Welcome to the third and final part of this chapter.submitted by getmrmarket to Forex [link] [comments]
Thank you all for the 100s of comments and upvotes - maybe this post will take us above 1,000 for this topic!
Keep any feedback or questions coming in the replies below.
Before you read this note, please start with Part I and then Part II so it hangs together and makes sense.
Squeezes and other risksWe are going to cover three common risks that traders face: events; squeezes, asymmetric bets.
EventsEconomic releases can cause large short-term volatility. The most famous is Non Farm Payrolls, which is the most widely watched measure of US employment levels and affects the price of many instruments.On an NFP announcement currencies like EURUSD might jump (or drop) 100 pips no problem.
This is fine and there are trading strategies that one may employ around this but the key thing is to be aware of these releases.You can find economic calendars all over the internet - including on this site - and you need only check if there are any major releases each day or week.
For example, if you are trading off some intraday chart and scalping a few pips here and there it would be highly sensible to go into a known data release flat as it is pure coin-toss and not the reason for your trading. It only takes five minutes each day to plan for the day ahead so do not get caught out by this. Many retail traders get stopped out on such events when price volatility is at its peak.
SqueezesShort squeezes bring a lot of danger and perhaps some opportunity.
The story of VW and Porsche is the best short squeeze ever. Throughout these articles we've used FX examples wherever possible but in this one instance the concept (which is also highly relevant in FX) is best illustrated with an historical lesson from a different asset class.
A short squeeze is when a participant ends up in a short position they are forced to cover. Especially when the rest of the market knows that this participant can be bullied into stopping out at terrible levels, provided the market can briefly drive the price into their pain zone.
There's a reason for the car, don't worry
Hedge funds had been shorting VW stock. However the amount of VW stock available to buy in the open market was actually quite limited. The local government owned a chunk and Porsche itself had bought and locked away around 30%. Neither of these would sell to the hedge-funds so a good amount of the stock was un-buyable at any price.
If you sell or short a stock you must be prepared to buy it back to go flat at some point.
To cut a long story short, Porsche bought a lot of call options on VW stock. These options gave them the right to purchase VW stock from banks at slightly above market price.
Eventually the banks who had sold these options realised there was no VW stock to go out and buy since the German government wouldn’t sell its allocation and Porsche wouldn’t either. If Porsche called in the options the banks were in trouble.
Porsche called in the options which forced the shorts to buy stock - at whatever price they could get it.
The price squeezed higher as those that were short got massively squeezed and stopped out. For one brief moment in 2008, VW was the world’s most valuable company. Shorts were burned hard.
Porsche apparently made $11.5 billion on the trade. The BBC described Porsche as “a hedge fund with a carmaker attached.”
If this all seems exotic then know that the same thing happens in FX all the time. If everyone in the market is talking about a key level in EURUSD being 1.2050 then you can bet the market will try to push through 1.2050 just to take out any short stops at that level. Whether it then rallies higher or fails and trades back lower is a different matter entirely.
This brings us on to the matter of crowded trades. We will look at positioning in more detail in the next section. Crowded trades are dangerous for PNL. If everyone believes EURUSD is going down and has already sold EURUSD then you run the risk of a short squeeze.
For additional selling to take place you need a very good reason for people to add to their position whereas a move in the other direction could force mass buying to cover their shorts.
A trading mentor when I worked at the investment bank once advised me:
Always think about which move would cause the maximum people the maximum pain. That move is precisely what you should be watching out for at all times.
Asymmetric lossesAlso known as picking up pennies in front of a steamroller. This risk has caught out many a retail trader. Sometimes it is referred to as a "negative skew" strategy.
Ideally what you are looking for is asymmetric risk trade set-ups: that is where the downside is clearly defined and smaller than the upside. What you want to avoid is the opposite.
A famous example of this going wrong was the Swiss National Bank de-peg in 2012.
The Swiss National Bank had said they would defend the price of EURCHF so that it did not go below 1.2. Many people believed it could never go below 1.2 due to this. Many retail traders therefore opted for a strategy that some describe as ‘picking up pennies in front of a steam-roller’.
They would would buy EURCHF above the peg level and hope for a tiny rally of several pips before selling them back and keep doing this repeatedly. Often they were highly leveraged at 100:1 so that they could amplify the profit of the tiny 5-10 pip rally.
Then this happened.
Something that changed FX markets forever
The SNB suddenly did the unthinkable. They stopped defending the price. CHF jumped and so EURCHF (the number of CHF per 1 EUR) dropped to new lows very fast. Clearly, this trade had horrific risk : reward asymmetry: you risked 30% to make 0.05%.
Other strategies like naively selling options have the same result. You win a small amount of money each day and then spectacularly blow up at some point down the line.
Market positioningWe have talked about short squeezes. But how do you know what the market position is? And should you care?
Let’s start with the first. You should definitely care.
Let’s imagine the entire market is exceptionally long EURUSD and positioning reaches extreme levels. This makes EURUSD very vulnerable.
To keep the price going higher EURUSD needs to attract fresh buy orders. If everyone is already long and has no room to add, what can incentivise people to keep buying? The news flow might be good. They may believe EURUSD goes higher. But they have already bought and have their maximum position on.
On the flip side, if there’s an unexpected event and EURUSD gaps lower you will have the entire market trying to exit the position at the same time. Like a herd of cows running through a single doorway. Messy.
We are going to look at this in more detail in a later chapter, where we discuss ‘carry’ trades. For now this TRYJPY chart might provide some idea of what a rush to the exits of a crowded position looks like.
A carry trade position clear-out in action
Knowing if the market is currently at extreme levels of long or short can therefore be helpful.
The CFTC makes available a weekly report, which details the overall positions of speculative traders “Non Commercial Traders” in some of the major futures products. This includes futures tied to deliverable FX pairs such as EURUSD as well as products such as gold. The report is called “CFTC Commitments of Traders” ("COT").
This is a great benchmark. It is far more representative of the overall market than the proprietary ones offered by retail brokers as it covers a far larger cross-section of the institutional market.
Generally market participants will not pay a lot of attention to commercial hedgers, which are also detailed in the report. This data is worth tracking but these folks are simply hedging real-world transactions rather than speculating so their activity is far less revealing and far more noisy.
You can find the data online for free and download it directly here.
Raw format is kinda hard to work with
However, many websites will chart this for you free of charge and you may find it more convenient to look at it that way. Just google “CFTC positioning charts”.
But you can easily get visualisations
You can visually spot extreme positioning. It is extremely powerful.
Bear in mind the reports come out Friday afternoon US time and the report is a snapshot up to the prior Tuesday. That means it is a lagged report - by the time it is released it is a few days out of date. For longer term trades where you hold positions for weeks this is of course still pretty helpful information.
As well as the absolute level (is the speculative market net long or short) you can also use this to pick up on changes in positioning.
For example if bad news comes out how much does the net short increase? If good news comes out, the market may remain net short but how much did they buy back?
A lot of traders ask themselves “Does the market have this trade on?” The positioning data is a good method for answering this. It provides a good finger on the pulse of the wider market sentiment and activity.
For example you might say: “There was lots of noise about the good employment numbers in the US. However, there wasn’t actually a lot of position change on the back of it. Maybe everyone who wants to buy already has. What would happen now if bad news came out?”
In general traders will be wary of entering a crowded position because it will be hard to attract additional buyers or sellers and there could be an aggressive exit.
If you want to enter a trade that is showing extreme levels of positioning you must think carefully about this dynamic.
Bet correlationRetail traders often drastically underestimate how correlated their bets are.
Through bitter experience, I have learned that a mistake in position correlation is the root of some of the most serious problems in trading. If you have eight highly correlated positions, then you are really trading one position that is eight times as large.
Bruce Kovner of hedge fund, Caxton Associates
For example, if you are trading a bunch of pairs against the USD you will end up with a simply huge USD exposure. A single USD-trigger can ruin all your bets. Your ideal scenario — and it isn’t always possible — would be to have a highly diversified portfolio of bets that do not move in tandem.
Look at this chart. Inverted USD index (DXY) is green. AUDUSD is orange. EURUSD is blue.
Chart from TradingView
So the whole thing is just one big USD trade! If you are long AUDUSD, long EURUSD, and short DXY you have three anti USD bets that are all likely to work or fail together.
The more diversified your portfolio of bets are, the more risk you can take on each.
There’s a really good video, explaining the benefits of diversification from Ray Dalio.
A systematic fund with access to an investable universe of 10,000 instruments has more opportunity to make a better risk-adjusted return than a trader who only focuses on three symbols. Diversification really is the closest thing to a free lunch in finance.
But let’s be pragmatic and realistic. Human retail traders don’t have capacity to run even one hundred bets at a time. More realistic would be an average of 2-3 trades on simultaneously. So what can be done?
The key thing is to start thinking about a portfolio of bets and what each new trade offers to your existing portfolio of risk. Will it diversify or amplify a current exposure?
Crap trades, timeouts and monthly limitsOne common mistake is to get bored and restless and put on crap trades. This just means trades in which you have low conviction.
It is perfectly fine not to trade. If you feel like you do not understand the market at a particular point, simply choose not to trade.
Flat is a position.
Do not waste your bullets on rubbish trades. Only enter a trade when you have carefully considered it from all angles and feel good about the risk. This will make it far easier to hold onto the trade if it moves against you at any point. You actually believe in it.
Equally, you need to set monthly limits. A standard limit might be a 10% account balance stop per month. At that point you close all your positions immediately and stop trading till next month.
Be strict with yourself and walk away
Let’s assume you started the year with $100k and made 5% in January so enter Feb with $105k balance. Your stop is therefore 10% of $105k or $10.5k . If your account balance dips to $94.5k ($105k-$10.5k) then you stop yourself out and don’t resume trading till March the first.
Having monthly calendar breaks is nice for another reason. Say you made a load of money in January. You don’t want to start February feeling you are up 5% or it is too tempting to avoid trading all month and protect the existing win. Each month and each year should feel like a clean slate and an independent period.
Everyone has trading slumps. It is perfectly normal. It will definitely happen to you at some stage. The trick is to take a break and refocus. Conserve your capital by not trading a lot whilst you are on a losing streak. This period will be much harder for you emotionally and you’ll end up making suboptimal decisions. An enforced break will help you see the bigger picture.
Put in place a process before you start trading and then it’ll be easy to follow and will feel much less emotional. Remember: the market doesn’t care if you win or lose, it is nothing personal.
When your head has cooled and you feel calm you return the next month and begin the task of building back your account balance.
That's a wrap on risk managementThanks for taking time to read this three-part chapter on risk management. I hope you enjoyed it. Do comment in the replies if you have any questions or feedback.
Remember: the most important part of trading is not making money. It is not losing money. Always start with that principle. I hope these three notes have provided some food for thought on how you might approach risk management and are of practical use to you when trading. Avoiding mistakes is not a sexy tagline but it is an effective and reliable way to improve results.
Next up I will be writing about an exciting topic I think many traders should look at rather differently: news trading. Please follow on here to receive notifications and the broad outline is below.
News Trading Part I
Disclaimer:This content is not investment advice and you should not place any reliance on it. The views expressed are the author's own and should not be attributed to any other person, including their employer.
Firstly, thanks for the overwhelming comments and feedback. Genuinely really appreciated. I am pleased 500+ of you find it useful.submitted by getmrmarket to Forex [link] [comments]
If you didn't read the first post you can do so here: risk management part I. You'll need to do so in order to make sense of the topic.
As ever please comment/reply below with questions or feedback and I'll do my best to get back to you.
Letting stops breatheWe talked earlier about giving a position enough room to breathe so it is not stopped out in day-to-day noise.
Let’s consider the chart below and imagine you had a trailing stop. It would be super painful to miss out on the wider move just because you left a stop that was too tight.
Imagine being long and stopped out on a meaningless retracement ... ouch!
One simple technique is simply to look at your chosen chart - let’s say daily bars. And then look at previous trends and use the measuring tool. Those generally look something like this and then you just click and drag to measure.
For example if we wanted to bet on a downtrend on the chart above we might look at the biggest retracement on the previous uptrend. That max drawdown was about 100 pips or just under 1%. So you’d want your stop to be able to withstand at least that.
If market conditions have changed - for example if CVIX has risen - and daily ranges are now higher you should incorporate that. If you know a big event is coming up you might think about that, too. The human brain is a remarkable tool and the power of the eye-ball method is not to be dismissed. This is how most discretionary traders do it.
There are also more analytical approaches.
Some look at the Average True Range (ATR). This attempts to capture the volatility of a pair, typically averaged over a number of sessions. It looks at three separate measures and takes the largest reading. Think of this as a moving average of how much a pair moves.
For example, below shows the daily move in EURUSD was around 60 pips before spiking to 140 pips in March. Conditions were clearly far more volatile in March. Accordingly, you would need to leave your stop further away in March and take a correspondingly smaller position size.
ATR is available on pretty much all charting systems
Professional traders tend to use standard deviation as a measure of volatility instead of ATR. There are advantages and disadvantages to both. Averages are useful but can be misleading when regimes switch (see above chart).
Once you have chosen a measure of volatility, stop distance can then be back-tested and optimised. For example does 2x ATR work best or 5x ATR for a given style and time horizon?
Discretionary traders may still eye-ball the ATR or standard deviation to get a feeling for how it has changed over time and what ‘normal’ feels like for a chosen study period - daily, weekly, monthly etc.
Reasons to change a stopAs a general rule you should be disciplined and not change your stops. Remember - losers average losers. This is really hard at first and we’re going to look at that in more detail later.
There are some good reasons to modify stops but they are rare.
One reason is if another risk management process demands you stop trading and close positions. We’ll look at this later. In that case just close out your positions at market and take the loss/gains as they are.
Another is event risk. If you have some big upcoming data like Non Farm Payrolls that you know can move the market +/- 150 pips and you have no edge going into the release then many traders will take off or scale down their positions. They’ll go back into the positions when the data is out and the market has quietened down after fifteen minutes or so. This is a matter of some debate - many traders consider it a coin toss and argue you win some and lose some and it all averages out.
Trailing stops can also be used to ‘lock in’ profits. We looked at those before. As the trade moves in your favour (say up if you are long) the stop loss ratchets with it. This means you may well end up ‘stopping out’ at a profit - as per the below example.
The mighty trailing stop loss order
It is perfectly reasonable to have your stop loss move in the direction of PNL. This is not exposing you to more risk than you originally were comfortable with. It is taking less and less risk as the trade moves in your favour. Trend-followers in particular love trailing stops.
One final question traders ask is what they should do if they get stopped out but still like the trade. Should they try the same trade again a day later for the same reasons? Nope. Look for a different trade rather than getting emotionally wed to the original idea.
Let’s say a particular stock looked cheap based on valuation metrics yesterday, you bought, it went down and you got stopped out. Well, it is going to look even better on those same metrics today. Maybe the market just doesn’t respect value at the moment and is driven by momentum. Wait it out.
Otherwise, why even have a stop in the first place?
Entering and exiting winning positionsTake profits are the opposite of stop losses. They are also resting orders, left with the broker, to automatically close your position if it reaches a certain price.
Imagine I’m long EURUSD at 1.1250. If it hits a previous high of 1.1400 (150 pips higher) I will leave a sell order to take profit and close the position.
The rookie mistake on take profits is to take profit too early. One should start from the assumption that you will win on no more than half of your trades. Therefore you will need to ensure that you win more on the ones that work than you lose on those that don’t.
Sad to say but incredibly common: retail traders often take profits way too early
This is going to be the exact opposite of what your emotions want you to do. We are going to look at that in the Psychology of Trading chapter.
Remember: let winners run. Just like stops you need to know in advance the level where you will close out at a profit. Then let the trade happen. Don’t override yourself and let emotions force you to take a small profit. A classic mistake to avoid.
The trader puts on a trade and it almost stops out before rebounding. As soon as it is slightly in the money they spook and cut out, instead of letting it run to their original take profit. Do not do this.
Entering positions with limit ordersThat covers exiting a position but how about getting into one?
Take profits can also be left speculatively to enter a position. Sometimes referred to as “bids” (buy orders) or “offers” (sell orders). Imagine the price is 1.1250 and the recent low is 1.1205.
You might wish to leave a bid around 1.2010 to enter a long position, if the market reaches that price. This way you don’t need to sit at the computer and wait.
Again, typically traders will use tech analysis to identify attractive levels. Again - other traders will cluster with your orders. Just like the stop loss we need to bake that in.
So this time if we know everyone is going to buy around the recent low of 1.1205 we might leave the take profit bit a little bit above there at 1.1210 to ensure it gets done. Sure it costs 5 more pips but how mad would you be if the low was 1.1207 and then it rallied a hundred points and you didn’t have the trade on?!
There are two more methods that traders often use for entering a position.
Scaling in is one such technique. Let’s imagine that you think we are in a long-term bulltrend for AUDUSD but experiencing a brief retracement. You want to take a total position of 500,000 AUD and don’t have a strong view on the current price action.
You might therefore leave a series of five bids of 100,000. As the price moves lower each one gets hit. The nice thing about scaling in is it reduces pressure on you to pick the perfect level. Of course the risk is that not all your orders get hit before the price moves higher and you have to trade at-market.
Pyramiding is the second technique. Pyramiding is for take profits what a trailing stop loss is to regular stops. It is especially common for momentum traders.
Pyramiding into a position means buying more as it goes in your favour
Again let’s imagine we’re bullish AUDUSD and want to take a position of 500,000 AUD.
Here we add 100,000 when our first signal is reached. Then we add subsequent clips of 100,000 when the trade moves in our favour. We are waiting for confirmation that the move is correct.
Obviously this is quite nice as we humans love trading when it goes in our direction. However, the drawback is obvious: we haven’t had the full amount of risk on from the start of the trend.
You can see the attractions and drawbacks of both approaches. It is best to experiment and choose techniques that work for your own personal psychology as these will be the easiest for you to stick with and build a disciplined process around.
Risk:reward and win ratiosBe extremely skeptical of people who claim to win on 80% of trades. Most traders will win on roughly 50% of trades and lose on 50% of trades. This is why risk management is so important!
Once you start keeping a trading journal you’ll be able to see how the win/loss ratio looks for you. Until then, assume you’re typical and that every other trade will lose money.
If that is the case then you need to be sure you make more on the wins than you lose on the losses. You can see the effect of this below.
A combination of win % and risk:reward ratio determine if you are profitable
A typical rule of thumb is that a ratio of 1:3 works well for most traders.
That is, if you are prepared to risk 100 pips on your stop you should be setting a take profit at a level that would return you 300 pips.
One needn’t be religious about these numbers - 11 pips and 28 pips would be perfectly fine - but they are a guideline.
Again - you should still use technical analysis to find meaningful chart levels for both the stop and take profit. Don’t just blindly take your stop distance and do 3x the pips on the other side as your take profit. Use the ratio to set approximate targets and then look for a relevant resistance or support level in that kind of region.
Risk-adjusted returnsNot all returns are equal. Suppose you are examining the track record of two traders. Now, both have produced a return of 14% over the year. Not bad!
The first trader, however, made hundreds of small bets throughout the year and his cumulative PNL looked like the left image below.
The second trader made just one bet — he sold CADJPY at the start of the year — and his PNL looked like the right image below with lots of large drawdowns and volatility.
Would you rather have the first trading record or the second?
If you were investing money and betting on who would do well next year which would you choose? Of course all sensible people would choose the first trader. Yet if you look only at returns one cannot distinguish between the two. Both are up 14% at that point in time. This is where the Sharpe ratio helps .
A high Sharpe ratio indicates that a portfolio has better risk-adjusted performance. One cannot sensibly compare returns without considering the risk taken to earn that return.
If I can earn 80% of the return of another investor at only 50% of the risk then a rational investor should simply leverage me at 2x and enjoy 160% of the return at the same level of risk.
This is very important in the context of Execution Advisor algorithms (EAs) that are popular in the retail community. You must evaluate historic performance by its risk-adjusted return — not just the nominal return. Incidentally look at the Sharpe ratio of ones that have been live for a year or more ...
Otherwise an EA developer could produce two EAs: the first simply buys at 1000:1 leverage on January 1st ; and the second sells in the same manner. At the end of the year, one of them will be discarded and the other will look incredible. Its risk-adjusted return, however, would be abysmal and the odds of repeated success are similarly poor.
Sharpe ratioThe Sharpe ratio works like this:
You don’t really need to know how to calculate Sharpe ratios. Good trading software will do this for you. It will either be available in the system by default or you can add a plug-in.
VARVAR is another useful measure to help with drawdowns. It stands for Value at Risk. Normally people will use 99% VAR (conservative) or 95% VAR (aggressive). Let’s say you’re long EURUSD and using 95% VAR. The system will look at the historic movement of EURUSD. It might spit out a number of -1.2%.
A 5% VAR of -1.2% tells you you should expect to lose 1.2% on 5% of days, whilst 95% of days should be better than that
This means it is expected that on 5 days out of 100 (hence the 95%) the portfolio will lose 1.2% or more. This can help you manage your capital by taking appropriately sized positions. Typically you would look at VAR across your portfolio of trades rather than trade by trade.
Sharpe ratios and VAR don’t give you the whole picture, though. Legendary fund manager, Howard Marks of Oaktree, notes that, while tools like VAR and Sharpe ratios are helpful and absolutely necessary, the best investors will also overlay their own judgment.
Investors can calculate risk metrics like VaR and Sharpe ratios (we use them at Oaktree; they’re the best tools we have), but they shouldn’t put too much faith in them. The bottom line for me is that risk management should be the responsibility of every participant in the investment process, applying experience, judgment and knowledge of the underlying investments.Howard Marks of Oaktree Capital
What he’s saying is don’t misplace your common sense. Do use these tools as they are helpful. However, you cannot fully rely on them. Both assume a normal distribution of returns. Whereas in real life you get “black swans” - events that should supposedly happen only once every thousand years but which actually seem to happen fairly often.
These outlier events are often referred to as “tail risk”. Don’t make the mistake of saying “well, the model said…” - overlay what the model is telling you with your own common sense and good judgment.
Coming up in part IIIAvailable here
Squeezes and other risks
Crap trades, timeouts and monthly limits
Disclaimer:This content is not investment advice and you should not place any reliance on it. The views expressed are the author's own and should not be attributed to any other person, including their employer.
Type in the correlation criteria to find the least and/or most correlated forex currencies in real time. Correlation ranges from -100% to +100%, where -100% represents currencies moving in opposite directions (negative correlation) and +100% represents currencies moving in the same direction. Click on a correlation number to view a historical correlation analysis and compare it against other ... Hi all, I wanted to share this chart with you - I am hoping it works when I publish it and the arrows stay inline with the text - something very interesting we all know about currencies moving in tandem with each other to some degree different economic events causing them to stop moving together but eventually they will again. As a forex trader, if you check several different currency pairs to ... And later, I’ll uncover the pairs that are affected by changing commodity prices as well as a few of the safe haven currencies. Don’t know what those are? No problem. By the time you finish this section, you’ll be a currency guru! Major Currency Pairs. Major currency pairs are to the Forex market what Apple and Amazon are to the stock market. To be an effective trader, understanding your entire portfolio's sensitivity to market volatility is important. This is particularly so when trading forex.Because currencies are priced in pairs ... Correlation is the ability of one trading asset to repeat the directed movements of another one. On the financial markets, this phenomenon can be visually identified in pairs with gold and silver, as well as various types of oil and oil products. For us, we trade only these Major Forex pairs because the liquidity of these pairs created very tight spread which is good for us as traders. Our recommendation if you want to be in the trading business in the long haul is to trade only these 7 Forex pairs. In fact, we usually trade only EURUSD and GBPUSD. We might dabble with the other but our focus is EURUSD and GBPUSD. We just love the tigh % OF AVERAGE DAILY TURNOVER:* 12.9% USD ADDITIONAL INFO COUNTRY: United States CENTRAL BANK: Federal Reserve System NICKNAME: Buck, Greenback % OF AVERAGE DAILY TURNOVER:* 84.9% COUNTRIES: United Kingdom/United States 2012 HIGHS & LOWS: 1.6309/1.5233 DAILY AVERAGE MOVEMENT IN PIPS: 110.4 PAIRS THAT CORRELATE: GBP/NZD, GBP/CAD, GBP/AUD PAIR TYPE ... The most volatile forex pairs (forex pairs that move the most) in the last several years are exotic pairs and then GBP cross pairs such as GBPNZD or GBPCAD etc. The least volatile currency pairs are EURCHF, EURUSD, AUDCHF, USDCHF, EURCAD, etc. But let us start with the explanation… Let we define volatility and see the difference between risk and volatility: Volatility is not always a bad ... My Google search for least correlated Forex pairs came up empty so I decided to run the analysis myself. Using information from this list on Oanda I created a JS script that would loop through the table entires and return the least correlated pairs based on the 1 year value. Major Currencies. Max correlation between -0.50 and 0.50. Learn about the major currency pairs in the forex market and how to start trading them. View the top currency pairs list and live forex pair prices.
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