Statement 3 is incorrect. Rebalancing ranges for non-US developed equity
should be wider than US equity under the cost-benefit (not proportional range)
because it has higher transaction costs. Rebalancing ranges under the
proportional range approach are defined as +/– 600 basis points for all asset
classes in this example and are computed as follows.
Rebalancing ranges for bonds under the proportional range approach:
20% × (1 + 600 bps) = 20% × 1.06 = 21.2%
20% × (1 – 600 bps) = 20% × 0.94 = 18.8%

How do we know that there are higher T costs for non-US developed equity? Or is it more of an assumption, than a certainty, to explain the wider range?

How do we calculate the Cost-Benefit range?

By the way, would Statement 3 have been correct if the range was narrower? i.e. Statement 3: Rebalancing ranges for non-US developed equity should be narrower than US equity under the proportional range approach because it has a higher currency risk.

The cost-benefit rebalancing approach is more dynamic and adapted way to rebalance a portfolio according to a specific scoring related to tax, correlation between assets classes, asset quality, tracking risk, bid ask spread, commissions, tax loss harvesting and so on as compared with balancing range approach (either fixed or proportional).

Cost-benefit approach leads to a proprietary quantitative and qualitative method of scoring according to specific variables (see above) that triggers or not opportunistic rebalancing so that to minimize dispersion of returns, tracking risk and tax.

In the first statement we just have to make the calculation to assess that the result provided is correct.

In the second statement, we are given a specific information relating to correlation and cost benefit approach which effectively can give a specific score to this variable for rebalancing purpose. We learned that a higher correlation between portfolio’s assets classes induces a wider corridor (because assets move in sync) and a lower correlation induces a narrower corridor.

In the third statement we are told that non US developed equities face higher currency risk (not higher transaction costs). We know that higher risk means higher volatility and that a higher volatility implies a narrower range. As a consequence statement 3 appears to be the only incorrect statement.

Note: you don’t need to make any calculation for statement 2 and 3. The second part provides «hypothetical » cost benefit balancing ranges for illustration purpose. But in fact we don’t need it.