NO.PZ2022122801000045
问题如下：
Sarzi also advises James
and Karen Rozeer, a married couple who recently retired with total assets of
USD 10 million. The Rozeers have two goals they wish to achieve during their
retirement:
Goal 1: The Rozeers wish to have an 85% chance of
transferring USD 7.5 million to their children in 10 years.
Goal 2: The Rozeers wish to have a 75% chance of being able to
donate USD 15 million to a charitable organization in 25 years.
Sarzi recommends
implementing a goals-based approach to construct a portfolio. He develops a set
of sub-portfolio modules, which are presented in Exhibit 3. Sarzi suggests
investing any excess capital in Module A.
Exhibit 3 “Highest Probability-and Horizon-Adjusted Return”
Sub-Portfolio Modules under Different Horizon and Probability Scenarios
C.
Construct the overall goals-based asset allocation for the Rozeers given their
two goals and Sarzi’s suggestion for investing any excess capital. Show your
calculations. (2018 Q9)
Note: The answer should be the percentage of total assets to be invested in each module.
选项：
解释：
The appropriate goals-based allocation for the Rozeers is as follows:
Goal 1 has a time horizon of 10 years and a required probability of success of 85%. As a result, Module B should be chosen because its 5.0% expected return is higher than the expected returns of all the other modules. The present value of Goal 1, discounted using the 5.0% expected return, is calculated as:
N = 10, FV = –USD 7,500,000, I/Y = 5.0%; PV = USD 4,604,349 (or USD 4.60 million)
So, approximately 46.0% of the total assets of USD 10 million (= USD 4.60 million / USD 10.00 million) should be allocated to Module B.
For Goal 2, which has a time horizon of 25 years and a required probability of success of 75%, Module C should be chosen because its 6.9% expected return is higher than the expected returns of all the other modules. The present value of Goal 2, discounted using the 6.9% expected return, is calculated as:
N = 25, FV = –USD 15,000,000, I/Y = 6.9%; PV = USD 2,829,102 (or USD 2.83 million)
So, approximately 28.3% of the total assets of USD 10 million (= USD 2.83 million / USD 10.00 million) should be allocated to Module C.
Finally, the surplus of USD 2,566,549 (= USD 10,000,000 – USD 4,604,349 – USD 2,829,102), representing 25.7% (= USD 2.57 million / USD 10.00 million), should be invested in Module A following Sarzi’s suggestion.
这种题是不是一般mathematical expectation这个条件是用不上的，不管是goal和portforlio的匹配还是折现算权重都用Minimum expectation来算。
