white paper and shows a Monte Carlo simulation of an hypotheticalÂ system over 5000 trades. Clearly this should not be taken as a realistic projection of a real life system and only serves to demonstrate the concept. The take away message is this: Over the life time of a systemÂ there isÂ an exponential delta between itsÂ theoretical and geometric compounding results.

Clearly missing out on ill-gotten gain is not a situationÂ we take lightly here at Evil Speculator. So I sat down and actually produced a handy spreadsheet which I invite you all to download and have a go with on your own. I’m only mildly versed in Excel and if you are able to offer an improvement then please share it with the rest of us. Now as you know I have quite a few systems in the running and what I wanted to find out if and how they would be affected. The results quite frankly were a bit surprising.

You may recall that I am currently live testing Scalpius which despite its name is more of an intra day swing trading system. It is based on some of my work on volatility cycles and thus far it’s looking extremely promising. After painstakingly running the stats on 10 forex and futures symbols over the past five years I arrived at the following stats:

• Win/Loss Percentage: 1:1.11 – which is 47 to 53.
• Average Win: 1.23R
• Average Loss: 0.76R
• Expectancy: 0.18R

The stats slightly vary between the various symbols but not excessively. There is a common theme which Scott often refers to as a ‘forest of good numbers’ – a term I really like as it describes the process of testing for possible system form fitting. I would characterize ScalpiusÂ as having a small but consistent edge. It won’t make you rich overnight but if you keep it in the running and if you are able to grabÂ good fills then it’s a very promising system..

Now if you ran Scalpius via 0.5% fixed fractional position sizing (FFPS) then you would theoretically bank a \$147k profit over 1,000 campaigns based on aÂ theoretical expectancy of 0.1815R. Yes, that is just a theoretical model – we need to be clear on that. In any case, when comparingÂ that with the geometric expectancy of 0.1765R we arrive at geometric returns of \$144k, the delta in US\$ being \$3,031. Not exactly chump changeÂ but given the overall context it represents only 2% of the theoretical returns, thus I’d submit it toÂ theÂ BFD department and move on.

However look at what happens when we increase the base risk percentage from 0.5% to 1.0%. Suddenly the numbers jump quite a bit. Obviously larger position sizing increased the compounding effect significantly but the delta between the arithmetic and geometric returns now amounts to 5.7%.

And in order to compensate for the loss in profits our position sizing has increased accordingly. If you look at the table in the center of the graph then you will find that the difference in position sizing has to increase alongside the base percentage. Whereas compensating expectancy loss at 0.5% only requires a small increase to 0.545% at a base of 1.0% you are now required to trade at 1.18% position sizes relative to your actual equity, as that percentage represents 1% of your ‘expected equity’.

But there’s more to this story yet. If you read the white paper then you remember that Dr. Smart used the standard hypothetical 40/60 – 2:1 system for his Monte Carlo simulation. I have used those stats in the graph above but have taken the liberty to reduce the risk percentage to 1.0%. Quickly apparent is that this system has a better expectancy of 0.2R which in turn changes the dynamicsÂ of the delta between arithmetic and geometric returns. We’re are banking a bit more here obviously but if you look at the table in the center you’ll see that we are also using larger adjusted position sizing. Now instead of \$100k we are calculating at an expected equity of \$120k. That’s a 20% increase and those numbers grow even more quickly as we are increasing the base percentage.

If you were to use 2% position sizing instead as per the white paper then you would have to calculate your positions via an expected equity of \$140k. Also the delta between arithmetic and geometric returns has jumpedÂ to a whopping 35.3%! So clearly time is not the only factor that affects compounding. The higher the SQL of your system the larger the loss in expectancy. Which to most of us would be counter intuitive, but the numbers do not lie. Systems with a higher win/loss rate require increased position sizing in order to keep up withÂ their theoretical expectancy.

### Take Away Points

Given the above dynamicsÂ there are several considerations for system developers. The first one is whether or not compensating for geometric returns via an increase in position sizing is worth the added risk. The white paper makes it clear that the increase in position sizing does also increase maximum drawdowns.

I have not run the numbers on that end myself but judging by the paper’s graph it seems that it is roughly in sync with the increase in risk percentage. So if you’re trading at an 1.2% adjusted position size instead of 1% then it’s realistic to expect at minimum 24% maximum drawdowns instead of 20% at fixed fractional position sizing.

And given that the dynamics between theoretical and geometric returns are highly system specific answering the question of whether it is worth it depends, as always, on your personal risk profile. The real question then changes from whether or not to use expected fixed fractional position sizing (EFFPS) to how much compensation you are willing to allow for. And if nothing else we also need to embrace the fact that theoretical compounding becomes less efficient with increasing SQN. Systems with smaller but consistentÂ edges (as for instance Scalpius)Â actually benefit quite bit more in comparison with high expectancy but low opportunity systems.

Meaning, if you could choose between a holy grail system whichÂ trades 200 times per year and produces 100R and one that takesÂ 1000 entries to produceÂ the same 100R then most of us would probably instinctively choose the former over the latter. The graph above shows such a hypothetical system – I have fiddled with the stats to produce almost exactly the theoretical returns of what Scalpius is promising at 1% position sizes. The delta between the theoretical and geometric returns is smaller, but look at the position sizing required to keep up! At a base ofÂ 1% we would have to use 1.91% to account for a 3.9% difference. Hardly worth the additional riskÂ I would say and I’m pretty sure most of you would agree.

Finally the more risk you are willing to take trading any system the higher will be the additional risk incurred in order to keep up with theoretical compounding. Increasingly larger position sizing means that draw downs will be deeper and generallyÂ your system will exhibitÂ higherÂ standard deviation. That is never a benefit to any system but especially systems that thrive via large outliers will be the most negatively affected. Drawing from some of the lessonsÂ we’ve learned about equity curve filters I believe that lowÂ dependency low standard deviation systems wouldÂ benefit the most (e.g. Scalpius) and highÂ dependency high standard deviation systemsÂ benefit the least from EFFPS. Reason being that a high number of consecutive losers will quickly do you in if you’re trading 3%+ position sizes.

The final take away is that we as traders need to be careful what we wish for. At some point in our career all of us have been on a hunt forÂ that holy grail system which prints money fast with a small amount of trades. Given the inherent power of compounding it remains that elusive path to quick riches which many of us hope for but very few ever achieve (and the one’s who do aren’t talking).

Over the years I however have slowly shifted away from that and am now more focused on creating systems which produce a small but reliable edge over time. And apparently when it comes to compounding it is these types of systems which require the least amount of risk when it comes to compensating for exponential lag due to the delta between theoretical expectancy and geometric expectancy. On paper lofty outlier systems may seem what you want but given enough opportunity (i.e. number of trades) ‘more realistic systems’ with a consistent edge may actually rival hypothetical ones over timeÂ courtesy ofÂ compounding. Quite some food for thought.

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The Mole
Mole created Evil Speculator amidst the chaos of the financial crisis in early August of 2008. His vision for Evil Speculator is a refuge of reason, hands-on trading knowledge, and inspiration for traders of all ages and stripes. You can follow him and his nefarious schemes at the usual social media waterholes.
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• ridingwaves

I think I missed this class….surf must have been good that day..

• topedge

Thanks for everything you do

AT&T

http://stockcharts.com/h-sc/ui?s=T&p=D&yr=0&mn=4&dy=0&id=p59033958141

I guess those \$32 puts guys knew what they were doing!!

• HD

ZW fib cluster at 520, SPX still 2789. VX bleeding 12.60

• HD

IMO System expectancy is where most break down. People enter a trade and think they deserve 100 handles, trade works for a few days, then they watch half their profits disappear, get stubborn, finally stop out at break even or worse.

The market is gonna give you what it gives you. We are back to very low volatility environment. 5 handles is a winner no matter what a hypothetical system says you should wait for.

• HD

I also found an error in the “geometric expectancy” math. Possible solution. https://uploads.disquscdn.com/images/6b8ae32c03360733fc62256a1981410b5a82472eadc68fdd173f4d8f351f7b2c.png

Unusual stock option activity yesterday..
TWTR \$45 puts. July 20 expiry.

• ridingwaves

Jamie Dimon: “Hey Alan, how is the caviar? The mistress? Need a favor of course the usual 500K payment is applied. Can you just say the economy is slowing? I have a couple billion CDO’s laddered incorrectly…Thanks….enjoy the Hamptons, see you in a couple weeks, that Powell dude is hard nosed SOB…” Alan Greenspan to Jamie: “No problem, don’t worry about Powell, I know his mistress, she’s greedy”

• https://evilspeculator.com Sir Mole III

hehe ðŸ™‚

• ridingwaves

put on your sun glasses, I swear, you’ll get it….hurry before it’s too late

• HD

\$RTN has been the gem for defense stocks. Yesterday’s news triggered a little selling. Would like to see a retrace. https://uploads.disquscdn.com/images/7f1e7e6c9d00113c15c79d3502616473bbd93f27289b1c1887872371e55529a2.png

I’m all out of bubble gum
ðŸ˜‰

the square root of a negative number is imaginary.
since, it’s squared – “it’s all good shit”.
ðŸ˜‰

• ridingwaves

I have a great story about the second brothel owner mentioned here in article…

• ridingwaves

BTC testing 6400 support, 6K next

cat houses, tattoo parlors, and pawn shops.
what has this great country stooped to?

• Julie 35 – 25 – 36

USO taking profits long ….. CSCO covered short this a.m on bounce off the conversion line (8) for breakeven
JULIE

• ridingwaves

HD,
u mentioned your looking for a play, any interest in non day trade symbol? I have bid down near 40 right now for AAOI, think it covers a gap in next 12 months and goes to 80-100 pps

• ridingwaves

the first one might help more than hinder, too much stress out there..the other 2 are fads….

• HD

good eyes! I’ve added it to my shopping cart.

• ridingwaves

whoa, large buyer at 6100? think the 6K buyers might be the target for some pain….

• Julie 35 – 25 – 36

CSCO Looking to re short 45.02
JULIE

• HD

wish I would have got in /BTC Monday when it broke down. Stupid SPX has me caught in the headlights. /BTC is worth \$3000 per since Monday open.

• ridingwaves

on weekly is quite possibly making inverse h&S to power it thru the gaps, sitting above 100sma weekly, like to see it get to 38-40pps for better buy, the h&S needs to build shoulder now to that level….could be some sweet pudding….daily below, firming up with 100sma trying to catch up to 200 above

• ridingwaves

might just be consolidating here, the 100sma break on volume is where I would short, looks very comfortable here…

• Julie 35 – 25 – 36

Hi RW CSCO https://uploads.disquscdn.com/images/677cb295ae8a39099cf21fdc5d2f095a809df82b5e56715ebc3a53e7da68cc24.png 45 is gap fill ; 61.8% retracement and upper cloud boundary JULIE

• ridingwaves

did you see the updated version attached….

• Julie 35 – 25 – 36

RW Your target for \$WTIC matched my USO 13 target .Went long at 13 …. took profits earlier this a.m USO short term overbought and going up into 38.2% retracement and confluence of the declining 21 and 55 ema’s Could go higher to gap window Too many sharks OIL . Will monitor closely as I want to short a lower high JULIE

• Julie 35 – 25 – 36
• https://evilspeculator.com Sir Mole III

How’s my crew? Nobody seems to have liked the post!

• Julie 35 – 25 – 36

USO Another chart Not only is USO going up into the 38.2% retracement and confluence of the declining 21 and 55 ema’s but also a backtest of a broken lower uptrend line. If it does go higher will monitor the 50% retracement matching the baseline (21) approx 13.87 JULIE

• Julie 35 – 25 – 36

I liked it. it’s realistic.
over the years I’ve seen lots of people come and go. get rich quick and all that.
you keep it real.
-GG

• HD

+.25

• Julie 35 – 25 – 36

Doing great Chief … I always like your posts and appreciate your hard work Thanks Chief !
JULIE

looks like a LGBTQ LKGB to me.

I did. was shocked actually.
(but it’s political to the Democrat side, so keeping it hush hush)

• ridingwaves

expected, went from 3 to 4 hikes….inflation, the other white meat…..its rearing its head for sure….

• http://www.captainboom.com/ captainboom

Ass deep in alligators. Fireworks season.

Ooooooh, *that* point two-five.
+1

• ridingwaves

good, I think I remember that post, it led me to consider instrument tuning….

• Julie 35 – 25 – 36

RW This song was on the radio this morning KBOZ Love it ! Brings back memories high school and college in OR …. Seaside and Cannon Beach JULIE https://uploads.disquscdn.com/images/fa252872bad930a174efa349c319d2107637e7450309deebf60d09c016f13260.png

• Julie 35 – 25 – 36

GG I have the same setup SPX
JULIE

how is that possible? I thought you were a Keltner girl?

• Julie 35 – 25 – 36
• HD

ES 2789 big level IMO

yes, I was looking at this.
when CCI hits 70, that’s when you take an entry short?

• ridingwaves

found a great short CVNA, was trying to get bid in at 38.80 but its getting hammered already…down to 36….think it sees 30 first and then 24, way overbought, they are hemmoraging money into a peak auto environment….Carvana

• BKXtoZERO

• Julie 35 – 25 – 36

GG and Everyone McDonalds Yes Too Funny …. 1st date with husband was FISHING ! We met at a party and I knew immediately Married him two weeks later in a whirlwind. He proposed and said let’s get married this Saturday…. I said “Make it Friday ” He said “Friday it is” Been with the Greatest Guy since…. !
JULIE

• ridingwaves

you keep living in just that small sector, you will just wither away..

long or short, worth watching IMHO.

sounds like a fish story to me
what a *catch*.
ðŸ˜‰

• HD

• Julie 35 – 25 – 36

could be tricky,
gold could hit 121, then reverse higher.
Of course the Market would need to roll over in fear of higher interest rates.

• Julie 35 – 25 – 36

GG My husband is the only boyfriend that my dad ever liked … !
JULIE

I think I found one or your family photos.
;-D

• Julie 35 – 25 – 36

Hedgie Update … A gap up today which they are selling into … Getting very dicey RSI now at 70 https://uploads.disquscdn.com/images/f27ae462d6b8967902e5d745372fb47f99a71153593e2d5cd57eb44930b0e864.png JULIE

remember, 70 can sustain..

• Julie 35 – 25 – 36

GG Unlikely with MFI going to 90 and now a negative divergence JULIE https://uploads.disquscdn.com/images/ffeb667341b7b49afb520b04538c3db5c64d49388c7f4cf8478e600453bd2871.png

I almost forgot,
Happy New Moon everybody!

It’s also my Wedding Anniversary. Lucky 13.

• BKXtoZERO

Waiting for metals entry… Thanks. You are right…. Man cannot live on vix alone.

• Julie 35 – 25 – 36

Happy Anniversary GG !
JULIE

Thanks!!

https://mysticalnumbers.com/number-13/

There are 13 weeks every Quarter. not 12.

• Julie 35 – 25 – 36

4 times 13 equals 52 …. 52 weeks in a year Blondes can even figure that one out LOL !
JULIE

• ridingwaves

filled, have another at just below today’s high for 1R….trend change trade…

• ridingwaves

that whale short that was playing 10 yr at 3 is still around…

• Julie 35 – 25 – 36

UNG YES ! The triangle breakout I was waiting for Needs a close above June 7 high 23.99 JULIE https://uploads.disquscdn.com/images/4d46ac34bf5a97d1c77fb29b362b2934880e0b6747765508b6e3629fe4d31bb2.png

• ridingwaves

though today low to high move is decent change if you could time it…quad witching on friday……good luck….

one eye on work, one eye on 5min chart.
wowser, rock n roll.

Time Check.

• ridingwaves

looks promising…

Mole, loved the post. For a system trader, this is a large part of the money management equation that directly effects the type of system one would choose. It is true, wealth gained hastily will dwindle, but whoever gathers little by little will increase it.

• Julie 35 – 25 – 36

RW CVNA The 38.2% retracement matches the channel mid line and the conversion line (8). The 50% retracement matches the price support ; 21 ema and the baseline (21) JULIE https://uploads.disquscdn.com/images/11d481dcad4b114d90ea9553d2b4f7c25941dad9a4dc0fc4f8907a9d4287fb2c.png

sweet mother of Perl, may I get those braces for my child!!!
[SLV]
http://stockcharts.com/h-sc/ui?s=SLV&p=D&yr=1&mn=1&dy=0&id=p18590425457

• Julie 35 – 25 – 36

JULIE

• Julie 35 – 25 – 36
• ridingwaves

great short, can’t believe I stumbled into it, heard someone gloating about it in auto sector event I attended yesterday….they called top perfectly

• HD

whipsaw Wednesday! 1 POV- 3 day correction, completing. IDK

Summer travels start manana. Will be keeping 1 eye on the markets for sure.

• Julie 35 – 25 – 36

Nice one RW IMO watch selling volume i.e. the key
JULIE

• ridingwaves

they might push it up in AM to distribute higher but it has begun…..they got a whole bunch of shorts in at 24 and the breakout short covering rally is now over…

• Julie 35 – 25 – 36

RW Just like T Completion of a short squeeze is a great short GG pegged T
JULIE

• Julie 35 – 25 – 36

T The miss of the year ! GG had it pegged on a short squeeze i.e. the completion of a short squeeze is a great short. I was thinking about shorting T yesterday. The black candle failure at the upper down trend line ; upper cloud boundary and approx 50% retracement. Overbought NICE CALL GG ! !
JULIE

• Julie 35 – 25 – 36
• Julie 35 – 25 – 36

Today SPX and SPY held their daily 5 ema’s GVIP now at RSI 70 with a MFI negative divergence (not shown this chart but in chart below in reply to GG ) Will short SPX when GVIP bearish close below it’s 5 ema and a support shoen. Confirmation will be a STOCHS 5,1 swing failure Going to nail it Guys !
JULIE

• Julie 35 – 25 – 36

in business speak, just trying to add value as a lowly leech.

I may never be an Indy racer, but I’m gonna make one Helluva taxi driver.
ðŸ˜‰

• Julie 35 – 25 – 36

GG You had T nailed Do not sell yourself short Bro ! great one !
JULIE

ðŸ™‚

Taxi Driver AND McDonalds, I have a talent.

• Julie 35 – 25 – 36

It’s great to share life experiences McDonalds never dated him again ! I was all dressed up and everything. The date was the twilight zone .. Dee Doo Dee Doo Dee Doo !
JULIE

• Julie 35 – 25 – 36

SPX A bearish close below the 5 ema and upper trend line … The Short is on ! JULIE https://uploads.disquscdn.com/images/4c8e05b31c5892232b36fcaf633285aae7fb1d58786c25777caf5afec31c607b.png

• Ian Naugler

Pain was \$38 down to \$2, this is a scratch comparatively!

• Julie 35 – 25 – 36

GLD I took a long at the close as mentioned previously https://uploads.disquscdn.com/images/37b6102d681c82988ac28c92bb8a13ca9c4690443d489ab4c0a36f475c82e402.png The bounce off the lower trend line closing above a support and it’s 5 ema JULIE

• Julie 35 – 25 – 36

BYD I shorted BYD and covered last week on the 21 ema. Looking to long approx 35.65 the confluenbce (1) price support (2) 38.2% retracement (3) lower Raff regression channel (4) 55 ema https://uploads.disquscdn.com/images/59a0de5e3e018935e766f36244eca9b814a6532ac26e117b71edae9ae6106eb0.png JULIE

• Julie 35 – 25 – 36

Guys EXAS Weekly Chart Checkout the pullback … Fib Arc — 38.2% retracement — Weekly 89 ema JULIE https://uploads.disquscdn.com/images/e9bee5733e893f7209ead0a28294a6053e8177d5f260bdc8fef1b7c6f19e4eab.png

• Julie 35 – 25 – 36

Miss type 50% not 38.2% retracement
JULIE

Is it safe to come out now?

• BKXtoZERO

I am aroused by this chart…

(face palm)

• Julie 35 – 25 – 36

GG BK USO can go either way .. Have a plan for both Re short bearish close below 13.26 (conversion line 8) which will break the lower channel and lower cloud boundary. Continues higher then the 50% retracement matching the baseline 21 JULIE https://uploads.disquscdn.com/images/e0626c92912d968213b7d96dd8e26068ed7c0f4cae1bf02f21807af129a7e544.png

Yes it could.

I’m biased to the downside.
http://stockcharts.com/h-sc/ui?s=USO&p=D&yr=0&mn=6&dy=0&id=p70722398124

A higher interest rate means deceleration in my book.
and that unemployment rate, can’t stay sub 4.0 forever!

• Julie 35 – 25 – 36

Thanks for the charts GG
JULIE

• Julie 35 – 25 – 36

Also GG USO weekly PMO has a negative crossover and daily PMO has not turned up
JULIE

• Julie 35 – 25 – 36

XHB Anyone going to join me in shorting a lower high ? Possible bounce at this level. Down to daily conversion line (8) and upper cloud boundary NOW 60 min chart oversold and down to it’s upper cloud boundary. Last 60 min candle positive. Watch 41.07 and 41.33 if it does bounce JULIE https://uploads.disquscdn.com/images/1a0603c591b0557c76b5f0824b2be6d4b302249b0897d121e162cf2f24057375.png

• Julie 35 – 25 – 36

Guys The dump in Homebuilders XHB is corroborated by a dump in XLRE (real estate ETF) Love it ! JULIE https://uploads.disquscdn.com/images/212d9d8edf5bdb591d04eec0c4e314a22b615e31dbd5d5a4ecc039926b28c9f9.png

• Julie 35 – 25 – 36

Guys The two candles today XHB and XLRE are bearish Marabuzo Candles with a line strike pattern One of Bulkowski’s favorite candles and patterns Mine too ! ! Love it !
JULIE

• BKXtoZERO

did someone say short!

• Julie 35 – 25 – 36

Hi BK What a week. Hope you are feeling better
JULIE

• BKXtoZERO

looks nasty girl!

• BKXtoZERO

I am thanks…. something kind of clicked now 6 months after last repair surgery… less pain. thanks.

• ridingwaves

headlines about gold surging are a bit overdone-\$7 is not a surge on a \$1300 base…
Gold surges above \$1,300 even as dollar gains on ECB policy update

• Mark Shinnick

The gold Bull narrative is a distinct and persistent bias.

• Mark Shinnick