The illustrations at this site generally assume an initial 36 year disbursement period, which would be long enough to make disbursements each year through age 100 for someone age 65. Many retirees, however, may start making disbursements well before age 65, and some may want to assume that disbursements may be necessary after age 100. Moreover, an organization might want to plan on perpetual disbursements. On the other hand, those who are not in good health may want to plan initially on making disbursements for only half as long as 36 years. For others, a turn for the worse in health may occur after they begin disbursements, and additional spending may be needed for assistance. As the horizon is now shorter than expected initially, an increase in the disbursements may be possible to cover any increase in expenses. Shorter horizons can significantly increase the disbursements that can be made, and longer horizons cause a reduction, but by how much?
For the pre 2008 illustration with a 36 year initial horizon, an initial disbursement of 3.5% has good sustainability. When the initial horizon is changed the first step is to find the initial disbursement that has comparably good sustainability. This initial disbursement is then successively increased by half a percentage point above this sustainable level. As in Increase these increases continue until there is doubt that the last increase is an improvement, and the Best Initial Disbursement (BID) is found.
Shorter Initial Horizons
Suppose initially that the beneficiary of the disbursements is not in good health, and that the longest the disbursements might be needed is 18 years. The first step is to find the initial disbursement for 18 years that has comparably good sustainability to 3.5% for a 36 year initial horizon. Chart I.2 in Increase shows for 3.5% with a 36 year initial horizon that the chances of a decline are very small and equal to about .05 at year 24. For an 18 year initial horizon, year 12 is two-thirds of the way through the initial period just as year 24 is for the 36 year initial horizon. For the 18 year initial horizon, simulations show that 6.0% has similarly low chances of a decline at year 12 under comparable conditions. In either case the best stock allocation is used and the RDR is set equal to .02 above the expected return of this allocation.
Now, as in Increase, successively increase the initial disbursement by half a percentage point above the sustainable level of 6.0% using the best stock allocation and an RDR that is .02 above the expected return each time. For the 36 year initial horizon, when the initial disbursement was increased, the increased risks at years 12 and 24 indicated the respective increased risks at the front and back of the period. For the 18 year initial horizon, the increased risks at the front and back of the period are indicated by the increased risks at years 6 and 12. When the initial disbursement is increased from 6.5% to 7.0% Chart H.1 shows that there is little increased risk at the front of the period. Chart H.2 shows, however, that there is an increase in risk at the back of the period. The increased risk at the back, however, does not seem so large that it cannot be discounted for the decreasing chances of survival given the assumed health issues of the beneficiary. Thus, the increased risk at the back does not seem large enough to cause doubt that the increase from 6.5% to 7.0% at the front of the period is an improvement.
In contrast, when the disbursement is further increased from 7.0% to 7.5% there is increased risk at the front of the period that is of concern, as well as at the back. In Chart H.3, when the initial disbursement is increased from 7.0% to 7.5% at the front of the period, note that the chances of a decline increase from .15 to about .30, and that the chances of a decline of 1.0 or more from the starting point increase from .025 to .10. Moreover, Chart H.4 shows significant further increased risk at the back of the period. With concern about increased risk at both the front and back of the period, there is doubt that the increase from 7.0% to 7.5% is an improvement. For the 18 year horizon, therefore, the Best Initial Disbursement (BID) is 7.0%. When the initial horizon is cut in half from 36 to 18 years the BID increases by slightly more than a half from 4.5% to 7.0%.
The possibility has just been considered that the beneficiary initially faces health issues that significantly reduce the length of time the disbursements may be required. Another possibility is that health issues arise after the disbursements begin that significantly reduce the number of disbursements that were thought to be necessary initially. In such a case, a similar analysis can be conducted using the remaining value of the portfolio at that time, and the reduced length of the remaining horizon. A significant increase in the disbursements may be possible to cover any additional expenses that may be necessary, such as for assistance. For instance, suppose a turn for the worse occurs in health soon after starting the disbursements assuming an initial horizon of 36 years. Suppose the value of the portfolio is still close to its initial value, but now no more than 18 years of disbursements might be necessary. Based on the analysis just conducted the disbursement can be increased from 4.5% to 7.0 % of initial portfolio value.
Larger Initial Horizons
Suppose now that the disbursement might be necessary for as long as 60 years. That would allow for retiring at age 50 and living up to age 110. The first step again is to find the initial disbursement that provides comparably good sustainability as 3.5% does for an initial horizon of 36 years. Simulations show that a 3.0% initial disbursement has about the same small chance of a decline at year 24 as a 3.5% initial disbursement with a 36 year initial horizon, using the best stock allocation, and an RDR that is .02 above expected return in either case. Now successively increase the initial disbursement by half a percentage point above 3.0%. For the 60 year initial horizon, years 18 and 36 show the increased risks at the front and back of the period, as years 6 and 12 do for the 18 year initial horizon.
For the 18 year initial horizon the initial disbursement can be increased one percentage point above the sustainable level without doubt that the increase is an improvement. For the 60 year horizon, however, only a half percentage point increase is possible without doubt of improvement. For the 60 year initial horizon, the increased risk for an increase from 3.0% to 3.5% at the front of the period is shown in Chart H.5, and at the back in Chart H.6. Chart H.5 shows little increase in risk at the front of the period, whereas Chart H.6 shows that there is increased risk at the back. The increased risk at the back, however, is remote and can be discounted for the decreasing chances of survival for the beneficiary. After this discounting the increased risk in Chart H.6 does not seem large enough to cause doubt that the increase from 3.0% to 3.5% in Chart H.5 at the front of the period is an improvement.
In contrast, when the initial disbursement is further increased from 3.5% to 4.0%, the increased risk at the front of the period is of concern, and there is more increased risk at the back. Note in Chart H.7, when starting at 4.0% that the chances of a decline increase from .10 to .20. Also, there is close to a .10 chance of a decline of 1.0 or more from the starting point, whereas when starting at 3.5% there is little chance of a decline that large. Moreover, Chart H.8 shows significant increased risk at the back of the period. Thus, increased risks at both the front and back of the period are of concern when the initial disbursement is increased from 3.5% to 4.0% causing doubt that this increase is an improvement. The Best Initial Disbursement (BID) for the 60 year initial horizon is therefore 3.5%. That compares with 4.5% for the 36 year initial horizon, and 7.0% for the 18 year horizon.
Perpetual Disbursements
Suppose now that there is not any limit on how long the disbursements may be needed, and that they are assumed to be perpetual, which might be reasonable for an organization. Perpetuity changes the calculation of the limit in Model for the value of the disbursement each year, as discussed in an endnote. For perpetual disbursements, the first step is to again find the initial disbursement that has the same good sustainability as a 3.5% initial disbursement for a 36 year initial horizon. Simulations show that a 2.75% initial disbursement for the perpetual disbursements has about the same small chance of a decline by year 24 under comparable conditions. As this initial disbursement is very close to the 3.0% initial disbursement with good sustainability for a 60 year initial horizon it will be assumed that the BID for perpetual disbursements is also half a percentage point above the initial disbursement with good sustainability, and equal to 3.25%. The best stock allocation for the initial perpetual disbursement with good sustainability of 2.75% is 30%. When the initial disbursement increases to 3.25% the best stock allocation rises to 35% and the RDR is set at .02 above the expected return of this allocation. Using these values, simulations provide the cumulative probability distributions of the disbursements up through any desired future year.
Chart H.9 shows these distributions up through year 240. Of particular interest in the chart is that there is a limit on the chances of a decline equal to about .20 at year 120. No limit on the chances of large declines, however, is evident in the chart. The chances of a decline equal to 3.0 or more from the starting point is .20 at year 120, and the chances of that decline or more increase to .24 at year 240. If there is a limit on the chances of a decline presumably more value is accumulating in the portfolio than is needed to protect the disbursement. When the disbursement becomes sufficiently small relative to the value of the portfolio it should therefore be possible to increase the disbursement with little risk of future declines. Suppose, for instance, that the disbursement is increased whenever it is less than 2.5% of the value of the portfolio. The modification of Model to do so is discussed in an endnote. The increases in the future disbursements obtained are shown in Chart H.10.
The chart shows on the vertical axis the chances that the disbursement will be greater than or equal to the values given on the horizontal axis. By year 24 there is about a .30 chance that the disbursement has increased by 1.0 percentage point or more of initial portfolio value. By year 36 there is about a .30 chance that it has increased by 2.0 percentage points or more. Moreover, the chances of declines at years 24 and 36 remain the same as those shown in Chart H.9, and there is only a slight increase in the chances of a decline at year 60. The chances of declines at years 120 and 240, however, are now somewhat higher, and the chances of a decline no longer reaches a limit at year 120 as the chances at year 240 are now somewhat higher. These slightly higher risks in the very remote future, however, are a very small price to pay for the increases shown in Chart H.10.
There is another risk of declines to consider, however, besides the declines from the initial disbursement of 3.25%. The increases shown in Chart H.10 are net of decreases that may have occurred in disbursements that are over the initial disbursement of 3.25%. Such declines will be disruptive with respect to sustaining habitual spending like the declines shown in Chart H.9. The size and likelihood of any such declines need to be investigated. An endnote discusses the relations that can be added to Model to do so. When these relations are included, the simulations show the chances that the sum of such declines up through a future year are greater than or equal to a given value for an iteration. Such declines, however, turn out not to be a problem when the disbursements are increased when they are less than 2.5% of portfolio value. Chart H.11 shows even by year 60 that there is only a .02 chance that the sum of such declines for an iteration will be equal to or more than 1.0 percentage point of initial portfolio value.
Conclusions
The illustrations at this site generally assume that initially disbursements may be needed for as long as 36 years. A much shorter initial horizon, however, may be appropriate for a beneficiary with health issues, and organizations may want to assume that the disbursements will be needed in perpetuity. For a 36 year initial horizon, and assuming the investment returns in the pre 2008 illustration, Increase argues that the Best Initial Disbursement (BID) is 4.5% of portfolio value. When the initial disbursement is cut in half from 36 to 18 years, the BID increases from 4.5% to 7.0%, whereas for a 60 year initial horizon the BID declines to 3.5%, and to 3.25% for perpetual disbursements. For perpetual disbursements and the pre 2008 returns, a limit of .30 occurs for the chances of a decline, after about 120 years. For perpetual disbursements, disbursements less than 2.5% of portfolio value can be increased with possible significant benefits, and little risk for many years.
Notes
1. For perpetual disbursements, the relation for the limit on the disbursement at the beginning of each year in Model, C*(t), is replaced by mV(t)/(1+m). To obtain this relation let x be the amount that can be disbursed in perpetuity at the beginning of each year including the first from a value, V, when a return, m, is earned each year. To disburse the same amount at the beginning of each year, V must remain the same at the beginning of the next year so V = (V – x)(1 + m). Solving for x gives the stated relation.
2. Suppose that the disbursement is increased when the prior disbursement is less than 2.5% of the current value of the portfolio. To provide some smoothing, the increase in any year is limited to 5% of the prior disbursement. Also, to avoid problems in evaluating the simulation statistics when there are some very large disbursements, the disbursement is limited to 25% of initial portfolio value. 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) < .025V(t), If( .025V(t) > 25, 25, If( .025V(t) <= 1.05C(t-1), .025V(t), 1.05C(t-1))),
Min( C(t-1), C*(t)) ) t = 2, 3, … , T
3. 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( 2:t’ ), where t’ is the year up through which the sum of declines is desired.
Horizons
Horizons
The illustrations at this site generally assume an initial 36 year disbursement period, which would be long enough to make disbursements each year through age 100 for someone age 65. Many retirees, however, may start making disbursements well before age 65, and some may want to assume that disbursements may be necessary after age 100. Moreover, an organization might want to plan on perpetual disbursements. On the other hand, those who are not in good health may want to plan initially on making disbursements for only half as long as 36 years. For others, a turn for the worse in health may occur after they begin disbursements, and additional spending may be needed for assistance. As the horizon is now shorter than expected initially, an increase in the disbursements may be possible to cover any increase in expenses. Shorter horizons can significantly increase the disbursements that can be made, and longer horizons cause a reduction, but by how much?
For the pre 2008 illustration with a 36 year initial horizon, an initial disbursement of 3.5% has good sustainability. When the initial horizon is changed the first step is to find the initial disbursement that has comparably good sustainability. This initial disbursement is then successively increased by half a percentage point above this sustainable level. As in Increase these increases continue until there is doubt that the last increase is an improvement, and the Best Initial Disbursement (BID) is found.
Shorter Initial Horizons
Suppose initially that the beneficiary of the disbursements is not in good health, and that the longest the disbursements might be needed is 18 years. The first step is to find the initial disbursement for 18 years that has comparably good sustainability to 3.5% for a 36 year initial horizon. Chart I.2 in Increase shows for 3.5% with a 36 year initial horizon that the chances of a decline are very small and equal to about .05 at year 24. For an 18 year initial horizon, year 12 is two-thirds of the way through the initial period just as year 24 is for the 36 year initial horizon. For the 18 year initial horizon, simulations show that 6.0% has similarly low chances of a decline at year 12 under comparable conditions. In either case the best stock allocation is used and the RDR is set equal to .02 above the expected return of this allocation.
Now, as in Increase, successively increase the initial disbursement by half a percentage point above the sustainable level of 6.0% using the best stock allocation and an RDR that is .02 above the expected return each time. For the 36 year initial horizon, when the initial disbursement was increased, the increased risks at years 12 and 24 indicated the respective increased risks at the front and back of the period. For the 18 year initial horizon, the increased risks at the front and back of the period are indicated by the increased risks at years 6 and 12. When the initial disbursement is increased from 6.5% to 7.0% Chart H.1 shows that there is little increased risk at the front of the period. Chart H.2 shows, however, that there is an increase in risk at the back of the period. The increased risk at the back, however, does not seem so large that it cannot be discounted for the decreasing chances of survival given the assumed health issues of the beneficiary. Thus, the increased risk at the back does not seem large enough to cause doubt that the increase from 6.5% to 7.0% at the front of the period is an improvement.
In contrast, when the disbursement is further increased from 7.0% to 7.5% there is increased risk at the front of the period that is of concern, as well as at the back. In Chart H.3, when the initial disbursement is increased from 7.0% to 7.5% at the front of the period, note that the chances of a decline increase from .15 to about .30, and that the chances of a decline of 1.0 or more from the starting point increase from .025 to .10. Moreover, Chart H.4 shows significant further increased risk at the back of the period. With concern about increased risk at both the front and back of the period, there is doubt that the increase from 7.0% to 7.5% is an improvement. For the 18 year horizon, therefore, the Best Initial Disbursement (BID) is 7.0%. When the initial horizon is cut in half from 36 to 18 years the BID increases by slightly more than a half from 4.5% to 7.0%.
The possibility has just been considered that the beneficiary initially faces health issues that significantly reduce the length of time the disbursements may be required. Another possibility is that health issues arise after the disbursements begin that significantly reduce the number of disbursements that were thought to be necessary initially. In such a case, a similar analysis can be conducted using the remaining value of the portfolio at that time, and the reduced length of the remaining horizon. A significant increase in the disbursements may be possible to cover any additional expenses that may be necessary, such as for assistance. For instance, suppose a turn for the worse occurs in health soon after starting the disbursements assuming an initial horizon of 36 years. Suppose the value of the portfolio is still close to its initial value, but now no more than 18 years of disbursements might be necessary. Based on the analysis just conducted the disbursement can be increased from 4.5% to 7.0 % of initial portfolio value.
Larger Initial Horizons
Suppose now that the disbursement might be necessary for as long as 60 years. That would allow for retiring at age 50 and living up to age 110. The first step again is to find the initial disbursement that provides comparably good sustainability as 3.5% does for an initial horizon of 36 years. Simulations show that a 3.0% initial disbursement has about the same small chance of a decline at year 24 as a 3.5% initial disbursement with a 36 year initial horizon, using the best stock allocation, and an RDR that is .02 above expected return in either case. Now successively increase the initial disbursement by half a percentage point above 3.0%. For the 60 year initial horizon, years 18 and 36 show the increased risks at the front and back of the period, as years 6 and 12 do for the 18 year initial horizon.
For the 18 year initial horizon the initial disbursement can be increased one percentage point above the sustainable level without doubt that the increase is an improvement. For the 60 year horizon, however, only a half percentage point increase is possible without doubt of improvement. For the 60 year initial horizon, the increased risk for an increase from 3.0% to 3.5% at the front of the period is shown in Chart H.5, and at the back in Chart H.6. Chart H.5 shows little increase in risk at the front of the period, whereas Chart H.6 shows that there is increased risk at the back. The increased risk at the back, however, is remote and can be discounted for the decreasing chances of survival for the beneficiary. After this discounting the increased risk in Chart H.6 does not seem large enough to cause doubt that the increase from 3.0% to 3.5% in Chart H.5 at the front of the period is an improvement.
In contrast, when the initial disbursement is further increased from 3.5% to 4.0%, the increased risk at the front of the period is of concern, and there is more increased risk at the back. Note in Chart H.7, when starting at 4.0% that the chances of a decline increase from .10 to .20. Also, there is close to a .10 chance of a decline of 1.0 or more from the starting point, whereas when starting at 3.5% there is little chance of a decline that large. Moreover, Chart H.8 shows significant increased risk at the back of the period. Thus, increased risks at both the front and back of the period are of concern when the initial disbursement is increased from 3.5% to 4.0% causing doubt that this increase is an improvement. The Best Initial Disbursement (BID) for the 60 year initial horizon is therefore 3.5%. That compares with 4.5% for the 36 year initial horizon, and 7.0% for the 18 year horizon.
Perpetual Disbursements
Suppose now that there is not any limit on how long the disbursements may be needed, and that they are assumed to be perpetual, which might be reasonable for an organization. Perpetuity changes the calculation of the limit in Model for the value of the disbursement each year, as discussed in an endnote. For perpetual disbursements, the first step is to again find the initial disbursement that has the same good sustainability as a 3.5% initial disbursement for a 36 year initial horizon. Simulations show that a 2.75% initial disbursement for the perpetual disbursements has about the same small chance of a decline by year 24 under comparable conditions. As this initial disbursement is very close to the 3.0% initial disbursement with good sustainability for a 60 year initial horizon it will be assumed that the BID for perpetual disbursements is also half a percentage point above the initial disbursement with good sustainability, and equal to 3.25%. The best stock allocation for the initial perpetual disbursement with good sustainability of 2.75% is 30%. When the initial disbursement increases to 3.25% the best stock allocation rises to 35% and the RDR is set at .02 above the expected return of this allocation. Using these values, simulations provide the cumulative probability distributions of the disbursements up through any desired future year.
Chart H.9 shows these distributions up through year 240. Of particular interest in the chart is that there is a limit on the chances of a decline equal to about .20 at year 120. No limit on the chances of large declines, however, is evident in the chart. The chances of a decline equal to 3.0 or more from the starting point is .20 at year 120, and the chances of that decline or more increase to .24 at year 240. If there is a limit on the chances of a decline presumably more value is accumulating in the portfolio than is needed to protect the disbursement. When the disbursement becomes sufficiently small relative to the value of the portfolio it should therefore be possible to increase the disbursement with little risk of future declines. Suppose, for instance, that the disbursement is increased whenever it is less than 2.5% of the value of the portfolio. The modification of Model to do so is discussed in an endnote. The increases in the future disbursements obtained are shown in Chart H.10.
The chart shows on the vertical axis the chances that the disbursement will be greater than or equal to the values given on the horizontal axis. By year 24 there is about a .30 chance that the disbursement has increased by 1.0 percentage point or more of initial portfolio value. By year 36 there is about a .30 chance that it has increased by 2.0 percentage points or more. Moreover, the chances of declines at years 24 and 36 remain the same as those shown in Chart H.9, and there is only a slight increase in the chances of a decline at year 60. The chances of declines at years 120 and 240, however, are now somewhat higher, and the chances of a decline no longer reaches a limit at year 120 as the chances at year 240 are now somewhat higher. These slightly higher risks in the very remote future, however, are a very small price to pay for the increases shown in Chart H.10.
There is another risk of declines to consider, however, besides the declines from the initial disbursement of 3.25%. The increases shown in Chart H.10 are net of decreases that may have occurred in disbursements that are over the initial disbursement of 3.25%. Such declines will be disruptive with respect to sustaining habitual spending like the declines shown in Chart H.9. The size and likelihood of any such declines need to be investigated. An endnote discusses the relations that can be added to Model to do so. When these relations are included, the simulations show the chances that the sum of such declines up through a future year are greater than or equal to a given value for an iteration. Such declines, however, turn out not to be a problem when the disbursements are increased when they are less than 2.5% of portfolio value. Chart H.11 shows even by year 60 that there is only a .02 chance that the sum of such declines for an iteration will be equal to or more than 1.0 percentage point of initial portfolio value.
Conclusions
The illustrations at this site generally assume that initially disbursements may be needed for as long as 36 years. A much shorter initial horizon, however, may be appropriate for a beneficiary with health issues, and organizations may want to assume that the disbursements will be needed in perpetuity. For a 36 year initial horizon, and assuming the investment returns in the pre 2008 illustration, Increase argues that the Best Initial Disbursement (BID) is 4.5% of portfolio value. When the initial disbursement is cut in half from 36 to 18 years, the BID increases from 4.5% to 7.0%, whereas for a 60 year initial horizon the BID declines to 3.5%, and to 3.25% for perpetual disbursements. For perpetual disbursements and the pre 2008 returns, a limit of .30 occurs for the chances of a decline, after about 120 years. For perpetual disbursements, disbursements less than 2.5% of portfolio value can be increased with possible significant benefits, and little risk for many years.
Notes
1. For perpetual disbursements, the relation for the limit on the disbursement at the beginning of each year in Model, C*(t), is replaced by mV(t)/(1+m). To obtain this relation let x be the amount that can be disbursed in perpetuity at the beginning of each year including the first from a value, V, when a return, m, is earned each year. To disburse the same amount at the beginning of each year, V must remain the same at the beginning of the next year so V = (V – x)(1 + m). Solving for x gives the stated relation.
2. Suppose that the disbursement is increased when the prior disbursement is less than 2.5% of the current value of the portfolio. To provide some smoothing, the increase in any year is limited to 5% of the prior disbursement. Also, to avoid problems in evaluating the simulation statistics when there are some very large disbursements, the disbursement is limited to 25% of initial portfolio value. 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) < .025V(t), If( .025V(t) > 25, 25, If( .025V(t) <= 1.05C(t-1), .025V(t), 1.05C(t-1))),
Min( C(t-1), C*(t)) ) t = 2, 3, … , T
3. 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( 2:t’ ), where t’ is the year up through which the sum of declines is desired.
Posted September, 2022