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Xiao si

In Sample and Out of Sample Size

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I see an ongoing debate in some forums about the duration of the data used to design, test, and optimize trading systems.

 

On one side i hear that some like Sunny Harris use 12 months of data only. Other still demand that anything less than a couple of years is just fitting to noise.....

 

If we go back too far we end up seeing a mess of noise related to the top and subsequent rapid decline of 2008. Before that and it was the late stages of the bull market.

 

I also hear some talk that now the markets are more mean reverting than prior to 2008, when they were more trendy.

 

My opinion from all of this so far is that one year of recent data is probably better to build a system that works well as the markets 'currently' behave.

 

This leads to the Out of Sample period reserved for proving the consistency of the systems performace.

 

I'm interested in opinions of the systematic traders here as to what they personally like to use for these data samples and why.

 

Also, what is your preferred roadmap for development of these strategies? example:

-develop the idea or concept

-test the basic entry

-test the entry with basic trade mgt.

-optimize the basic trade management

-back-test in sample

-etc....

 

Thanks in advance to all those systematic traders in the house:thumbs up:

 

Cheers,

 

 

XS

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It's all very complicated - Thomas Stridman's 'Trading Systems That Work' is probably the best book for reading up on this topic. Especially important are his thoughts one percentage-change scaled backtesting rather than dollar-based tests.

 

I use data prior to the in-sample as my out of sample (there's absolutely know reason why the market one year prior to the in-sample is any more likely to resemble it than the year after the in-sample does).

 

If you're testing a fixed percent stop-loss, say, then you're going to want to test this over a long period to get a result that reflects changes in market volatility. If, however, your stop was a dynamic, volatility-based stop, then there would be less of an argument for this.

 

Also, it depends on how frequently your system trades. If you were testing a long term trend-following system then you'd want at least 10 years in sample, I would say. Whereas an HFT firm may use just the last year or two. Significant sample size is the important factor.

 

I would definitely think about how you can remove variables from your system so that there is very little optimisation to be done.

 

Hope that helps.

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It's all very complicated - Thomas Stridman's 'Trading Systems That Work' is probably the best book for reading up on this topic. Especially important are his thoughts one percentage-change scaled back-testing rather than dollar-based tests.

 

I use data prior to the in-sample as my out of sample (there's absolutely know reason why the market one year prior to the in-sample is any more likely to resemble it than the year after the in-sample does).

 

If you're testing a fixed percent stop-loss, say, then you're going to want to test this over a long period to get a result that reflects changes in market volatility. If, however, your stop was a dynamic, volatility-based stop, then there would be less of an argument for this.

 

Also, it depends on how frequently your system trades. If you were testing a long term trend-following system then you'd want at least 10 years in sample, I would say. Whereas an HFT firm may use just the last year or two. Significant sample size is the important factor.

 

I would definitely think about how you can remove variables from your system so that there is very little optimization to be done.

 

Hope that helps.

 

Thanks BH, i share your view on simplicity.

 

XS

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Xiao si, are you talking about EOD or intraday systems?

 

I know that most use 30% of the data for development and the remaining 30% for out of sample testing. Some argue that the in sample should be long enough to include a variety of market conditions. I agree. At least 10 years for EOD and 5 years for intraday is what I use. Other do not agree. This is trading.:)

 

As far as the roadmap you outlined, in my opinion it is a time consumig and inefficient process. It can be compared to trying to divide decimal numbers by hand instead of using a calculator. More and more traders turn to machine generated strategies. If you like indicators and evolutionary algorithms then Adaptrade is a popular program. If you like price patterns only then Price Action Lab is another popular program. The use of such programs automates development and testing with significant advantages. Good luck to you!

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Xiao si, are you talking about EOD or intraday systems?

 

I know that most use 30% of the data for development and the remaining 30% for out of sample testing. Some argue that the in sample should be long enough to include a variety of market conditions. I agree. At least 10 years for EOD and 5 years for intraday is what I use. Other do not agree. This is trading.:)

 

As far as the roadmap you outlined, in my opinion it is a time consumig and inefficient process. It can be compared to trying to divide decimal numbers by hand instead of using a calculator. More and more traders turn to machine generated strategies. If you like indicators and evolutionary algorithms then Adaptrade is a popular program. If you like price patterns only then Price Action Lab is another popular program. The use of such programs automates development and testing with significant advantages. Good luck to you!

 

This is great stuff Equ....At the moment my focus is intra-day on the equity index futures in my time zone, so Asian, Australian and Eurpean. I'm actually using Adaptrade's Builder as well as developing my own systems as i learn to code.

 

I've got quite a bit of data now (thanks to a few on here) so i'll be working my way through some of that. I find that the last few years were pretty diverse in terms of market action. If i build a system on 2009-2010 data its more apt to perform on OOS data from 2010 - 2011 than if i use something that includes 2008. Talk about a rough patch.

 

Just wondered how people were using that period, avoiding it or using it?

 

Cheers,

 

 

XS

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...Some argue that the in sample should be long enough to include a variety of market conditions. I agree. At least 10 years for EOD and 5 years for intraday is what I use. Other do not agree....

 

I think it MUST be long enough to include a variety of market conditions.

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I think it MUST be long enough to include a variety of market conditions.

 

But should that variety include a period like we saw from July 2008 to December 2008? Should we expect a system to be able to trade through that huge increase in volatility and still be able to deal with a trending market?

 

I do think that different parts of the trading year are important though. I try and use data that covers all of these seasons evenly.

 

XS

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But should that variety include a period like we saw from July 2008 to December 2008? Should we expect a system to be able to trade through that huge increase in volatility and still be able to deal with a trending market?

 

I do think that different parts of the trading year are important though. I try and use data that covers all of these seasons evenly.

 

XS

 

I think it is crucial to see how your system will perform if a part of the history repeats itself again. If you know your system's weaknesses, you can prepare yourself what to do next. if your system is not performing well under a certain market condition, then you can either choose not to trade or add some filters to the system...just my thoughts...

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I think it is crucial to see how your system will perform if a part of the history repeats itself again. If you know your system's weaknesses, you can prepare yourself what to do next. if your system is not performing well under a certain market condition, then you can either choose not to trade or add some filters to the system...just my thoughts...

 

You know, i usually run it over that nasty 2008 decline just to see what it does, but I've never really looked it that way before...thanks, that's great advice.

 

XS

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But should that variety include a period like we saw from July 2008 to December 2008? Should we expect a system to be able to trade through that huge increase in volatility and still be able to deal with a trending market?

 

I do think that different parts of the trading year are important though. I try and use data that covers all of these seasons evenly.

 

XS

 

Hi XS,

 

Why don't you do out-of-sample testing using the 2008 months you mentioned? I would be curious about how my system would have performed in that high vola period.

 

Regards,

k

 

EDIT: Sorry, posted too late... ;)

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Hi XS,

 

Why don't you do out-of-sample testing using the 2008 months you mentioned? I would be curious about how my system would have performed in that high vola period.

 

Regards,

k

 

EDIT: Sorry, posted too late... ;)

 

Yeah, i think i'm going to start reserving that period for OOS testing and making a point of always testing over it.

 

Cheers,

 

 

XS

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Yeah, i think i'm going to start reserving that period for OOS testing and making a point of always testing over it.

 

Cheers,

 

XS

 

I would be careful with this approach if I were you. A lot of the strategies that I trade or track performed conspicuously well in that 2008 period (to the extent that the equity curve pretty much brickwalls). This is probably because they are contrarian in nature and therefore doing roughly the opposite of whatever your strategy is trying to do when it struggles in 2008.

 

However, if I developed such a strategy now and then used 2008 for my out of sample period, then I would get a wildly optimistic and hopelessly wrong-headed impression of my strategy's likely performance.

 

. . . A much more interesting period to look at is 2007. This is when the volatility really started to ramp up, as all the higher tranched credit default swaps etc went belly-up behind the scenes - how did your strategy respond to this steadily increasing volatility? Did it adapt?

 

Hope that helps

 

Bluehorseshoe

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You know, i usually run it over that nasty 2008 decline just to see what it does, but I've never really looked it that way before...thanks, that's great advice.

 

XS

 

you are welcome, just shared a piece of my experience :)

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Great stuff guys thanks heaps...

 

There is a raging debate on this on another forum regarding OOS testing which then leads to the topic of optimization.

 

I sort of think that for my current tie frame, 15 minutes i need only a year of data to construct and 1 year for the first OOS period. Then i use a three to six month period reserved for optimizing...then WF from there. I know i'll get some flack for this...but that seems to work best. I think i'm getting too much variety in the market behavior if i use too much data to develop the system on. More recent data works better.

 

Opinions?

 

Cheers,

 

 

XS

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... More recent data works better.

 

 

 

Hi XS,

 

More recent data works only better, if your different walk-forward testing periods prove so. Otherwise you did just curve-fitting to the recent data.

 

Regards,

k

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Hi XS,

 

More recent data works only better, if your different walk-forward testing periods prove so. Otherwise you did just curve-fitting to the recent data.

 

Regards,

k

 

Exactly, and that's where the debate starts going about what is curve fitting and what is over fitting...Many are saying that curve fitting is ok for intraday systems as long as they prove themselves on OOS data. I'm still trying to get the difference between curve fitting and over-fitting.....

 

XS

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Xiao,

 

In my opinion you have to worry about presenting your setup to make the greatest possible amount of operational situations. This not only concerns to OOS, but the combination IS + OOS.

 

Why?

 

1) When you define an IS window period, you need to worry about the degrees of freedom for your model optimization. You need to make room for the model to find the best combinations of parameters to the setup´s rules. Thus, for ranges of 200 MA periods ex., you need to consider that the period will comprise your model extension.

 

2) Once granted an appropriate period, you must remember that the optimizer will (try to) set global maximum to your objective function, specifically for that IS window period. So you're training the model to get the best performance according to that market conditions. You are fitting your model to that market.

 

3) Once you finished the optimization, you will apply the model on the OOS next window period. And see how it behaves. The better will be the result, the better is the predictive capacity of your model. But you must remember the IS period. When you optimized, which was the IS period kind of market? Trend, range, up, down. And now, in the OOS? The market may be similar or completely different. What counts are the combinations: IS in trend and OOS in range, IS in uptrend and OOS in downtrend, OOS in range and IS in up trend, and so on.

 

The final analysis will be done on the cumulative results of all OOS windows. I use WFA precisely because of the various possible IS+OOS testing combinations and thus manage to evaluate the predictive capacity of the model in many different situations. So I can have more confidence when it comes to operational phase.

 

Another important aspect of the OOS window is the number of operations. It is not recommended to have windows with few operations. In my case its worries me more because the strategy (I prefer setups with high trades number) and less because of the statistics. That's because I consider all the operations of all OOS windows to analyze the possible distributions with MC.

 

That's my opinion. Sorry for my poor english and I hope you understood my point of view.

 

Regards

Marcelo

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Exactly, and that's where the debate starts going about what is curve fitting and what is over fitting...Many are saying that curve fitting is ok for intraday systems as long as they prove themselves on OOS data. I'm still trying to get the difference between curve fitting and over-fitting.....

 

XS

 

I think the point is not fitting or over-fitting. The point is if your parameter adjustment creates a completely different random animal. There is an interesting thread in the Adaptrade forum where a user tries to reverse engineer a system and he ends up getting a different each time he tries. I think this is not only fitting but random fitting:

 

Reverse engineering a known system - Adaptrade Builder | Google Groups

 

I like the classification of curve-fitted systems this guy has come up with:

 

Curve-fitting and Optimization | Price Action Lab Blog

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I think the point is not fitting or over-fitting. The point is if your parameter adjustment creates a completely different random animal. There is an interesting thread in the Adaptrade forum where a user tries to reverse engineer a system and he ends up getting a different each time he tries. I think this is not only fitting but random fitting:

 

Reverse engineering a known system - Adaptrade Builder | Google Groups

 

I like the classification of curve-fitted systems this guy has come up with:

 

Curve-fitting and Optimization | Price Action Lab Blog

 

Yes, i agree. I fact i have been only optimizing MM stops and Exits for sometime now. It makes sense as well if you are using indicators for the basis of a system and you optimize those that the curve fit is much more likely to fail, almost certin IMO. Them being the PAL, using only price patterns of course they are selling that particular POV.

 

I've noticed that the majority of systems that Adaptrade's Builder constructs are actually more Price Action based even if i do not narrow down the range of choices to this, especially the volatility systems.

 

Thanks for the link..curious of the others POV too.

 

Cheers,

 

 

XS

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Yes, i agree. I fact i have been only optimizing MM stops and Exits for sometime now. It makes sense as well if you are using indicators for the basis of a system and you optimize those that the curve fit is much more likely to fail, almost certin IMO. Them being the PAL, using only price patterns of course they are selling that particular POV.

 

PAL posted another article yesterday on their blog about curve-fitting. I think it points to programs that offer a lot of different stop options to nicely curve-fit results

 

Article link here

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I would definitely think about how you can remove variables from your system so that there is very little optimisation to be done.

 

I would possibly comment on this, even if the thread is no longer updated.

 

On another forum I had the occasion of discussing about the usefulness of optimizations and especially of walk forward optimizations with reference to the INS/OOS balance.

 

My point was basically as follows: WFO is probably NOT always a must in comparison with traditional optimization. In particular conditions of market and time, there's a chance that a WFO is NOT necessary and/or useful.

 

Just a specific case, to make my point clear.

 

I’m currently testing a (purely automated/mechanical) strategy with very few parameters, and most of them seem to be unrelated to any kind of periodical change in the market I‘m trading (QM futures contract). I basically started asking myself: is it necessary/useful to include these parameters in the optimization, if they don’t seem to be correlated to any specific change in market behavior? (i.e. they basically seem to casually change from one period to another).

 

One of my mechanical strategies uses a fixed stop loss and evaluates the opening session gap size before taking action. I would usually prefer to set the stop loss just once, by considering the general MAE of the historical backtest. As for the gap size, I usually cannot see any particular change between the sizes of 2002 gaps and the ones related to today’s markets (I can provide data for this). So, does it make sense to include these parameters in the optimization?

 

I agree with your suggestion about reducing the number of the parameters. In fact, my point is that a specific optimization may not be needed for strategies that have very few variables/parameters.

 

By the way, I was replied that in most cases even a strategy with no parameters at all can hide an "implicit" (over-fitting) adaptation to the markets because of the way it's programmed and conceived.

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    • Date: 17th April 2024. Market News – Appetite for risk-taking remains weak. Economic Indicators & Central Banks:   Stocks, Treasury yields and US Dollar stay firmed. Fed Chair Powell added to the recent sell off. His slightly more hawkish tone further priced out chances for any imminent action and the timing of a cut was pushed out further. He suggested if higher inflation does persist, the Fed will hold rates steady “for as long as needed.” Implied Fed Fund: There remains no real chance for a move on May 1 and at their intraday highs the June implied funds rate future showed only 5 bps, while July reflected only 10 bps. And a full 25 bps was not priced in until November, with 38 bps in cuts seen for 2024. US & EU Economies Diverging: Lagarde says ECB is moving toward rate cuts – if there are no major shocks. UK March CPI inflation falls less than expected. Output price inflation has started to nudge higher, despite another decline in input prices. Together with yesterday’s higher than expected wage numbers, the data will add to the arguments of the hawks at the BoE, which remain very reluctant to contemplate rate cuts. Canada CPI rose 0.6% in March, double the 0.3% February increase BUT core eased. The doors are still open for a possible cut at the next BoC meeting on June 5. IMF revised up its global growth forecast for 2024 with inflation easing, in its new World Economic Outlook. This is consistent with a global soft landing, according to the report. Financial Markets Performance:   USDJPY also inched up to 154.67 on expectations the BoJ will remain accommodative and as the market challenges a perceived 155 red line for MoF intervention. USOIL prices slipped -0.15% to $84.20 per barrel. Gold rose 0.24% to $2389.11 per ounce, a new record closing high as geopolitical risks overshadowed the impacts of rising rates and the stronger dollar. Market Trends:   Wall Street waffled either side of unchanged on the day amid dimming rate cut potential, rising yields, and earnings. The major indexes closed mixed with the Dow up 0.17%, while the S&P500 and NASDAQ lost -0.21% and -0.12%, respectively. Asian stock markets mostly corrected again, with Japanese bourses underperforming and the Nikkei down -1.3%. Mainland China bourses were a notable exception and the CSI 300 rallied 1.4%, but the MSCI Asia Pacific index came close to erasing the gains for this year. Always trade with strict risk management. Your capital is the single most important aspect of your trading business. Please note that times displayed based on local time zone and are from time of writing this report. Click HERE to access the full HFM Economic calendar. Want to learn to trade and analyse the markets? Join our webinars and get analysis and trading ideas combined with better understanding on how markets work. Click HERE to register for FREE! Click HERE to READ more Market news. Andria Pichidi Market Analyst HFMarkets Disclaimer: This material is provided as a general marketing communication for information purposes only and does not constitute an independent investment research. Nothing in this communication contains, or should be considered as containing, an investment advice or an investment recommendation or a solicitation for the purpose of buying or selling of any financial instrument. All information provided is gathered from reputable sources and any information containing an indication of past performance is not a guarantee or reliable indicator of future performance. Users acknowledge that any investment in FX and CFDs products is characterized by a certain degree of uncertainty and that any investment of this nature involves a high level of risk for which the users are solely responsible and liable. We assume no liability for any loss arising from any investment made based on the information provided in this communication. This communication must not be reproduced or further distributed without our prior written permission.vvvvvvv
    • Date: 16th April 2024. Market News – Stocks and currencies sell off; USD up. Economic Indicators & Central Banks:   Stocks and currencies sell off, while the US Dollar picks up haven flows. Treasuries yields spiked again to fresh 2024 peaks before paring losses into the close, post, the stronger than expected retail sales eliciting a broad sell off in the markets. Rates surged as the data pushed rate cut bets further into the future with July now less than a 50-50 chance. Wall Street finished with steep declines led by tech. Stocks opened in the green on a relief trade after Israel repulsed the well advertised attack from Iran on Sunday. But equities turned sharply lower and extended last week’s declines amid the rise in yields. Investor concerns were intensified as Israel threatened retaliation. There’s growing anxiety over earnings even after a big beat from Goldman Sachs. UK labor market data was mixed, as the ILO unemployment rate unexpectedly lifted, while wage growth came in higher than anticipated – The data suggests that the labor market is catching up with the recession. Mixed messages then for the BoE. China grew by 5.3% in Q1 however the numbers are causing a lot of doubts over sustainability of this growth. The bounce came in the first 2 months of the year. In March, growth in retail sales slumped and industrial output decelerated below forecasts, suggesting challenges on the horizon. Today: Germany ZEW, US housing starts & industrial production, Fed Vice Chair Philip Jefferson speech, BOE Bailey speech & IMF outlook. Earnings releases: Morgan Stanley and Bank of America. Financial Markets Performance:   The US Dollar rallied to 106.19 after testing 106.25, gaining against JPY and rising to 154.23, despite intervention risk. Yen traders started to see the 160 mark as the next Resistance level. Gold surged 1.76% to $2386 per ounce amid geopolitical risks and Chinese buying, even as the USD firmed and yields climbed. USOIL is flat at $85 per barrel. Market Trends:   Breaks of key technical levels exacerbated the sell off. Tech was the big loser with the NASDAQ plunging -1.79% to 15,885 while the S&P500 dropped -1.20% to 5061, with the Dow sliding -0.65% to 37,735. The S&P had the biggest 2-day sell off since March 2023. Nikkei and ASX lost -1.9% and -1.8% respectively, and the Hang Seng is down -2.1%. European bourses are down more than -1% and US futures are also in the red. CTA selling tsunami: “Just a few points lower CTAs will for the first time this year start selling in size, to add insult to injury, we are breaking major trend-lines in equities and the gamma stabilizer is totally gone.” Short term CTA threshold levels are kicking in big time according to GS. Medium term is 4873 (most important) while the long term level is at 4605. Always trade with strict risk management. Your capital is the single most important aspect of your trading business. Please note that times displayed based on local time zone and are from time of writing this report. Click HERE to access the full HFM Economic calendar. Want to learn to trade and analyse the markets? Join our webinars and get analysis and trading ideas combined with better understanding on how markets work. Click HERE to register for FREE! Click HERE to READ more Market news. Andria Pichidi Market Analyst HFMarkets Disclaimer: This material is provided as a general marketing communication for information purposes only and does not constitute an independent investment research. Nothing in this communication contains, or should be considered as containing, an investment advice or an investment recommendation or a solicitation for the purpose of buying or selling of any financial instrument. All information provided is gathered from reputable sources and any information containing an indication of past performance is not a guarantee or reliable indicator of future performance. Users acknowledge that any investment in FX and CFDs products is characterized by a certain degree of uncertainty and that any investment of this nature involves a high level of risk for which the users are solely responsible and liable. We assume no liability for any loss arising from any investment made based on the information provided in this communication. This communication must not be reproduced or further distributed without our prior written permission.
    • Date: 15th April 2024. Market News – Negative Reversion; Safe Havens Rally. Trading Leveraged Products is risky Economic Indicators & Central Banks:   Markets weigh risk of retaliation cycle in Middle East. Initially the retaliatory strike from Iran on Israel fostered a haven bid, into bonds, gold and other haven assets, as it threatens a wider regional conflict. However, this morning, Oil and Asian equity markets were muted as traders shrugged off fears of a war escalation in the Middle East. Iran said “the matter can be deemed concluded”, and President Joe Biden has called on Israel to exercise restraint following Iran’s drone and missile strike, as part of Washington’s efforts to ease tensions in the Middle East and minimize the likelihood of a widespread regional conflict. New US and UK sanctions banned deliveries of Russian supplies, i.e. key industrial metals, produced after midnight on Friday. Aluminum jumped 9.4%, nickel rose 8.8%, suggesting brokers are bracing for major supply chain disruption. Financial Markets Performance:   The USDIndex fell back from highs over 106 to currently 105.70. The Yen dip against USD to 153.85. USOIL settled lower at 84.50 per barrel and Gold is trading below session highs at currently $2357.92 per ounce. Copper, more liquid and driven by the global economy over recent weeks, was more subdued this morning. Currently at $4.3180. Market Trends:   Asian stock markets traded mixed, but European and US futures are slightly higher after a tough session on Friday and yields have picked up. Mainland China bourses outperformed overnight, after Beijing offered renewed regulatory support. The PBOC meanwhile left the 1-year MLF rate unchanged, while once again draining funds from the system. Nikkei slipped 1% to 39,114.19. On Friday, NASDAQ slumped -1.62% to 16,175, unwinding most of Thursday’s 1.68% jump to a new all-time high at 16,442. The S&P500 fell -1.46% and the Dow dropped 1.24%. Declines were broadbased with all 11 sectors of the S&P finishing in the red. JPMorgan Chase sank 6.5% despite reporting stronger profit in Q1. The nation’s largest bank gave a forecast for a key source of income this year that fell below Wall Street’s estimate, calling for only modest growth. Apple shipments drop by 10% in Q1. Always trade with strict risk management. Your capital is the single most important aspect of your trading business. Please note that times displayed based on local time zone and are from time of writing this report. Click HERE to access the full HFM Economic calendar. Want to learn to trade and analyse the markets? Join our webinars and get analysis and trading ideas combined with better understanding on how markets work. Click HERE to register for FREE! Click HERE to READ more Market news. Andria Pichidi Market Analyst HFMarkets Disclaimer: This material is provided as a general marketing communication for information purposes only and does not constitute an independent investment research. Nothing in this communication contains, or should be considered as containing, an investment advice or an investment recommendation or a solicitation for the purpose of buying or selling of any financial instrument. All information provided is gathered from reputable sources and any information containing an indication of past performance is not a guarantee or reliable indicator of future performance. Users acknowledge that any investment in FX and CFDs products is characterized by a certain degree of uncertainty and that any investment of this nature involves a high level of risk for which the users are solely responsible and liable. We assume no liability for any loss arising from any investment made based on the information provided in this communication. This communication must not be reproduced or further distributed without our prior written permission.
    • The morning of my last post I happened to glance over to the side and saw “...angst over the FOMC’s rate trajectory triggered a flight to safety, hence boosting the haven demand. “   http://www.traderslaboratory.com/forums/topic/21621-hfmarkets-hfmcom-market-analysis-services/page/17/?tab=comments#comment-228522   I reacted, but didn’t take time to  respond then... will now --- HFBlogNews, I don’t know if you are simply aggregating the chosen narratives for the day or if it’s your own reporting... either way - “flight to safety”????  haven ?????  Re: “safety  - ”Those ‘solid rocks’ are getting so fragile a hit from a dandelion blowball might shatter them... like now nobody wants to buy longer term new issues at these rates...yet the financial media still follows the scripts... The imagery they pound day in and day out makes it look like the Fed knows what they’re doing to help ‘us’... They do know what they’re doing - but it certainly is not to help ‘us’... and it is not to ‘control’ inflation... And at some point in the not too distant future, the interest due will eat a huge portion of the ‘revenue’ Re: “haven” The defaults are coming ...  The US will not be the first to default... but it will certainly not be the very last to default !! ...Enough casual anti-white racism for the day  ... just sayin’
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