Investment management performance is easily measured at any frequency and easily compared to publicly traded benchmarks such as S&P500 and Barclays Agg indices. In contrast, wealth management is concerned with custom portfolios evolving over multi-decade horizons. Such long horizons make it impractical to assess the quality of employed strategies ex-post, while singularly personalized nature of the objective - funding a set of goals specific to each individual - makes it impossible to create a single observable benchmark similar to an index. We suggest that indexing should be done not at the level of portfolios but strategies, in a way reminiscent of target date funds, and evaluation should be done using Monte-Carlo simulations. We propose a simple methodology for building personalized benchmarks based on a combination of user starting financial state and arbitrary list of goals. Such benchmarks can be used to realistically evaluate a client’s current financial situation and serve as a point of departure for providing nuanced advice.

1. Goal-based wealth
management benchmarks
SF DSCO 2023

2. Outline
1. Fundamental problem(s) of wealth management.
2. Breaking apart: solving elementary problem.
3. Asset-allocation benchmarks.
4. Affecting the outcomes.
5. Nano-RL for goal funding.
6. Conclusions.

3. Fundamental Problem of Wealth Management
How To Finance Life?
- Have I been saving “enough”?
- If not how much should I be saving?
- What should be the “realistic” values of
goals?
- How should the current and future savings
be invested for “best” results?
There is no shortage of well-intentioned
resources …

4. Fundamental problem with Wealth Management
Horizons are long - difficult to evaluate quality of advice until
it’s too late - it is a given we need to use simulations.
Each user’s objectives are unique - there’s no objective “index
investment” you can compare your portfolio to.
Portfolio risk is growing together with its size over time.
Tax considerations could be non-trivial.
Too many moving parts!
Goal of this presentation - outline an MVP of a relative value framework
allowing one to get a ballpark evaluation of their situation as well as
best things to do to improve.

5. Incomplete view of proper wealth management solution
Simulations
Of Asset
Returns
Proposed
Allocation
Strategy
Simulations of
Wealth
Income,
Expenses,
Funding
Objectives
Outcomes
Conditional goal
decision making
Conditional
adjustments to
allocation
strategy

6. Investment universe and treatment of inflation
Data: (monthly frequency)
“Stocks” - S&P 500 Total Return index (Y!Finance ticker ^SP500TR )
“Bonds” - “ICE BofA US Corporate Index Total Return Index Value” (FRED ticker BAMLCC0A0CMTRIV )
“Cash” - 3-month discount T-Bill rate (FRED ticker DTB3 )
“Inflation” - monthly CPI index percent change (FRED ticker CPIAUCSL )
What to simulate:
(1) Outright investment returns and Inflation, resize goals in the future to adjust for inflation.
OR
(2) Investment returns net of Inflation, measure everything in today’s dollars.

7. Investment Universe and Inflation - historical data (~35y)

8. Asset Returns Simulations - Net of Inflation
Fit Asymmetric GARCH(1,1) for each of the return series. Use block resampling with Poisson
distributed block length with average block size of 36 months to preserve macro correlations.

9. Given the need to spend $1 at time t what is the amount W(0)
needed today (and how should it be invested).
Elementary Problem - “Arrow-Debreu price”
Since the future is stochastic the question needs to have
probability in it:
What is the amount W(0) needed today so that at time t we’ll
have W(t) > 1 with probability p0
?

10. Elementary Problem - observations
Suggested Allocations:
At t = 0: 100% cash.
At t ≅1.5 years: 75%/25% cash and bonds
At t ≅8.0 years: 75%/25% bonds and stocks
Smooth transitions in between.

11. “Glidepath Kernel”
Hope: allocation at time t = 0 requiring least amount of wealth W0
s.t. Wt
> $1 with probability 90% at time t > 0.
Notation:
K(t,x) = [St
(x), Bt
(x), Ct
(x)]

12. Constructing glidepath from kernel
Glidepath for a single bullet goal at time t0
, g(t)= g0
ẟ(t-t0
) is just the kernel played in
reverse.
Glidepath for a set of goals [g1
,...,gk
] is a weighted sum of glidepaths
“Benchmark Property”: same fixed kernel can be used to construct glidepath for any user

13. Sample Profiles

14. Empirical Benchmark Glidepaths
Glidepath reacts to immediate funding needs by raising some cash, but
overall stays the course of steady risk reduction.

15. Sensitivity of glidepath to the risk reduction horizon tx
Lower values ⇔more weight in stocks:
Risk reduction horizon ⇔ Risk Tolerance

16. Simulations with glidepaths
Wt
= Incomet
- Expensest
- Goalst
+ Wt-1
( 1 + rt
[GPt-1
] )
WInv
t
= Incomet
- Expensest
+ Wt-1
( 1 + rt
[GPt-1
] )
Metrics of Interest
- W = 0 is an “absorbing boundary” (no borrowing => no recovery)
- No explicit taxes (included in expenses)
- Annual rebalancing
Expected Realized Utility Probability of survival Financial Risk
Average Fail Time

17. Metrics Visualization
R2
= 16%, T0
= 0.68 R2
= 10%, T0
= 0.69
R2
= 6%, T0
= 0.48
Utility and Probability are correlated but are far from being synonymous.
Probability is a superficial metric as it does not account for the quality of unsuccessful trajectories.

18. Affecting Outcomes
Modular Structure of the set-up allows to easily swap different components while leaving everything else:
● Don’t like Simulated Returns - provide your own in a form of 3-d array (T,Nassets
,Npaths
)
● Don’t like the Wealth evolution calculation (want to add taxes, tax-free accounts, ability to borrow,
etc.) - change one function.
● Don’t like the glidepath kernel - provide your own.
● Want to compare your amazing RL dynamic allocation strategy - just replace one function.

19. Affecting Outcomes - Easy
Given desired level of P or U and fixed x (hence, glidepath) we can answer the following questions:
○ Keeping Income and W0
fixed, what is the level of Expenses (as a fraction of Income)?
○ Keeping Income, Expenses, and W0
fixed what are the acceptable Goals’ values (as a fraction of initial values)?
○ What is the optimal combination of changes to spending and adjustment to goals that gives the best lift?
○ Keeping Income and Expenses fixed, what is the required value of W0
? - let’s keep this in mind
Example targeting Utility ~ 0.9 using goal scaling

20. Affecting Outcomes - Risk vs Success
Financial Risk and Wealth Management Risk are negatively correlated.
But does financial risk matter if outcomes are improving as you increase it?
- Yes, because goals and spending can be very stochastic IRL - constraining risk allows for that.
- Yes, if adding more risk has only minimal impact on the outcomes.

21. Conditional Consumption (microstrategy)
Wt
= Incomet
- Expensest
+ Wt-1
( 1 + rt
[GPt-1
] ) - Goalst
W1
t
= Incomet
- Expensest
+ Wt-1
( 1 + rt
[GPt-1
] )
Wt
= W1
t
- I[W1
t
> Wmin
t
]Goalst
Requirement: Wmin
t
must be calculable Today
For each time t in the future answer the question -
What is the minimum level of W0
required to achieve the
desired level of U on the remaining period [t, T]?

22. Conditional Consumption - optimal strategy
U target = 90
Low targets - too careless
High targets - too cautious
Optimal target depends on the distribution of goals.

23. Conclusions
● We proposed the concept of benchmarking wealth management advice as long as it is based
on Monte-Carlo simulations using the idea of Glidepath Kernel.
● “100% stocks” deserves to be a benchmark of its own.
○ Constraining financial risk from first principles requires additional assumptions.
● The concept of Target Starting Wealth allows construction of a strategy benchmarks for
conditional goal funding along each path.
○ An optimal target can be found for each profile.