In sstoeckl/pensionfinanceLi: Optimal Pension Decisions in Liechtenstein

In the following we will describe all parameters that are necessary as input to the program. We will give details on the parameter, specify where it is used, give a possible/feasible range and determine the steps for their simulation for the final output grid of our Machine Learning approach.

Given Variables

Given by the user

Current Age c_age

This variable specifies the current age of the user in full years (the algorithm assumes that calculation day = birthday)

• Possible Range: 18-70
• Feasible Range: 20-60
• Optimization grid: Optimally: 18, Steps of 5: 20-50, Steps of 2: 51-60, steps of 1: 61-70. Feasibly: 20:10:60
• Functions: Utility util, Total CF TotalCF, First Pillar CF fpCF, Second Pillar CF spCF, Third Pillar CF Work tpCFwork and Retirement tpCFret
• Checks: Must be below ret_age and between 18 and 70 (checked in fpCF, spCF, tpCFwork)
• Open Questions: What happens in case of c_age>60?

Gender gender

The gender of the user.

• Possible Range: 0=male and 1=female
• Optimization grid: 0 and 1
• Functions: Utility util, Total CF TotalCF (through: taxCFlumpsum)
• Checks: none
• Open Questions: none

Gross Labor Income li

This variable specifies the gross labor income in the past year (that ends on calculation day/birthday). If the users labor income changed /is expected to change significantly within the next year, use the new number discounted by lg to create an artificial "last year income".

• Possible Range: 0-2m
• Feasible Range: 50.000-200.000
• Optimization grid: Optimally: 1, 30.000, 50.000, 75.000, 100k, 125k, 150k, 175k, 200k, 250k, 300k, 350k, 400k, 500k, 750k, 1m, 1.5m , 2m, Feasibly: 50.000, 125.000, 200.000
• Functions: Utility util, Total CF TotalCF, First Pillar CF fpCF, Second Pillar CF spCF
• Checks: li>0 in fpCF, spCF
• Open Questions: --

Labor Growth Rate lg

This variables specifies how much more the users expects to earn (on average) every year, after accounting for inflation. So given the users expects his labor income to grow by 2% on average, and the average inflation is expected to be 1%, then lg=0.01.

• Possible Range: 0-0.2
• Feasible Range: 0.01-0.05
• Optimization grid: Optimally: 0:0.01:0.1, 0.12, 0.15, 0.2, 0.3, 0.5, 1, Feasibly: 0.01, 0.03, 0.05
• Functions: Utility util, Total CF TotalCF, First Pillar CF fpCF, Second Pillar CF spCF
• Checks: Warnings if li<0 or li>1
• Open Questions: What happens if lg=0 or lg=1?

First Pillar Saving Rate c1

This variable determines the fraction of his gross labor income the users saves in the first pillar.

• Possible Range: 0-0.2 (maybe fixed at 0.07?)
• Feasible Range: 0.07 ?
• Optimization grid: Optimally: 0:0.01:0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.3, 0.5, 1, Feasibly: 0.07 (& 0.1)
• Functions: Utility util, Total CF TotalCF
• Checks: none
• Open Questions: Is this a fixed parameter?

Average savings in first Pillar s1

This variable fixes how much the user has already paid into the first pillar. It is a vector consisting of two components: (1) the number of contribution years at c_age and (2) the historical average yearly income until c_age

• Possible Range: (0-(c_age-18),0-2m)
• Feasible Range: (0-(c_age-18),20.000-100.000)
• Optimization grid: Optimally: c(c(18,20:5:50,52),c(1, 30.000, 50.000, 75.000, 100k, 125k, 150k, 175k, 200k, 250k, 300k, 350k, 400k, 500k, 750k, 1m, 1.5m , 2m)), Feasibly: ([c_age-20],[30.000,75.000])
• Functions: Utility util, Total CF TotalCF, First Pillar CF fpCF
• Checks: stop if length(s1)!=2, s1[1]>c_age, s1[2] < 0
• Open Questions: Tie reasonable values of s1 and s2 to li (avoid discontinuities)

Savings in second pillar s2

This number fixes the amount of the user's savings in the second pillar at c_age.

• Possible Range: 0-2m
• Feasible Range: 20.000-100.000
• Optimization grid: Optimally: 0, 30.000, 50.000, 75.000, 100k, 125k, 150k, 175k, 200k, 250k, 300k, 350k, 400k, 500k, 750k, 1m, 1.5m , 2m, Feasibly: 30.000, 75.000
• Functions: Utility util, Total CF TotalCF, Second Pillar CF spCF
• Checks: stop if s2<0
• Open Questions: none

Investments in third Pillar s3

The amount of "liquid wealth", the user has disposable at c_age - assumed to be invested in the third pillar. As we currently do not assume any tax advantage (aka Pillar 3a in Switzerland) - the entire sum can be treated as any investments/free savings that are not dedicated to anything else and therefore saved for retirement (aka Pillar 3b in Switzerland).

• Possible Range: -2m-5m (needs to be larger than s12/s2?)
• Feasible Range: -200.000-200.000
• Optimization grid: Optimally: 0, 30.000, 50.000, 75.000, 100k, 125k, 150k, 175k, 200k, 250k, 300k, 350k, 400k, 500k, 750k, 1m, 1.5m , 2m, 3m, 4m, 5m, Feasibly: -200.000 -100.000 100.000, 200.000
• Functions: Utility util, Total CF TotalCF, Third Pillar CF Work tpCFwork
• Checks: warning if s3<0 in tpCFwork
• Open Questions: Attention: Portfolio weights w3 must fit to this case CHECK!! Attention: s3 <0 is possible - relate it to w0?

Non-disposable wealth w0

The amount of "non-liquid wealth", the user has available (e.g. invested in real estate). The assumption is, that this wealth is still available at retirement and stays the same over time (no interest). One does however pay wealth taxes for it.

• Possible Range: 0-10m
• Feasible Range: 200.000-2m
• Optimization grid: Optimally: 0, 30.000, 50.000, 75.000, 100k, 125k, 150k, 175k, 200k, 250k, 300k, 350k, 400k, 500k, 750k, 1m, 1.5m , 2m, 3m, 4m, 5m, 7m, 10m, Feasibly: 250k, 1m
• Functions: Utility util, Total CF TotalCF, Third Pillar CF Work tpCFwork
• Checks: none
• Open Questions: none

Conversion factor in the second pillar rho2

The conversion factor in second pillar given regular retirement age. Can be taken from the second pillar documents provided to the user. Depends on the age/insurance policy/wealth/gender (aka Mortality Table) of the user.

• Possible Range: 0.01-0.1 (regularly between 0.04 and 0.05)
• Feasible Range: 0.04-0.05
• Optimization grid: Optimally: 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04:0.001:0.05, 0.06, 0.08, 0.1, feasibly: 0.04, 0.05
• Functions: Utility util, Total CF TotalCF, Second Pillar CF spCF
• Checks: warning if rho2<=0 and rho2>0.2 in TotalCF and spCF
• Open Questions: Do we go to 0.2 or 0.1? Adapt grid or warning? Gender-specificity?

Conversion factor in the third pillar rho3

The conversion factor for the piece of the wealth in the third pillar that the user decides to put into a pension insurance (given by nu3) at retirement. Depends on the age/insurance policy/wealth/gender (aka Mortality Table) of the user.

• Possible Range: 0.01-0.1 (regularly between 0.04 and 0.05)
• Feasible Range: 0.04-0.05
• Optimization grid: Optimally: 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04:0.001:0.05, 0.06, 0.08, 0.1, feasibly: 0.03, 0.04
• Functions: Utility util, Total CF TotalCF
• Checks: warning if rho3<=0 and rho3>0.2 in TotalCF
• Open Questions: Do we go to 0.2 or 0.1? Adapt grid or warning? Gender-specificity?

Spread for negative libor investments in the third pillar psi

This variable determines, by how much the interest rate (LIBOR) will be increased if savings in the third pillar are negative. Depends on the credit rating of the user.

• Possible Range: 0-0.1
• Feasible Range: 0.01-0.03
• Optimization grid: Optimally: 0:0.01:0.05, 0.075, 0.1, Feasibly: 0.15
• Functions: Utility util
• Checks: none
• Open Questions: none

Bequest utility weight beta

How important is it for the user to leave something to his heirs (bequest)?

• Possible Range: 0-1
• Feasible Range: 0.25-0.75
• Optimization grid: Optimally: 0:0.1:1, Feasibly: 0.5, 0.75
• Functions: Utility util
• Checks: none
• Open Questions: none

Risk Aversion ra

The parameter of risk aversion of the user.

• Possible Range: 0-50 (0 risk neutral - 50 very risk averse)
• Feasible Range: 2-20 (?)
• Optimization grid: Optimally: 0:0.5:10, 15, 20:10:50, Feasibly: 2, 5, 10, 20
• Functions: Utility util
• Checks: none
• Open Questions: none

Time preference delta

This variable gives the time preference of the user to determine whether it is more important to consume now or later.

• Possible Range: 0-1 (0 no preference - 1 consume everything now)
• Feasible Range: 0-0.1
• Optimization grid: 0Optimally: :0.01:0.2, 0.3:0.1:1, feasibly: 0.01-0.03
• Functions: Utility util
• Checks: none
• Open Questions: check

Given by the system

These variables are given by the system and therefore do not need any optimization grid.

Portfolio Allocation in second Pillar w2

The portfolio allocation in the second pillar. Assumed to be fixed for all second pillar investments (roughly equal across pension funds, calculated within project). This variable is fixed in the background and not to be changed by the program!

• Possible Range: Fixed at setNames(c(.30,.30,.30,.10,0),c("msci","b10","recom","libor","infl"))
• Optimization grid: none
• Functions: Utility util, Total CF TotalCF, Second Pillar CF spCF
• Checks: stop if names do not match with simulated processes (!setequal(names(w2),colnames(ret[,,1]))) and when the portfolio does not sum to one.
• Open Questions: none

Nominal and real investment return ret and retr

These variables hold the (pre-specified) 10'000 nominal and real scenarios created for investments in broad indices. The processes are analysed and specified in vignette("INPUT_returns").

• Possible Range: Fixed in 10'000 scenarios for investments c("msci","b10","recom","libor","infl"), created according to vignette("INPUT_returns")
• Optimization grid: none
• Functions: Utility util, Total CF TotalCF, First Pillar CF fpCF, Second Pillar CF spCF, Third Pillar CF Work tpCFwork and Retirement tpCFret
• Checks: none
• Open Questions: none

Gender Mortality Tables gender_mortalityTable

The mortality Tables are given by the system, but maybe adapted to cohort and gender.

• Possible Range: Given by the Mortality Tables of the specific country/cohort/gender
• Optimization grid: gender/cohort-specific?
• Feasible Range: none
• Functions: Utility util
• Checks: none
• Open Questions: none

Decision Variables

Retirement Age ret_age

The first and most important output variable is the age of retirement.

• Possible Range: 60-70
• Feasible Range: 60-70
• Optimization: Requires bounded optimization between 60 and 70
• Optimization grid: Optimally: 60:70, Feasibly: 62, 65, 68
• Functions: Utility util, Total CF TotalCF, First Pillar CF fpCF, Second Pillar CF spCF, Third Pillar CF Work tpCFwork and Retirement tpCFret
• Checks: stop if ret_age<60|ret_age>70 in fpCF, spCF and tpCFwork
• Open Questions: none

Consumption c

This tells the user how much to optimally consume during his work life (and therefore also how much to save for his pension in the different pillars).

• Possible Range: 0-1
• Feasible Range: 0.2-0.8 (?)
• Optimization: Requires bounded optimization between 0 and 1
• Optimization grid: Optimally: 0:0.01:0.2 0.3:0.1:1, Feasibly: 0.2:0.2:0.8
• Functions: Utility util, Total CF TotalCF
• Checks: none
• Open Questions: none

Second Pillar saving rate c2

Output telling the user how much of his gross income to contribute to the second pillar. Is doubled by the employer up to 12% (?).

• Possible Range: 0-0.12
• Feasible Range: 0.08-0.12 (?)
• Optimization: Requires bounded optimization between 0 and 0.12
• Optimization grid: Optimally: 0:0.01:0.2 0.3:0.1:1, Feasibly: 0.08, 0.12
• Functions: Utility util, Total CF TotalCF, Second Pillar CF spCF
• Checks: none
• Open Questions: 12% max employer contribution!

Lumpsum payout of second pillar nu2

This output tells the user how much of his second pillar savings to convert to a life-long pension (annuity) at retirement and conversely, how much to pay out as a lumpsum to himself.

• Possible Range: 0-1
• Feasible Range: 0.2-0.8
• Optimization: Requires bounded optimization between 0 and 1
• Optimization grid: Optimally: 0:0.1:1, Feasibly: 0.25, 0.5, 0.75
• Functions: Utility util, Total CF TotalCF, Second Pillar CF spCF
• Checks: stop if <0 or >1 in spCF
• Open Questions: Tax treatment different in both cases? We still have to cover health and and a-fonds-perdu payments!

Lumpsum payout of third pillar nu3

This output tells the user how much of his third pillar savings to convert to a life-long pension (annuity) at retirement and conversely, how much to pay out as a lumpsum to himself.

• Possible Range: 0-1
• Feasible Range: 0.2-0.8
• Optimization: Requires bounded optimization between 0 and 1
• Optimization grid: Optimally: 0:0.1:1, Feasibly: 0.25, 0.5, 0.75
• Functions: Utility util, Total CF TotalCF,
• Checks: TotalCF
• Open Questions: none

Fraction of Wealth not to be consumed in retirement alpha

This output tells the user how much of his savings to keep invested (not consume) during his retirement.

• Possible Range: 0-1
• Feasible Range: 0.9-1
• Optimization: Requires bounded optimization between 0 and 1
• Optimization grid: Optimally: 0:0.1:1, Feasibly: 0.9, 0.93, 0.96
• Functions: Utility util, Total CF TotalCF, tpCFret
• Checks: none
• Open Questions: 12% max employer contribution?

Optimal investment in third pillar w3

This output tells the user how to invest his third pillar savings (currently only constant over time) optimally during saving and retirement phase.

• Possible Range: Between -1 and 1 for MSCI/b10/real estate
• Optimization grid: Requires bounded optimization between -1 and 1. Libor is determined as 1-sum(...)
• Functions: Utility util, Total CF TotalCF, tpCFret, tpCFwork
• Checks: stop if not sum(w3)=1 (guaranteed by modelling of optimization function)
• Open Questions: What are the outputs given very extreme values? Shall the weights really be cut at +-100%?
• Recommendation for the future: Allow changing weights modelled by a linearly decreasing allocation to stocks.
• NOTE: We allow for leverage. Also, interpret constant weights as average weights over lifetime.

sstoeckl/pensionfinanceLi documentation built on Dec. 2, 2020, 3:26 a.m.