In my reply to this, I should have been more explicit. When you have two or more instruments that you are not sure what their connection is, the right tool to use is something like a VAR model. When you have two or more instruments where you are pretty certain there is a fundamental tie between them, then it is more useful to use a VEC model. Notice that thinking about both of those it is useful to think of them under a more general category of Factor Models. That answer I think is more useful than the one I gave.
What are your ratios or the ratios of the chart posted? 1:1/1:1 ??? Also, update the chart to show the last few months that have been critical. So let me break this down. You go long/short the US medium terrm IRs against the Canadian dollar, and play that long/short against the SPX in dollar terms. Let me think about this. It seems like a reasonable assumption, but this is probably 80% play on oil, since Canada, and UUP in general at least at the moment are highly correlated to oil (Although Canada seems to have completely come off that rail recently). I would add one more symbol. USD/NOK to balance it out. If the trend goes away, you got something. That can be done with another logical symbol, and/or the right ratio. I need to think about it. Regardless, I think you are approaching your trading in the "right" way. Right is in quotes because if you had a continuously adjusting model instead of a position type model, the right strategy would be different. Think about an options position and how you dynamically delta hedge it. Notice they are both about risk. dR/dt, risk(s) over time of position, determines correct strategy. Once you control risk in trading, the sky is the limit.
Excuse/ignore the dates at the bottom of the chart. I agree it is mis leading but i havent fixed that yet for public display. The EOD data is indeed current. The ratio of the legs is presently to neutralize volatility( I use a 60 trading day average of daily returns) so , for example I would have to have twice the dollar amount of UUP to expect the same daily returns as SPY. However, your question exposes a possible problem. I run two iterations of the same program to create a 4 legged position. The 1st neutralizes two symbols to a 2 legged spread. The 2nd iteration creates a 4 legged position from two spreads. I need to check that average daily returns of the spreads are neutralized as well. Funny, that you mention oil etc. when posting the chart, one thinks of "off the chart" assets Like oil and euro etc..and the catalysts in those assets that may cause, and do comtribute to "regime change". Regarding dynamically measuring and hedging risk well, i am walking down that path further within my present capabilities. That is why this thread is appreciated but yes, most of the math is not presently in my tool kit. I would have CB things like FOMC meetngs and minutes( asset changing events every three weeks) alomg with like events in Europ ,Japan , China, Brazil at the very top of my list but....we all know that. Over time you do get a good feel for ranking the importance of the eco list by noticing their effect on broad asset classes. I have a very informal data collection of event dates that move assets and would like to work more on this area as well.
This is a great thread and thank you for the detailed reply. My mathematical background is limitedLike @eurusdzn my set of mathematical techniques for research is growing. I'm currently utilising regression and simple ADF to find suitable spreads for 2 assets. Next, I will be exploring spreads consisting of more than 2 assets using johansen cointegration, which I assume is another factor model like PCA. How it compares to PCA? - I yet don't know. Edit - I'm not from a mathematical background so please be gentle
"A regime is a region in state-space in which a complex system retains the same attributes such as structure,functions,and feedbacks. An attractor refers to a stable equilibrium state and the basin of attraction, which is equivalent to a regime,defines the state-space region in which initial conditions will tend to move towards the attractor (Walker et al., 2004). Complex systems often possess more than one attractor between which repellers (or unstable equilibrium state) exist as a boundary for the basins of attraction (Scheffer, 2009). Regime shift occurs when the system crosses such repellers.Dynamics of the system will be governed by completely different processes in an alternative regime (Scheffer et al.,2001). Regime shifts are often driven by external stochastic events or drivers. Stochastic events, characterized by fast variables, cause regime shifts by pushing the complex system toward alternate regime across the repeller. External drivers,characterized by slow variables,also can cause regime shifts by gradually changing the size of the regimes(Walkeretal.,2012). When an external driver reaches a critical value, which is known as bifurcation point, the original regime disappears and only the alternative regime remains(Lenton,2013;May, 1977;Scheffer et al., 2001). Thus, the complex system ends up being in an alternate regime because that is the only regime existing under the new conditions as changed by the external driver(s). Here,both external drivers and stochastic events are referred toas external forcing(s)..." https://www.academia.edu/8646869/Re..._Model_and_Case_Studies_in_Hydrologic_Systems From hydrology, but the similarities between complex systems are at least homeomorphic. In any event, it is useful to learn multiple mathematical languages when describing time series. For those that like to categorize using the "Chaos" or more generally Complexity Theory point of view. One of the biggest impediments to learning anything is picking up the idioms. Already, we can learn that "regimes" (often used in economics) in the language of complexity theory is a "basin of attractor". We begin to wonder what the Categorical Homomorphisms allows us to carry the dictionary of our vocabulary to complexity theory. For example, what is a PDF in complexity theory? That gives us a map from one part of our brains understanding to another.
Does your chart represent the actual units you are using in trading these instruments. Or are they 1:1:1:1 in the chart?
To tone it down a bit from the somewhat complicated mathematics, we can still read useful articles on how we should approach trading and why. "All" trading may come down to finding probability distributions (density functions, likelihood functions, survival, etc, etc), whether you are aware of it or not. Then, if you bet with an edge (expectation is positive) repeatedly, the central limit theorem becomes your best friend. That is all HFT firms do. In the figure in the article below, it is neat to see how your probability distribution from rolling one die changes when you roll two die. Similar things happpen when you trade cointegrated instruments, only more so. Every trader should frame this: "We start to see the effects of a most amazing theorem: the central limit theorem. The central limit theorem boldly promises that the sum or average of a series of independent variables will tend to become normally distributed, regardless of their own distribution. Our dice are individually uniform but combine them and - as we add more dice - almost magically their sum will tend toward the familiar normal distribution!" If you don't impose a probability density function on your trading, the market will impose one on you. May you vaya con Dios. Find The Right Fit With Probability Distributions http://www.investopedia.com/articles/06/probabilitydistribution.asp P.S. Notice that a die has point probabilities whereas stochastic variables have probability densities.
All momentum traders wish that their PDF looked like this: This is the famous Arcsine distribution. Do you notice something? The probabilities edge upwards instead of downwards. But the strangest thing is that this distribution is talking about a Random Walk!! How can this be? The classic arcsine law says that a random walk will spend most of its time on one side of the axis with probabilities closer to either 1 or 0, than to be near 0.5. The result defies intuition because you would expect that the proportion of time the walk spends on one side of the axis would be 1/2. In fact thats the least probable. We can use our usual coin toss to explain this. If Heads, A wins 1 unit and if the coin comes up Tails, B wins 1unit . After twenty iterations, the probability that either player A or player B has been in the lead for each and all of the twenty rounds is about 32% !! In other words, the probability that a player is being behind for each and all twenty rounds. In contrast, the probability that one of the players was in the lead ten of the twenty rounds is only like 10%. This explains a great deal of momentum returns, and therefore one has to be very careful with "hot hands" - they are totally within the realm of randomness. It is useful to know that the arcsin distribution is a special case of the beta distribution, which in turn is a Conjugate prior for the Bernoulli, binomial, negative binomial and geometric distributions.
The chart ratios are roughly( based on 60 day volatility) 526 shares IEI ------------- 200 shares FXC. Over 100 shares SPY ---------- 216 shares UUP Away from computer. Would have to check accuracy later.