Since the external VIG holdings are so large, they cannot be accommodated simply by reducing the internal dividend ETF holdings: even if we buy no dividend ETFs with the $1,000,000, the aggregate portfolio will have 20% of dividend stocks ($250,000 divided by $1,250,000), versus the target of 8%.
Of course, this 20% will fluctuate somewhat over time due to price movements, but not by much. Therefore, for purposes of this discussion, we will focus on the first day for simplicity.
Our target for dividend stocks is 8% * $1,250,000 = $100,000. We have $250,000, none of which we can sell, because it is externally managed. So we must buy $150,000 less of everything else, in some combination.
Here are various possible ways to deal with this problem:
The purpose of this simulation is to show that the factor-based approach does better at tracking the target allocation than the simple approach.
When we use the factor model , the total account value (black) is closer to the benchmark after fees (blue) than when do do not. You can also see both lines in the same chart here.
Benchmark after fees represents the best achievable result in practice, and is a more fair way to look at performance than the plain benchmark; even if we rebalance daily without transaction costs to track the target allocation perfectly, AUM fees would still cause a small amount of underperformance.
You can see how these better results are achieved by looking at the 'Asset Tracking' tab in the simple and factor model cases. In both cases, the US dividend stocks ("div" - mint green) asset class misallocation (actual percentage minus target) is large at about 12% (20% actual holdings minus 8% target). This is unavoidable because of the large external VIG holding. (Note: it is more like 14%-15% overweight towards right half, but VIG goes up more than the benchmark, and the system cannot reduce it further).
You can also see this is in the 3D risk model charts. In the chart for the factor-based approach, click on any of the individual securities (e.g. VTI) on the legend on the right, so as to hide all stocks and make the effect easier to see. The black square labeled 'All' (i.e. the portion held by us, plus the external holdings) is very close to the yellow (target). Because the squares are large enough to overlap, this is easier to see either if you zoom in (use the buttons on the top right of the chart), or if you look at the projections below (the small 'shadows'). However, if you repeat this with the chart for the simple approach, the square for 'All' is farther from the yellow (target). The charts default to the first day in the trading simulation; however, you should also observe the same if you choose a different date.
We are not aware of any firms in this space that can accommodate external holdings in a fully automated fashion. We took things a step further by jumping directly to an improved factor-based approach.