The Portfolio Optimizer for Wealth Management

Improved risk reduction using a dynamic factor model

Summary

When a client has external unsellable assets, giving them the correct portfolio is not trivial. We use a sophisticated approach to invest the money that we have control over, so that their total assets match their target allocation as closely as possible.

Scenario parameters

This is a simple example for purposes of demonstration.

Held by us: $1,000,000 in cash, which we are free to invest.
External: $250,000 in VIG (Vanguard Dividend Appreciation ETF).
Target allocation: A balanced mix of 7 asset classes, with a target of 8% in the high-dividend US stocks asset class. (Note: it is slightly lower, as we reserve 20 bps of the total for cash)
AUM fees: 25 bps annually, charged ~2 bps / month.

Background

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:

Simple: We could spread the effect equally across all asset classes. We can buy $150,000 / 6 = $25,000 of each of the remaining asset classes. Although it is not the case here, this may run into problems if there are asset classes where the target is for less than $25,000. A slightly better variant is to make the reduction bigger for asset classes that have a bigger target percentage. This pro-rata approach is better, because it maintains the relative balance of the 6 remaining asset classes.
Factor-based risk: noting the correlation between the various asset classes, we can reduce the holdings of the asset classes that have the most similar behavior to US dividend stocks, based on a mathematical model. For example, the model can notice that all equity asset classes are more correlated to each other than to bond-like asset classes, so it can add or subtract one equity class to compensate for another. Things are more complicated in practice, but this illustrates the main idea.

The purpose of this simulation is to show that the factor-based approach does better at tracking the target allocation than the simple approach.

Results

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).

In the simple case, the allocations to all classes are reduced. The only thing that matters is the percentage in the target allocation - not the similarity to dividend stocks. Therefore, equities are overweight as a whole, leading to worse tracking.
In the factor-based case, the allocations to developed foreign equity markets ("dev" - blue) and total US equity ("useq" - cyan) are decreased more than in the simple case, so as to compensate for the large external stock holding. Another way to see this is is to notice that the line for municipal bonds ("muni" - red) is higher - closer to 0 - in the factor-based case, which means we are less underweight MUB.

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.

Conclusion

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.