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Using Monte Carlo Simulations to Value Partial Interests of Trusts


The most important considerations in trust management litigation are related to the investment and distribution decisions made by trustees, and their relative impact on each of the trust's partial interest holders.

The financial interests of a trust's beneficiaries are often diametrically opposed. Income beneficiaries, who are entitled to distributions of trust income, may prefer lower-risk investments that produce income, while remainder beneficiaries may prefer higher-risk, higher-return securities. Not surprisingly, conflict among trust beneficiaries is common. One of the trustees' responsibilities is to balance the tradeoffs that exist between distributing significant amounts of income to the income beneficiary and growing trust assets for remainder beneficiaries. This is especially true during periods of low interest rates, high inflation or declining investment values.

When a trust disagreement lands in court, two of the things the court considers are how much of the trust is supposed to go to each beneficiary and how to measure the allocation. Different states use different methods to figure out how to measure the allocation to each beneficiary. Some states have adopted a statutory 'straight-line' percentage method, whereby trust assets are divided between the income beneficiary and remainder beneficiaries based on a predetermined fraction regardless of each beneficiary's life expectancy, the trust's portfolio composition, or distribution rates - and therefore, regardless of any portfolio decisions made by the trustee. A more flexible approach is the tax valuation method, which accounts for the life expectancy of the income beneficiary. The age of the income beneficiary and a statutory interest rate are used to create a discount factor, which is multiplied by the trust's assets at a particular date to determine the present value of the remainder beneficiary's interest. However, the tax valuation method does not account for the trust's distributions to income beneficiaries or what the expected return is on trust assets.

We suggest using Monte Carlo simulations to estimate how a trust's investment portfolio allocates wealth between beneficiaries, without the shortcomings of the straight-line and tax valuation methods. The basic idea behind Monte Carlo simulations is to draw many random paths of random processes (in this case portfolio returns and beneficiary mortality), and see what the average result is (e.g., what the average value of the trust is when the remainder beneficiary receives it). If the probability distributions of the random processes are specified correctly and enough random paths are drawn, the average result is an accurate reflection of what people can expect to happen. In this way, Monte Carlo simulations can show how the trustee's investment decisions affect both the income and remainder beneficiaries. In a litigation context, Monte Carlo simulations can quantify the effect of a trustee's failure to diversify or otherwise balance the interests of each beneficiary. If a court finds that a trustee has breached his duty to diversify the portfolio, Monte Carlo simulations can be used to estimate damages and suggest possible future portfolio allocations.

Monte Carlo simulations are similar to the tax valuation method in that each uses mortality tables and reasonable assumptions about portfolio growth to calculate the value of a beneficiary's partial interest. Monte Carlo simulations go further by accounting for portfolio asset allocations and whether distributions to the income beneficiary are a constant dollar amount, a constant percentage of the trust, or variable over time. In addition, the medical history or personal health of the income beneficiary can be taken into account by using an alternative mortality table or tables modified based on statistical distributions of the life expectancy given certain conditions (smoker/nonsmoker, family histories, etc.).

The simulation-based approach to valuing partial interests in trusts is not new in academics. Collins et al. (2001) used Monte Carlo methods to generate return distributions for income and remainder beneficiaries under a variety of conditions and portfolio compositions.1 They demonstrate both the effectiveness of the method and the importance of incorporating distributions to the income beneficiary and the portfolio's asset allocation. We propose expanding on their work by incorporating the mortality of the income beneficiary and by discounting the results back to the date of interest. We have written a paper on this subject, which can be found here on our website.


1 Collins, P., Savage, S., & Stampfli, J. (2001). Financial Consequences of Distribution Elections from Total Return Trusts. Real Probate & Trust Journal.

Craig J. McCann

Joshua S. Mallett
Manager, Valuation Services703.539.6777
Eddie O'Neal