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May be only a subset of four assets is uncorrelated. Some of the other assets have very substantial correlations as apparent from running the correlation heatmap script on the Z8 asset list. What has motivated this particular collection of assets? Yes, the Z8 ETFs have been selected by fundamental considerations only, such as covering market sections with a positive perspective. They were not selected by their correlation.
But you can replace them with any other assets if you want. Please keep us up to date like this. I added some etfs to the script but when i run it, it prints a negative number for some. TLT — 3 contracts at Do you have any idea why this might be or how to fix it? If you have nothing changed with the script, let me know which assets you have added. When I get negative numbers too, I can most likely tell you their reason.
I just removed one and now everything works fine! Hi Johann, does this work for stocks? BTW, how does one make use of the output?
The price for 1 unit of AAPL now is I think the former makes more sense. Yes, this also works for stocks, however they have higher volatility than ETFs, so you need more different stocks for diversification. You buy the position at market. The displayed price is only from the Yahoo history from the day before. Hi Johann, thanks for the helpful reply. You mentioned that the script shall be run once a month to open or close a position. Hi Johann, thanks for the reply.
I have compiled a list of stocks that I wanted to trade and there are about I am running Zorro 1. If you changed NN to a large value, put also all arrays outside the function, or make them static.
If I remember right, the default stack size is some KB, so too large local arrays can exceed it. Could you mail me tell me how to create account and work with your system step by step? A short one can be found in the Zorro manual, a more extensive course is offered by a fellow blogger, Robotwealth. Yes, prices in backtests should be and are adjusted when not otherwise mentioned. I add script below to your MVO script and expect to see an equity curve, but nothing happened, what I did wrong?
Since there are no optimized parameters in the script, there is also no WFO. How can I do the same thing to MVO? I still need to grab a sense how its results look like before I put it into live trading. In ther word, how can I test MVO? By entering and closing positions. Z8 does this, while the scripts here only plot the return curves. I think we have three metrics here for asset candidates, mean, variance and correlation, which one you think is more important? When looking at a single asset, mean divided by square root of variance is a more important metric than mean or variance alone.
And the correlation is insofar important as it affects the total variance of a portfolio — lower correlation means lower total variance. Unfortuntately my boss does not allow me to check out program code of more than 10 lines — at least not without demanding money. But whatever does not work with your code, you can easily find out with the debugger. Help yourself, so help you god. You gave out 2 versions of MVOtest, when you calculate BestVariance, you use different weight cap, 0. Did I understand correctly?
From our experiments so far, many assets and low weight caps are better than few assets and high weight caps. When you say better, I guess you mean low variance, not necessarily high return or high Sharp Ratio, is it? Only when it has positive expectancy, such as assets derived from stocks or indices. Maybe XIV, which can rise to high levels, but might impose high risk. Any metrics to measure overall correlation of all assets like mean divided by sqrt of the variance except the heatmap?
There is no such metrics as to my knowledge, but you can easily invent some. For instance the sum of all elements of the correlation matrix divided by the number of elements. Or should we modify the assets list periodically? Or we should not modify the asset list at all! By all means feel free to use other assets. From what I hear, most people use their own asset lists with the Z8 strategy, instead of the default assets. I understand we can use other assets than AssetZ8, my question is: Or we simple add the new ones to the list, then we have a longer list.
I understand your question, but that is completely up to you and the performance of the system. If an asset performs spectacularly bad, or if you got bad news about it, remove or replace it.
Or if you encounter some promising new assets, add them. The system just determines the optimal portfolio weights. Aside from trading costs there is no particular disadvantage in adding or removing assets. Thanks for posting the wonderful articles. I enjoyed reading all of them. The backtest performance of the Z8 strategy is remarkable, with very little drawdowns.
I tested the open script you included in this blog using the same 24 ETFs as in the Z8 strategy. But the results are not nearly as good as Z8. You mentioned in an earlier post that Z8 is just a pimped-up version of the script. Would you mind shedding more light on the major differences between the two? Thank you very much! Z8 is a bit optimized. AFAIK it uses a days lookback period for faster adaption, and a position on the EF very close to minimum variance.
Thank you for your reply, Johann. Conventionally, covariance is defined as the Sum divided by LookBack Because the difference is just a scaling matter, it should not affect the backtest performance with the same parameters. Can you please look in it? I can not see a difference with the MVOTest script when I multiply the covariance with a factor or divide them by Lookback With which test did you get a difference? I meant the last script included in your article.
I think there may be a small typo in the script. Yes, zero is correct. The release version had a Cap parameter added to the markowitz function. Why Zorro could not download from Yahoo? I tried a couple of times, but failed and gave out error code I checked Yahoo, it looks fine.
It used to work very well. If we can, how? Sure, you can optimize it just as any other parameter. Set LookBack to the maximum period and optimize the period used for calculating the means and covariance matrix. Is it possible to modify the Markowitz function to allow constraints on the maximum weight of each asset?
If not, do you know of any good Quadratic Programming package written in C that you recommend to use with Zorro? Hi, can I understand more about this line in the code? The result does vary.
Did a lot of work and coding of this in Python. Having followed trends in the futures market for many years I was looking for something very different. Unfortunately this approach is TF thinly disguised. Yes, with long term returns for calculating portfolio weights, most algorithms end up with some sort of trend following, since trend is the main market inefficiency of long periods.
For something very different, you have to switch to short term trading and exploit mean reversion or other market anomalies. Not necessarily, I think. Perhaps certain carry trades perform a useful role in supplementing trend following. But more specifically interest carry trades on currencies although there is again perhaps a trend following element contrary to interest rate parity , roll premium on futures and premium selling with options.
None of which, sadly, are risk free. Actually, the problem with slow, long term systems is much the same as with short term stuff. Nothing has much predictive power and what worked yesterday may well not work tomorrow. Look at the shitty CTA returns of the past 5 years.
Your article on HFT and arb is a much better bet with those who have the right skillset even though we both know HFT returns have been on the decline in the recent low vol environment over the past few years. If you happen to have the many hundreds of thousands of dollars for the infrastructure. If you mean a portfolio for shorting, a possibility would be MVO applied to the inverse momentum.
Yes, exactly, for shorting. The idea is if you have a pairs trading strategy or any strategy that is capable of going long or short, how to properly allocate amongst a large set of pairs. So I presume you could potentially take the trades for these pairs, split them into Long and Short and then run MVO and the inverse momentum MVO to figure out how you should allocate to any particular trade.
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