The focus so far has been on avoiding declines in the disbursements as that is presumably the priority of those making disbursements. To achieve sustainability, large buffers are sometimes accumulated to absorb the possible effects in the future of worse than expected investment returns. Such accumulations may also be used to cover extra expenditures for emergencies. If not needed for emergencies, these funds are available to increase bequests. Another possibility to consider, however, is to limit the size of these accumulations, and use the funds to increase the disbursements. In particular, suppose in the future for the New 4% Rule that the disbursement is increased whenever the margin of the current disbursement below the current limit becomes greater than the initial margin in percentage terms. Some smoothing can be provided by limiting any increase in the disbursement in any one year to say 5%. Simulations can be used to find the chances of the increases that would be allowed by such a process. Simulations can also be used to see whether following this process has costs in terms of increasing the declines in the disbursements that may occur. Both the benefits and costs of this process will be investigated.
Benefits
For the New 4% Rule the initial limit based on a 36 year horizon and an RDR of .055 is 6.1%. This limit provides a protective margin for the disbursement of (6.1-4.0)/6.1, or about 35%. Thus, the limit could decline as much as 35% due to lower portfolio values before requiring a reduction in the disbursement. Suppose in the future that the disbursement is increased when the value of the portfolio increases sufficiently to increase this margin above 35%. Any annual increase in the disbursement, however, is limited to 5%. The modifications of the model required to implement this process are discussed in a note.
Chart 8.1 shows the chances of the increases obtained by years 12, 24, and 36 when following this procedure. The vertical axis for this chart shows the chances that the disbursement is larger than or equal to a disbursement on the horizontal axis. For instance, the curve for year 24 at 5.0% on the horizontal axis is at .40 on the vertical axis. Thus, there is a .40 chance by year 24 that the disbursement is 5.0% or more of initial portfolio value. Moreover, there is a .20 chance of this happening by year 12, and much smaller chances of much larger increases by year 24. Thus, there are meaningful chances that significant increases in future disbursements will be possible. If such opportunities arise, beneficiaries can decide at the time whether to take advantage of them. To do so, however, beneficiaries need to know the costs of making the increases in terms of the increased chances of declines that may be caused by doing so.
Costs
Increases in the disbursements only occur when the margin that protects the disbursement exceeds the protection provided by the initial margin. Nevertheless, losing this additional protection will cause some increase in the chances of declines in the disbursements below 4.0%. The solid curves in Chart 8.2 show the chances of declines below 4.0% when the disbursements are being increased as shown in Chart 8.1. The dashed curves show the chances of the declines below 4.0% when such increases in the disbursements are not being made. At year 12 there is little difference, but at years 24 and 36 there is some increase in the chances of smaller declines, and in particular about a .05 increase in the chances that there will be declines at those years. Nevertheless, these increased chances of declines below 4.0% seem unlikely to be sufficient to dissuade beneficiaries from making increases.
Another possible cost is that there may be declines from the increased disbursements in Chart 8.1 that could be sufficient to be troublesome. The increases reported by Chart 8.1 are net of any declines that may occur when the disbursements are over 4.0%. When beneficiaries have become accustomed to higher levels of spending, however, such declines will be disruptive just like declines from the initial 4.0% disbursement. Modifications can be made to the model so that simulations show the chances of the sum of such declines in any iteration. These modifications are discussed in a note. The chances that the sum of such declines for an iteration will be greater than or equal to the values shown on the horizontal axis are given on the vertical axis of Chart 8.3 for years 12, 24, and 36. Even at year 36, there is only a .06 chance that the sum of such declines will be greater than 1.0% of initial portfolio value. Moreover, such declines are negligible by year 12, and by year 24 there is only a 07 chance that the sum of such declines will be more than 0.5% of initial portfolio value. It appears unlikely that beneficiaries will be sufficiently concerned by such declines to not make the increases in Chart 8.1.
Emergencies
A problem that may well dissuade beneficiaries from making increases, however, is the possibility that extra disbursements may be necessary to cover emergencies. Assumptions to include the possibility of emergencies in the model are discussed in Model, along with the modifications required to do so. When the possibility of emergencies is included in the model the page, BID, shows that the initial disbursement must be reduced by about a half percentage point of initial portfolio value to avoid an increase in sustainability risk. The New 4% Rule, however, assumes that beneficiaries are willing to take their chances as to whether or not extra disbursements for emergencies will be necessary, so as to avoid this retrenchment.
Increasing disbursements, however, is not retrenchment, and beneficiaries may well want to consider the possibility that extra disbursements may be needed for emergencies in deciding whether or not to increase disbursements. When possible emergencies are included in the simulations the increases in the disbursements shown in Chart 8.1 are significantly reduced, and the costs in Chart 8.2 significantly increased. Chart 8.4 shows the chances of the increases above 4.0% when the possibility of emergencies is included in the simulations. Compared to Chart 8.1, the chances of increases at the back of the period are significantly less. For instance, in Chart 8.1 there is a .40 chance that the disbursement will be 5.0% or more by year 24. In Chart 8.4 these chances have declined from .40 to .20.
Chart 8.5 shows that including emergencies also significantly increases the chances of large declines below 4.0% at the back of the period. In Chart 8.5 as in Chart 8.2 the chances of declines from 4.0% without the increases are shown by the dashed curves. The chances of declines from 4.0% with the increases are shown by the solid curves. The large difference caused by adding the possibility of emergencies in Chart 8.5 is obvious. In Chart 8.2, without the possibility of emergencies, the dashed curves are not below the solid curves below 3.0% on the horizontal axis. Thus, the increases do not cause any increase in the chances of declines of more than 1.0%. In contrast, in Chart 8.5, for years 24 and 36 the dashed curves are well below the solid curves over their entire length. Moreover, the far left of the solid curves for years 24 and 36 are above zero showing that there is some chance of essentially running out of funds when the increases above 4% are made when there is the possibility that extra disbursements will be needed for emergencies. Thus, after considering the possibility of extra disbursements for emergencies, beneficiaries may decide that increases in the disbursements over 4.0% no longer look attractive. This is even if those increases are made only when the protective margin for the disbursement below the limit is not reduced below its initial value.
Conclusions
Large values can accumulate in the portfolio in excess of what is needed to provide the initial protective margin of the disbursement below its limit. The possibility of using those excess funds to increase the disbursement in the future has been investigated. Doing so provides meaningful chances of significant future increases in the disbursements. Making such increases does not appear to significantly increase the chances of future declines in the disbursements as long as the possible need for extra disbursements to cover emergencies is not considered. When large extra disbursements to cover emergencies are considered, the chances of the larger declines caused by making the increases may be unacceptable. If not needed to cover emergencies, the value in the portfolio is available to increase bequests.
Notes
Suppose that the disbursement is increased when the prior disbursement is less than 65% of the current value of the limit. To provide some smoothing, the increase in any year is limited to 5% of the prior disbursement. Under these conditions the value of the disbursement each year is obtained by replacing the relation given for C(t) in Model with the following relation:
To obtain the sum up through year t’ of any declines that occur when the disbursement is over its initial value, two columns are added to the spreadsheet. Each row of the first column has the relation:
If(And(C(t-1)>C(1),C(t)<C(t-1)),C(t-1)-C(t),0) t = 2, 3, … , T
The second column adds the values in the rows of the first column up through t’ using the relation, SUM(X(2):X(t)) in each row where X is the column that contains the values of the relation in each row, and t’ is the year up through which the sum of declines is desired.
Increases
Increases
The focus so far has been on avoiding declines in the disbursements as that is presumably the priority of those making disbursements. To achieve sustainability, large buffers are sometimes accumulated to absorb the possible effects in the future of worse than expected investment returns. Such accumulations may also be used to cover extra expenditures for emergencies. If not needed for emergencies, these funds are available to increase bequests. Another possibility to consider, however, is to limit the size of these accumulations, and use the funds to increase the disbursements. In particular, suppose in the future for the New 4% Rule that the disbursement is increased whenever the margin of the current disbursement below the current limit becomes greater than the initial margin in percentage terms. Some smoothing can be provided by limiting any increase in the disbursement in any one year to say 5%. Simulations can be used to find the chances of the increases that would be allowed by such a process. Simulations can also be used to see whether following this process has costs in terms of increasing the declines in the disbursements that may occur. Both the benefits and costs of this process will be investigated.
Benefits
For the New 4% Rule the initial limit based on a 36 year horizon and an RDR of .055 is 6.1%. This limit provides a protective margin for the disbursement of (6.1-4.0)/6.1, or about 35%. Thus, the limit could decline as much as 35% due to lower portfolio values before requiring a reduction in the disbursement. Suppose in the future that the disbursement is increased when the value of the portfolio increases sufficiently to increase this margin above 35%. Any annual increase in the disbursement, however, is limited to 5%. The modifications of the model required to implement this process are discussed in a note.
Chart 8.1 shows the chances of the increases obtained by years 12, 24, and 36 when following this procedure. The vertical axis for this chart shows the chances that the disbursement is larger than or equal to a disbursement on the horizontal axis. For instance, the curve for year 24 at 5.0% on the horizontal axis is at .40 on the vertical axis. Thus, there is a .40 chance by year 24 that the disbursement is 5.0% or more of initial portfolio value. Moreover, there is a .20 chance of this happening by year 12, and much smaller chances of much larger increases by year 24. Thus, there are meaningful chances that significant increases in future disbursements will be possible. If such opportunities arise, beneficiaries can decide at the time whether to take advantage of them. To do so, however, beneficiaries need to know the costs of making the increases in terms of the increased chances of declines that may be caused by doing so.
Costs
Increases in the disbursements only occur when the margin that protects the disbursement exceeds the protection provided by the initial margin. Nevertheless, losing this additional protection will cause some increase in the chances of declines in the disbursements below 4.0%. The solid curves in Chart 8.2 show the chances of declines below 4.0% when the disbursements are being increased as shown in Chart 8.1. The dashed curves show the chances of the declines below 4.0% when such increases in the disbursements are not being made. At year 12 there is little difference, but at years 24 and 36 there is some increase in the chances of smaller declines, and in particular about a .05 increase in the chances that there will be declines at those years. Nevertheless, these increased chances of declines below 4.0% seem unlikely to be sufficient to dissuade beneficiaries from making increases.
Another possible cost is that there may be declines from the increased disbursements in Chart 8.1 that could be sufficient to be troublesome. The increases reported by Chart 8.1 are net of any declines that may occur when the disbursements are over 4.0%. When beneficiaries have become accustomed to higher levels of spending, however, such declines will be disruptive just like declines from the initial 4.0% disbursement. Modifications can be made to the model so that simulations show the chances of the sum of such declines in any iteration. These modifications are discussed in a note. The chances that the sum of such declines for an iteration will be greater than or equal to the values shown on the horizontal axis are given on the vertical axis of Chart 8.3 for years 12, 24, and 36. Even at year 36, there is only a .06 chance that the sum of such declines will be greater than 1.0% of initial portfolio value. Moreover, such declines are negligible by year 12, and by year 24 there is only a 07 chance that the sum of such declines will be more than 0.5% of initial portfolio value. It appears unlikely that beneficiaries will be sufficiently concerned by such declines to not make the increases in Chart 8.1.
Emergencies
A problem that may well dissuade beneficiaries from making increases, however, is the possibility that extra disbursements may be necessary to cover emergencies. Assumptions to include the possibility of emergencies in the model are discussed in Model, along with the modifications required to do so. When the possibility of emergencies is included in the model the page, BID, shows that the initial disbursement must be reduced by about a half percentage point of initial portfolio value to avoid an increase in sustainability risk. The New 4% Rule, however, assumes that beneficiaries are willing to take their chances as to whether or not extra disbursements for emergencies will be necessary, so as to avoid this retrenchment.
Increasing disbursements, however, is not retrenchment, and beneficiaries may well want to consider the possibility that extra disbursements may be needed for emergencies in deciding whether or not to increase disbursements. When possible emergencies are included in the simulations the increases in the disbursements shown in Chart 8.1 are significantly reduced, and the costs in Chart 8.2 significantly increased. Chart 8.4 shows the chances of the increases above 4.0% when the possibility of emergencies is included in the simulations. Compared to Chart 8.1, the chances of increases at the back of the period are significantly less. For instance, in Chart 8.1 there is a .40 chance that the disbursement will be 5.0% or more by year 24. In Chart 8.4 these chances have declined from .40 to .20.
Chart 8.5 shows that including emergencies also significantly increases the chances of large declines below 4.0% at the back of the period. In Chart 8.5 as in Chart 8.2 the chances of declines from 4.0% without the increases are shown by the dashed curves. The chances of declines from 4.0% with the increases are shown by the solid curves. The large difference caused by adding the possibility of emergencies in Chart 8.5 is obvious. In Chart 8.2, without the possibility of emergencies, the dashed curves are not below the solid curves below 3.0% on the horizontal axis. Thus, the increases do not cause any increase in the chances of declines of more than 1.0%. In contrast, in Chart 8.5, for years 24 and 36 the dashed curves are well below the solid curves over their entire length. Moreover, the far left of the solid curves for years 24 and 36 are above zero showing that there is some chance of essentially running out of funds when the increases above 4% are made when there is the possibility that extra disbursements will be needed for emergencies. Thus, after considering the possibility of extra disbursements for emergencies, beneficiaries may decide that increases in the disbursements over 4.0% no longer look attractive. This is even if those increases are made only when the protective margin for the disbursement below the limit is not reduced below its initial value.
Conclusions
Large values can accumulate in the portfolio in excess of what is needed to provide the initial protective margin of the disbursement below its limit. The possibility of using those excess funds to increase the disbursement in the future has been investigated. Doing so provides meaningful chances of significant future increases in the disbursements. Making such increases does not appear to significantly increase the chances of future declines in the disbursements as long as the possible need for extra disbursements to cover emergencies is not considered. When large extra disbursements to cover emergencies are considered, the chances of the larger declines caused by making the increases may be unacceptable. If not needed to cover emergencies, the value in the portfolio is available to increase bequests.
Notes
Suppose that the disbursement is increased when the prior disbursement is less than 65% of the current value of the limit. To provide some smoothing, the increase in any year is limited to 5% of the prior disbursement. Under these conditions the value of the disbursement each year is obtained by replacing the relation given for C(t) in Model with the following relation:
If(C(t-1)<.65*C*(t),If(.65*C*(t)<=1.05*C(t-1),.65*C*(t),1.05*C(t-1)),Min(C(t-1),C*(t)))
t = 2, 3, … , T
To obtain the sum up through year t’ of any declines that occur when the disbursement is over its initial value, two columns are added to the spreadsheet. Each row of the first column has the relation:
If(And(C(t-1)>C(1),C(t)<C(t-1)),C(t-1)-C(t),0) t = 2, 3, … , T
The second column adds the values in the rows of the first column up through t’ using the relation, SUM(X(2):X(t)) in each row where X is the column that contains the values of the relation in each row, and t’ is the year up through which the sum of declines is desired.
Posted October 2024