location mix will be identical within each of the three entities. If there is a 10 percent allocation to public equity, 10 percent of each entity will be allocated to public equity. We will, however, allow each entity to choose between taxable and municipal bonds as appropriate.

Figure 31.2 shows the improvement in the efficient frontier derived from the estate plan. Based on the 8 percent volatility solution, the expected future real wealth increased by 28 percent, from $20.6 million to $26.3 million. Most of the increase came in a meaningful reduction of estate taxes from $37.3 million to just $12.1 million (in nominal dollars).

Now we will introduce asset location. We will use optimization techniques to find the ideal mix of assets and location for varying levels of risk. The optimizer will be allowed to manipulate the allocation to asset class and location according to the following instructions:

Maximize: Expected future value net of income and transfer taxes

Subject To:

Initial grantor trust assets = $8 million Initial direct assets = $15 million Initial retirement assets = $2 million Cash in direct assets S 4% of direct assets Total hedge fund ë 10% of total assets Total private equity ë 15% of total assets Total initial risk ë X

FIGURE 31.2 Impact of Estate Planning: Expected Real Wealth of Children in 20 Years Net of Income and Transfer Taxes

The optimizer uses standard programming techniques to find the best solution to the stated problem. The best solution is the mix of asset allocation and location that gives the most expected future value of net income and estate taxes while abiding by the constraints specified earlier. We imposed limits on the allocation to illiquid assets and required that there be some cash in Mr. and Mrs. Jones' personal account. These are typical requirements. From a practical point of view, investors do want to limit their allocation to illiquid investments.

We mapped the efficient frontier by optimizing at different levels of total risk.3

3The optimization process treats each entity as a separate pool of assets. Within each pool we assume there is continuous rebalancing to maintain the target asset allocation of that entity. In the case where there are no entities, and also in the case where each entity has the same asset allocation, portfolio risk should remain constant over time. However, in the case of optimized asset location, each entity will have a different asset allocation mix. Over time, the relative sizes of the entities will change and therefore the overall asset allocation and risk level will change. The optimization process tends to place the riskier, more appreciating assets into the tax-advantaged entities. Over time, these entities are expected to grow faster and therefore there is a tendency for the overall risk level to increase. The degree to which overall portfolio risk increases is related to the excess performance of risky assets over less risky assets. In practice, this comes down to the performance of equities. When equities do well, the risk level will tend to increase and vice versa.

Continuous rebalancing to retain the target level of risk is one option available to an investor. However, that would require a complex multiperiod optimization process. For the sake of simplicity, we decided to impose a constraint that the expected risk level could not drift up by more than 10 percent; that is, if the target initial risk level is 8 percent, the ending risk level should not exceed 8.8 percent.

FIGURE 31.3 Benefits of Optimized Location: Expected Real Wealth of Children in 20 Years Net of Income and Transfer Taxes

Figure 31.3 demonstrates the results. The introduction of asset location allows for further improvement in the efficient frontier. Using the 8 percent volatility solution as a point of comparison, the expected future wealth rose an additional 9 percent to $28.6 million. This is the equivalent of adding 0.43 percent to the annualized after-tax nominal return on all assets. Table 31.3 highlights the changes in future wealth and asset allocation.

Table 31.4 shows the optimal asset allocation and location for the 8 percent

TABLE 31.3 Jones Family: Improvements in Expected Future Wealth

All results in $ millions and are based

on 8% annual volatility solution.

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