# Remington Wealth Partners Case Scenario

Extract of question:

Finally, Remington and Montgomery discuss Isabelle Sebastian. During a recent conversation, Sebastian, a long-term client with a \$2,900,000 investment portfolio, reminded Remington that she will soon turn age 65 and wants to update her investment goals as follows:

• Goal 1: Over the next 20 years, she needs to maintain her living expenditures, which are currently \$120,000 per year (90% probability of success). Inflation is expected to average 2.5% annually over the time horizon, and withdrawals take place at the beginning of the year, starting immediately.
• Goal 2: In 10 years, she wants to donate \$1,500,000 in nominal terms to a charitable foundation (85% probability of success).

Exhibit 2 provides the details of the two sub-portfolios, including Sebastian’s allocation to the sub-portfolios and the probabilities that they will exceed the expected minimum return.

Exhibit 2

Investment Sub-Portfolios & Minimum Expected Return for Success Rate

Sub-Portfolio BY CZ
Expected return (%) 5.70 7.10
Expected volatility (%) 5.10 7.40
Current portfolio allocations (%) 40 60
Probability (%) Minimum Expected Return (%)
Time horizon: 10 years
99 2.90 2.50
90 3.40 2.80
85 3.60 3.00
Time horizon: 20 years
95 5.10 5.40
90 5.20 5.70
85 5.60 5.90

Assume 0% correlation between the time horizon portfolios.

Question

Using Exhibit 2, which of the sub-portfolio allocations is most likely to meet both of Sebastian’s goals?

A. The current sub-portfolio allocation
B. A 43% allocation to sub-portfolio BY and a 57% allocation to sub-portfolio CZ
C. A 37% allocation to sub-portfolio BY and a 63% allocation to sub-portfolio CZ

C is correct. Sebastian needs to adjust the sub-portfolio allocation to achieve her goals. By adjusting the allocations to 37% × \$2,900,000 = \$1,073,000 in BY and 63% × \$2,900,000 = \$1,827,000 in CZ, she will be able to achieve both of her goals based on the confidence intervals.

Goal 1: Sebastian needs to maintain her current living expenditure of \$120,000 per year over 20 years with a 90% probability of success. Inflation is expected to average 2.5% annually over the time horizon.

Sub-portfolio CZ should be selected because it has a higher expected return (5.70%) at the 90% probability for the 20-year horizon. Although sub-portfolio CZ has an expected annual return of 7.10%, based on the 90% probability of success requirement, the discount factor is 5.70%.

Goal 1: k = 5.70%; g = 2.50%.

Determine the inflation-adjusted annual cash flow generated by sub-portfolio CZ:

\$1,827,000×(0.057−0.025)1−(1+0.0251+0.057)20=\$120,432.04>\$120,000

Goal 2: Sebastian wants to contribute \$1,500,000 to a charitable foundation in 10 years with an 85% probability of success.

Sub-portfolio BY should be selected because it has a higher expected return (3.60%) at the 85% probability for the 10-year horizon. Although sub-portfolio BY has an expected annual return of 5.70%, based on the 85% probability of success requirement, the discount factor is 3.60%.

Goal 2: k = 3.60%.

Determine the amount needed today in sub-portfolio BY:

\$1,500,000(1+0.036)10=\$1,053,158.42<\$1,073,000

A is incorrect: 40% × \$2,900,000 = \$1,160,000 in BY, and 60% × \$2,900,000 = \$1,740,000 in CZ.

I don’t quite get their solution. I did it another way:

For Goal 1: To find PV, N=20 , I/Y = 3.12195% [(1 + r / 1 + g) - 1], FV = 0 PV = \$1,820,445.792

For Goal 2: 1,500,000/(1.036^10) = 1,053.422

Total (G1+G2) = 2,873,604.214

Allocation to CZ = 1,820,445.792/2,873,604.214 = 0.6335 (63%)
Allocation to BY = 1-0.63 = 0.37 (37%)

Would just like to check if this is a legit/sound way or if I just coincidentally got the same answer as the solutions? Many thanks.

I just did this question. Such a headache. Easiest way to do is work backwards by choosing the MC percentages first and seeing if it works. Look ok to me

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