CONSTRUCTING SUB-PORTFOLIOS AND THE OVERALL PORTFOLIO
https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2562313/constructing-sub-portfolios-and-the-overall-portfolio-1
CONSTRUCTING SUB-PORTFOLIOS AND THE OVERALL PORTFOLIO
Learning Outcome
recommend and justify an asset allocation using a goals-based approach
Having defined the needs of the investor in as much detail as possible, the next step in the process is to identify the amount of money that needs to be allocated to each goal and the asset allocation that will apply to that sum. For most advisers, the process will start with a set of sub-portfolio modules (such as those we briefly discussed in Section 15 and will study in more depth in Section 17). When using a set of pre-optimized modules, the adviser will then need to identify the module best suited to each of the specific goals of the client. That process is always driven by the client’s time horizon and required probability of success, and it involves identifying the module that offers the highest possible return given the investor’s risk tolerance as characterized by a given required probability of success over a given time horizon.
To illustrate, consider the set of six modules shown in Exhibit 33;28 these modules result from an optimization process that will be explained later.29 In the exhibit, the entries for minimum expected return are shown rounded to one decimal place; subsequent calculations for required capital are based on full precision.
Exhibit 33:
“Highest Probability- and Horizon-Adjusted Return” Sub-Portfolio Module under Different Horizon and Probability Scenarios
A
B
C
D
E
F
Portfolio Characteristics
Expected return
4.3%
5.5%
6.4%
7.2%
8.0%
8.7%
Expected volatility
2.7%
4.5%
6.0%
7.5%
10.0%
12.5%
Annualized Minimum Expectation Returns
Time Horizon (years)
5
Required Success
99%
1.5%
0.9%
0.2%
−0.6%
−2.4%
−4.3%
95
2.3
2.2
2.0
1.7
0.7
−0.5
90
2.7
3.0
3.0
2.9
2.3
1.5
75
3.5
4.2
4.6
4.9
5.0
4.9
Time Horizon (years)
10
Required Success
99%
2.3%
2.2%
2.0%
1.7%
0.7%
−0.5%
90
3.2
3.7
4.0
4.1
4.0
3.6
75
3.7
4.6
5.1
5.6
5.9
6.0%
60
4.1
5.2
5.9
6.6
7.2
7.7
Time Horizon (years)
20
Required Success
95%
3.3%
3.9%
4.2%
4.4%
4.4%
4.1%
90
3.5
4.3
4.7
5.0
5.2
5.1
85
3.7
4.5
5.0
5.4
5.7
5.8
75
3.9
4.9
5.5
6.0
6.5
6.8
Time Horizon (years)
25
Required Success
95%
3.4%
4.1%
4.4%
4.7%
4.7%
4.6%
90
3.6
4.4
4.9
5.2
5.5
5.5
85
3.7
4.6
5.2
5.6
6.0
6.1
75
3.9
4.9
5.6
6.2
6.7
7.0
In Exhibit 33, the top section, on portfolio characteristics, presents the expected return and expected volatility of each module. Below that are four sections, one for each of four time horizons: 5, 10, 20, and 25 years. In a given section, the entries are the returns that are expected for a given required probability of achieving success. For example, at a 10-year horizon and a 90% required probability of success, Modules A, B, C, D, E, and F are expected to return, respectively, 3.2%, 3.7%, 4.0%, 4.1%, 4.0%, and 3.6%. In this case, Module D would be selected to address a goal with this time horizon and required probability of success because its 4.1% expected return is higher than those of all the other modules. Thus, Module D offers the lowest “funding cost” for the given goal. The highest expected return translates to the lowest initially required capital when the expected cash flows associated with the goal are discounted using that expected return.
EXAMPLE 10
Selecting a Module
Address the following module selection problems using Exhibit 33:
A client describes a desire to have a reserve of €2 million for business opportunities that may develop when he retires in five years. Assume that the word “desire” points to a wish to which the adviser will ascribe a probability of 75%.
Solution to 1:
The time horizon is five years. Exhibit 33 shows that Module E has the highest expected return (5.0%) over the five-year period and with the assumed 75% required probability of success.
A 70-year-old client with a 20-year life expectancy discusses the need to be able to maintain her lifestyle for the balance of her life and wishes to leave US$3 million to be split among her three grandchildren at her death.
Solution to 2:
The time horizon is 20 years. The first goal is a need, while the second is a wish. We assume a required probability of success of 95% for a need and 75% for a wish. Exhibit 33 shows that Module D provides the highest horizon- and required-probability-adjusted return (4.4%) for the first goal. Module F is better suited to the second goal because, even though the second goal has the same time horizon, it involves only a 75% required probability of success; the appropriately adjusted return is 6.8%, markedly the highest, which means the initially required capital is lower.
Returning to the Smiths, let us use that same set of modules to look at their four specific goals. The results of our analysis are presented in Exhibit 34.
The first goal is a need, with a five-year time horizon and a 95% required probability of success. Looking at the 95% required probability line in the five-year time horizon section of Exhibit 33, we can see that the module with the highest expected return on a time horizon- and required probability-adjusted basis is Module A and that the appropriately adjusted expected return for that module is 2.3%. Discounting a US$500,000 annual cash flow, inflated by 2% a year from Year 2 onwards, required a US$2,430,000 initial investment. This amount represents 9.7% of the total financial wealth of the Smiths.
The second goal is a want, with a 25-year time horizon and an 85% required probability of success. The corresponding line of the table in Exhibit 33 points to Module F and a discount rate of 6.1%. Discounting their current expenses with the same assumption over the 25 years starting in Year 6 with a 6.1% rate points to an initially required capital of US$6,275,000, representing 25.1% of the Smiths’ wealth.
The third goal is another need, with a 10-year time horizon and a 90% required probability of success. Module D is the best module, and the US$6,691,000 required capital reflects the discounting of a US$10 million payment in 10 years at the 4.1% indicated in Exhibit 33.
Finally, the fourth goal is a wish with a 20-year time horizon and a 75% required probability of success. Module F is again the best module, and the discounting of a US$10 million payment 20 years from now at the 6.8% expected return from Exhibit 33 points to a required capital of US$2,683,000 today.
Note that different goals may, in fact, be optimally addressed using the same module; thus, an individual module may be used more than once in the allocation of the individual’s overall financial assets. Here, Goals 2 and 4 can both be met with the riskiest of the six modules, although their time horizons differ, as do the required probabilities of success, with Goal 2 being characterized as a want and Goal 4 as a wish.
Exhibit 34:
Module Selection and Dollar Allocations (US$ thousands)
Total Financial Assets
25,000
Goals
Surplus
Overall Asset Allocation
1
2
3
4
Horizon (years)
5
25
10
20
Required probability of success
95%
85%
90%
75%
E(Rt)
7.2%
Discount rate
2.3%
6.1%
4.1%
6.8%
σ(Rt)
8.0%
Module
A
F
D
F
C
Required capital
In currency
2,430
6,275
6,691
2,683
6,921
25,000
As a % of total
9.7%
25.1%
26.8%
10.7%
27.7%
100.0%
Note also that the Smiths’ earlier worry, that they might not be able to meet all their goals, can be addressed easily. Our assumptions suggest that, in fact, they have excess capital representing 27.7% of their total financial wealth. They can either revisit their current goals and bring the timing of payments forward or raise their probability of success. The case suggests that they would rather think of additional goals but will want to give themselves some time to refine their intentions. Their adviser then suggests that a “middle of the road” module be used as a “labeled goal” for that interim period, and they call this module (Module C) “capital preservation.”
The Overall Portfolio
Assuming the same six modules, with their detailed composition shown in Exhibit 35, one can then derive the overall asset allocation by aggregating the individual exposures to the various modules. In short, the overall allocation is simply the weighted average exposure to each of the asset classes or strategies within each module, with the weight being the percentage of financial assets allocated to each module. Exhibit 36 presents these computations and the overall asset allocation, which is given in bold in the right-most column. The overall portfolio’s expected return and volatility are also shown. In Exhibit 35, liquidity30 is measured as one minus the ratio of the average number of days that might be needed to liquidate a position to the number of trading days in a year. (Note that the column B values add up to 101 because of rounding.)
Exhibit 35:
Asset Allocation of Each Module
A
B
C
D
E
F
Portfolio Characteristics
Expected return
4.3%
5.5%
6.4%
7.2%
8.0%
8.7%
Expected volatility
2.7%
4.5%
6.0%
7.5%
10.0%
12.5%
Expected liquidity
100.0%
96.6%
90.0%
86.1%
83.6%
80.0%
Portfolio Allocations
Cash
80%
26%
3%
1%
1%
1%
Global investment-grade bonds
20
44
45
25
0
0
Global high-yield bonds
0
5
11
25
34
4
Lower-volatility alternatives
0
9
13
0
0
0
Global developed equities
0
9
13
19
34
64
Global emerging equities
0
2
2
3
6
11
Equity-based alternatives
0
0
0
8
0
0
Illiquid global equities
0
0
5
10
15
20
Trading strategy alternatives
0
1
3
6
7
0
Global real estate
0
5
5
3
3
0
Total
100%
100%
100%
100%
100%
100%
Exhibit 36:
Goals-Based Asset Allocation (US$ thousands)
Total Financial Assets
25,000
Goals
Surplus
Overall Asset Allocation
1
2
3
4
Horizon
5
25
10
20
Required success
95%
85%
90%
75%
E(Rt)
7.2%
Discount rate
2.3%
6.1%
4.1%
6.8%
σ(Rt)
8.0%
a “Trading strategy alternatives” refers to discretionary or systematic trading strategies such as global macro and managed futures.
Module
A
F
D
F
C
Required capital
In currency
2,430
6,275
6,691
2,683
6,921
25,000
As a % of total
9.7
25.1
26.8
10.7
27.7
100.0
Cash
80%
1%
1%
1%
3%
9%
Global investment-grade bonds
20
0
25
0
45
24
Global high-yield bonds
0
4
25
4
11
12
Lower-volatility alternatives
0
0
0
0
13
4
Global developed equities
0
64
19
64
13
28
Global emerging equities
0
11
3
11
2
5
Equity-based alternatives
0
0
8
0
0
2
Illiquid global equities
0
20
10
20
5
10
Trading strategy alternativesa
0
0
6
0
3
3
Global real estate
0
0
3
0
5
2
Total
100
100
100
100
100
100
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