Quant basket trader? I need your help!

Are there quant basket traders out there? I need a hand from those of you who use quantitative methods to size and time the opening and the closing of their basket trades --as opposed to "I close when I feel happy with my profit"--

I'm not myself a basket trader. My motivation comes from the fact that I'm trying to develop a system that some times, mainly in the ranging periods, is equivalent or at least very similar to basket trading.

I tried to find if there is an optimal method to open and close a trade under the assumption that the instrument is mean reverting. I found a very complicated method trying to solve this "double stopping problem" (in the pdf). The solution is based on the subjective cost of staying in the market longer vs the expected increase of the reward. But the interest rates are low nowadays. It may be interesting for people using options, because of the time decay, but it doesn't seem to fit my needs.

I also found a very simple method which consists in maintaining a lot size linearly proportional and opposite to the distance of the price to the mean measured in deviations. In short I add on my losers at every standard dev. A grid. But I don't get the rational behind this idea. Say the price is at the mean. I'm flat. It goes 1 SD below the mean. I open a lot long. It goes to the second SD below the mean. I add another 1 lot long. If the price returns at 1 SD shall I close one lot to keep the linear exposure?

In the case the price goes to the 3rd SD I've 3 positions open and a floating loss of (2+1+0=) 3 times the SD. I only get 3 SD if it returns straight to the mean but a 6 SD floating loss should it reach the 4th SD. At first it seems better to hold on and wait the price to come back to the mean and get a 6 SD profit. But since the price is wandering up and down before returning to the mean perhaps the method makes sense. If price goes -1, -2, -1, -2, -1, -2, -1, 0 the profit is 4 instead of 3. For sure I dislike the idea of adding on the losers while the price is going against my positions. Especially because I'm conscious the range won't last forever and I clearly don't want to add against a breakout. I checked the ranges don't last long enough to offset this loss.

Because of the mean reversion assumption the probability of winning can't be used: per assumption/definition it is 100%! I kept thinking and found out that it would make sense to weight the exposure by the probability of being at a given level. I use a normal distribution to keep it simple. The most probable position of the price is on the mean. But it is the target level so no profit. The farther from the mean the more profit but also the less probability of being there. It is better to be more exposed when there is more potential. Let's multiply the potential profit (the distance in SD) by the probability N(x), N the normal distribution:


The exposure is maximal at 1 SD above or below the mean. Using the formula I scale out my losers. Sounds good in case of a breakout of the range. But I also scale out of the winners. And if the price ping-pongs between two levels I take a loss even if the price eventually reverts! Clearly not good. I feel like the exposure can't be solely based on the position of the price in the range.

How do you manage it?

PipMeUp,

If the market you are targeting is not really mean reverting, then the question "find the optimal..." is ill posed. If the market is really mean reverting then any simple strategy to maximize the number of trades * (open - close) prices will do - then it just becomes an optimization problem and has to do more with assumptions about price excursions (how far and how frequent before reversion).

But I think you are talking about the former case where the mean is actually drifting over time. Are you assuming the basket is mean reverting or the individual components are mean reverting?

And it isn't even that simple. The mean can drift so those 3 positions at the 3SD level can tun into a loss at mean reversion. This is why I don't put much faith in mathematical models that rely on a zero mean for doing such computations. I think simulation is the only way to get an idea about how these strategies could turn out when applied over a large sample size of trades. And even there a new case that isn't in the simulation can break the model. I've soured on mean reversion because the underlying market structure indicates the presence of trends. I don't feel comfortable adding to infinity which is essentially what optimal means in terms of adding in a mean reversions strategy. The question of where (if) to place a stop for a mean reversion is a hard problem but it is discussed here and more ideas here and may give you some ideas.

If I were quoting for a bank, and a large price shock hit, I would stop quoting (not take on new trades), and only start quoting again once the price stabilized so I wouldn't get a bunch of under water inventory. There are variations where you require price to go above 3 standard deviations, for the add but only add once price has gone below say 2.9 or 2.8 deviations. You may filter out many cases where price runs to 4 deviations but you give up something for that assurance, and this can still get it wrong if the market pulls back at the wrong moment.

PipMeUp,

I've tried various mean reverting strategies. First (1) individual pairs, and (2) cointegrated baskets (a) 2 pairs and (b) 3 pairs. Both strategies on multiple TF's (1 hr to WK).

IMO after countless hrs of research and trading (live / demo): don't waste your time on this.

I did extensive statistical analysis of pivot levels for example. Stats show for weekly pivots (more or less for all pairs), if its an up week, then probability of H > R1 is about 0.8, and P L < S1 is about 0.2. Vice-versa for shorts. You can extend the stats to R2/R3/S2/S3 or any fraction in between. Basically its a normal distribution shifted up / down if its an up/down week.

Now of course we don't know before hand it it will be an up or down week, so I assumed a distribution between the two up/down weekly analysis.

So, I wrote an EA to test this. I assumed a probability distribution with the mean at the weekly pivot, and and position sizes which were inversely proportional to the probabilities at each pivot level.

So if P(R1) =0.6 and P(R2) = 0.1 (combined up and down wks), position sizes were a multiple of the inverse of this (so larger positions at extreme levels from weekly pivots).

This worked great in ranges, but then trends start and it lost.

Similar story to cointegrated pairs/baskets.

So I tend to agree with FxEZ: mean reverting strategies don't work so well.

Current research / trading is into direction grids based upon longer term trend screening (first weekly, then D/4hr directional agreement).

Edit: Forgot to mention, preliminary directional grid tests doing well. This requires (a) weekly analysis of trend, and (b) daily analysis of D/4hr trend to align with weekly to start grid. If divergence between (a) and (b), then hedge till conditions change to remove hedge. Also trade many non-correlated pairs, or all major crosses (25 or so) in small size.




Regards,
EZ

Oh ... forgot to mention in my directional grid test ... some human intervention I do. For ex: after looking at weekly trends, I look if (1) major news is coming out the next day (ex: NFP on F, so I shut down grids on Th), or (2) near major S/R for that pair, and (3) mid term (D/4hr) trends for component currencies for a pair (ex: EUR trend, CAD trend) for EURCAD.

With my prior rules and some manual human intervention, demo grid is doing well in 3 wks (2/1 equity/max DD ration based upon 1:1 leverage).

EZ

ezcurrency, since you brought it up here, my current thinking regarding why cointegration has trouble when applied to currency pairs has to do with the linearity assumption of regression. I think it's too much to ask two pairs to move in the same direction and in the same amounts (unless they are pegged). The relationship between correlated currency pairs may be more monotonic than linear and there may not be any truly long term cointegrated pairs, but many correlated pairs and correlated currencies. But it also may not be that simple as the relationship can morph into nonlinear also depending on changing fundamentals. In other words, the relationship between these pairs (and the function that best describes it) is complex and may change over time. By the way, this brilliant post changed my view about the viability of 2 pair cointegrations (hint it basically assumes a pair will be stationary around a mean which is the moving coefficient).

PipMeUp, the breakout of a range can occur at any point, temporarily invalidating the simple reversion assumption. You can maximize the variance of a basket, or minimize the variance of a basket. In either case the opposite condition, low / high variance is likely to occur at any point. Keeping variance in a fixed range may be futile. The harder you optimize / overfit for a certain level of variance, the more likely future variance conditions will be different from what you were optimizing. So PipMeUp, perhaps the way to increase your probability of getting low variance is to maximize it. Or more to the point, by maximizing a non-ranging characteristic in your basket, a ranging period may ensue next in your basket! I've done some cursory examination of the opposite - minimizing variance and trading the breakouts but haven't gone very far with the idea.

Thank you for your replies.

As I said, I'm trying to "adapt" some basket method to a ranging market (=one single instrument) because of their similarity. Don't worry ezcurrency I, as well, never found any cointegration between two currencies or pairs of currencies. I found something between Brent and WTI and also between CAC and DAX. I bit less between CAC and IBER. Strangly DAX and IBER aren't (no transitivity). For the currencies, nothing. Some people still believe Oil vs CAD but no longer since 2010. Currency pairs are highly correlated but that's only because of USD like an elephant on a see-saw swing. @FXEZ, I'm afraid searching a non-linear relationship would wide open the door to overfitting. But that's an idea to explore.

For sure my question/problem is definitely ill-posed. I shall explain more. My idea is that if/when the market trends I'm better off holding on my position(s) as long as the trend is in force (and sometimes a bit more but that's off topic). If the market is in a range, holding the position will simply let the unrealized profits return to zero: I have to take profit. In a trend going contrarian is doomed to fail and even when it works it is suboptimal. In a range I can trade both directions. This is perhaps the answer to the question "is the market ranging?": the market is ranging if and only if it is safe to trade both directions.

Regarding your concern about the "where you we stop adding?", as I said in the first post I don't really like the idea of adding to a losing set of positions. A quadratic drain on the account is NO-GO. I was more thinking taking a loss and reentering lower/higher. And when do we completely stop? If the price goes beyond the 3rd SD (=> http://www.forexfactory.com/showthre...06#post6772106) or if the estimation of the trend rejects the ranging market assumption.

The ranging condition is too short lived. There isn't enough data to regress an OU process. I can't know/estimate the half time to reversion for instance. FXEZ's 2nd link made me wonder if I could estimate some "energy" to guess how far I can expect the price to move away from the mean, so that I could choose either the scenario B) or C). I just had a very very quick look at some charts. It looks like (to be confirmed) that the Hurst exponent can be used: range+persistent=wait 2nd SD, range+antipersistent=buy 1st SD.

If this works where is the exit? the mean or the opposite signal?

I thought about this optimization problem. To optimize I need a loss function. I'd like to evaluate, thanks to the hindsight, if it would have been better to be long or short at a given point in time.

Let's say I pick two points A and B on a chart and I ask the question "would it have been better to be long or short at the point A?". You will tell me, dude that's obvious, if B is above A you should have been long!

Now let's say B is above A and I pick a point M inbetween A and B. Say M is below A. I ask the question "would it have been better to be long or short at the point A?". You will tell me, dude that's obvious, X is below A you should have been short.

It was obvious I should have been long, now it is obvious I should have been short but nothing changed except I looked at another point on the chart!

Now let's imagine I pick another point, X, before A. Let's say X is below both A and M. We get a HHHL zig zag. I ask the question "would it have been better to be long or short at the point A?". Despite the perfect hindsight scenario, is it wise to include the counter trend in the loss function?

Ultimately any machine learning is about estimating the joint probability of the state of some model and the data. Can we build a loss function that favors the "let the profits run" tenet given that the trend shall by no mean be included in the definition of this function (otherwise it become biaised)?

After some more thinking I built such a loss function. The problem is that I can't use it to determine the best exposure I should have at a given point in time in the market!

Why? Because the best exposure I can have at a given point in time doesn't only depend on the market and what it will do next but it also depends on my current exposure in the market. For instance if you knew the market is certainly about to start an up trend you would want to be long as much as the trend is in force and take profit at the end. You would give a high value to this trade (big size). But if this trend is about to end you would surely value much less opening a position (small size).

Imagine two traders who see this trend about to end. One of them is already long since the beginning and the other one is not in the market. The first one has no reason the close, even partially. He's better off waiting the top. But the second may not even consider opening a trade at all because he's too late. Each see the same market and have the same expectation about the future. Yet their respective optimal exposure in the market are totally different!

I'm going to be as discretionary as possible, so take it with a grain of salt:

1 - Everything about the strategy should be objective. This includes entries and targets (ie: no subjectivity towards "trends").
2 - Positions should be dynamic in accordance towards the variance of said target (you seem to already have this down).
3 - Build the system in such a manner that allows you to measure the market from your strategy alone (meaning, you have a good idea where the market is at due to the results of your strategy. Furthermore, this will allow you to understand when abnormalities are present, and how to position yourself accordingly).
4 - Stay the hell away from MT4. (Build your own system / frame from the ground up. Know how your system will interact with databases, and choose the appropriate languages / tools accordingly. Personally, I would steer one away from using Windows whatsoever).
5 - If you aren't parsing tick data, you're wasting your time.
6 - If you aren't parsing level 2 data, you're wasting your time.
7 - Last but not least, stay the hell away from MT4.

It seems to me you missed the point of the previous post. Two very exact same traders, with the same mindset, skillset, risk tolerance, discipline and the same anything you could think of; two clones. Both trading the same market at the same time, getting the same information being candles, ticks, level 2, news, fundamentals and/or anything else you could think of. Both having the same vision on the market, the same expectation and the same forecast. Yet their mathematically optimal next trading decision will be different depending on the fact that one is already in the market but the other is not!

1- There is always subjectivity in the trend because there is no such thing as THE trend. YOUR trend depends on your trading horizon, which is
personal and non-objective. There is no preferable trading horizon. Once the trading horizon is set the trend can be objectively defined.
2- Yes. But how given the first paragraph?
3- How to build a strategy if I need it to estimate the market which is required to build a strategy? I see a chicken-egg problem here.
4- 7- MT what??
5- 6-
I'm eager to read a thread of yours or someone else about a statistically validated edge found in ticks and/or L2 data. I couldn't find historical L2 to make stats. I have never found any value in ticks not even at the very short term. At least not beyond trading fees. Note that I'm not a scalper and I don't want to be a scalper. I know what is behind "I'm right 95% of the time". The only strongly statistically significant edge I found is in the trend. Any indicator I could test or write myself are always only working if they go with the trend (= they are random and the trend does the job).

Despite the apparent paradox there seems to exist statistical validity to Benevolent's statement. The strategy itself is part of the elements to determine if the market is bearish or bullish!

To estimate if it is preferable to buy of to sell at a point in the chart I use a loss function which contains a free parameter. This parameter controls how much you consider the risk of entering the market. Originally I used it because the estimation is done in hindsight. Therefore it is trivial to buy if the next swing is up. But I wanted to simulate the uncertainty. So I introduced a parameter to penalize over trading.

By varying this parameter the optimal positionning changes. For instance if the strategy considers a small SL (risk unit 1), it prefers catching a lot of small moves. The strategy disregards the trend because its effect is limited in the short term. If the strategy considers a very big SL (risk unit 5), it prefers fading the extremes and let the profits run: it tries to catch the big trends from the start.

In the excel file the horizontal axis is the (estimation of the) trend. Left side is extreme down trend, right side is extreme up trend. The bolded column is the range condition. The vertical axis is the position of the price with respect to the mean. The upper part is above the mean. The bolded row is the mean level. The units are in standard deviation. The numbers in the cells are just a unitless score (focus on the color instead). Red=sell, Green=buy.

Why do I keep posting in this forum seeking for an educated discussion with people trading out of Chinese proverbs?

keep posting, some of us are very interested in your point of view. I only wish i could contribute something meaningful to the conversation

Confucius say: "Better a diamond with a flaw than a pebble without."

Can you upload your template? Where do you put your SL and TP? Let's make it an EA!

Since the SL seems to have a great impact on what the optimal strategy is let's fix it so some arbitrary value. Let's say I want to trade a 10 pip range chart with a 10 pips SL. Where shall I buy and sell?

The black line is the estimated mean (which is not a straight horizontal line btw). The shades around it are the first 3 standard deviations. The color of the shade indicates the strength of the trend

And this is the heatmap generated for it:

Examples of the three circles on the heatmap (not exact, just visual to fit on the same screenshot)

Hello PipMeUp,

Both your statements are correct. The definition of a trend is always subjective and yet a trading system needs to be objective in defining a trend, identifying a potential start of said trend and defining a point where, if reached, the trend can be said to have ended. A trading system is therefore an objective set of criteria used to execute trading based on subjective beliefs about markets.
A trading strategy should be built from a logical assumption that flows from your beliefs about the market.