I now put both alternatives (start from zero, start from optimal rounded) to a broad range of tests with different portfolios, time frames and capital.
Some qualitative observations:
Zero has more leeway to put on large instruments that get selected in the first few iterations and reduce the tracking error by a big chunk. Because of that it looks a little bit more diversified than rounded in the individual positions but overall there is not much difference in performance. I would consider them as equals on a long backtest. Rounded has about 10% higher costs but makes that up by a little bit lower volatility. In general it undershoots the risk target more than zero. In position selection rounded tends to track the smaller sized instruments more exactly and therefore looks a little bit less diversivied.
I also tested different shrinkage methods on the correlation and covariance matrices. On the full backtest the differences are neglible.
Now to the ugly part: All these differences can make a huge difference in the shortterm. You may end up with completely different performance for something like 2 years. I did not expect so much sensitivity of shrinkage methods, shadows costs, cost buffer or the search algorithms. It could be quite a frustrating experience if you have an unlucky combination running. But I guess a trend follower is kind of used to that.
Average tracking error itself is a pretty useless measure in absolute terms. It does not reflect closeness to the whole portfolio.
When in doubt do everything? As a little gimmick version I added up the positions of both search methods and divided by 2 (rounding up). It actually is the best version by a small margin and hits the risk target best.
Some qualitative observations:
Zero has more leeway to put on large instruments that get selected in the first few iterations and reduce the tracking error by a big chunk. Because of that it looks a little bit more diversified than rounded in the individual positions but overall there is not much difference in performance. I would consider them as equals on a long backtest. Rounded has about 10% higher costs but makes that up by a little bit lower volatility. In general it undershoots the risk target more than zero. In position selection rounded tends to track the smaller sized instruments more exactly and therefore looks a little bit less diversivied.
I also tested different shrinkage methods on the correlation and covariance matrices. On the full backtest the differences are neglible.
Now to the ugly part: All these differences can make a huge difference in the shortterm. You may end up with completely different performance for something like 2 years. I did not expect so much sensitivity of shrinkage methods, shadows costs, cost buffer or the search algorithms. It could be quite a frustrating experience if you have an unlucky combination running. But I guess a trend follower is kind of used to that.
Average tracking error itself is a pretty useless measure in absolute terms. It does not reflect closeness to the whole portfolio.
When in doubt do everything? As a little gimmick version I added up the positions of both search methods and divided by 2 (rounding up). It actually is the best version by a small margin and hits the risk target best.