The length of the horizon is a major factor affecting the sustainability of an initial disbursement, and warrants significant attention. The simulations so far have assumed an initial horizon of 36 years. That would be the horizon of someone just reaching 65 and planning to make a last disbursement upon reaching 100. Many, however, have health issues, and a far shorter horizon. Others may be making disbursements from a retirement portfolio starting well before 65, or want to plan on making disbursements longer than to 100. The original 4% Rule study assumed a 30-year horizon. Thus, of interest is the initial disbursement that would give comparable sustainability if the initial horizon is half as long or 25% longer than 36 years. Also, sometimes disbursements are being made from a portfolio by a trust or an organization with no limit on how long they will last. In such cases, the disbursements can be considered as perpetual. Moreover, for perpetual disbursements, the possibility of increases in the disbursements is of particular interest. Beneficiaries may be willing to let excess funds accumulate in case they are needed for an emergency, realizing that if not needed for that purpose the funds will be available to increase bequests. For perpetual disbursements, however, there is not an estate.
Shorter Horizons
Beneficiaries with serious health issues will surely not want to plan on making disbursements initially with a 36-year horizon. Cutting the horizon by half to 18 years in some such cases may be reasonable. Suppose that other than the shorter horizon the conditions are the same as for the New 4% Rule, except the stock allocation is reduced somewhat due to the shorter horizon. For an 18-year initial horizon years 6 and 12 are respectively a third and two- thirds of the way through the period, the same as years 12 and 24 for a 36-year horizon. Charts 9.1 and 9.2 show the cumulative probability distributions at years 6 and 12 for initial disbursements of 6.0% and 6.5% when there is an 18-year initial horizon. Compare these curves with those for the 3.5% and 4.0% initial disbursements in Charts 5.13 and 5.14 at page, BID, for a 36-year horizon. The curves are virtually the same except that the curves in Charts 9.1 and 9.2 are shifted to the right on the horizontal axis by 2.5 percentage points. Thus, the sustainability risk is similar in either case. The 50% reduction in the horizon, however, has allowed a somewhat more than 50% increase in the initial disbursement.
Another possibility to consider is that a significant deterioration in health occurs after the disbursements begin. In this latter case, the horizon being used to calculate the limit can be significantly reduced to reflect the new situation. The past budget can be ignored given the additional need for assistance, and the additional spending can be accommodated by the new higher limit based on the shorter horizon. In effect, basing initial plans on a long horizon provides insurance for assistance if that should become necessary. The case just considered shows that significant funds may be available if a turn for the worse in health occurs early in the disbursement period. The value of the portfolio may be little changed, and if the horizon has been reduced by a half, the funds available to cover assistance may have increased by more than half of current spending.
Longer Horizons
Suppose now instead of being 50% shorter that the initial disbursement period is 25% longer, and equal to 45 instead of 36 years. This initial disbursement period would, for instance, cover starting at age 58 and making a final disbursement at age 102, which seems reasonable. For a 45-year initial horizon, years 15 and 30 are respectively a third and two-thirds of the way through the disbursement period. Charts 9.3 and 9.4 show the cumulative probability distributions at years 15 and 30 when starting at initial disbursements of 3.0% and 3.5% for the 45-year horizon. The curves are virtually the same as those starting at 3.5% and 4.0% in Charts 5.13 and 5.14 in page, BID, for a 36-year horizon except that they are shifted to the left by half a percentage point. Thus, the stainability risk is similar when the initial disbursement is reduced by half a percentage point for the longer horizon.
Perpetuity
Suppose now that the beneficiary of the disbursements is not an individual, but an organization, or a trust that has been set up to pursue a specified objective. In either case, there is not any limit on how long the disbursements may continue, and they can be considered as perpetual. Suppose furthermore that the conditions are otherwise the same as those just considered when the initial horizon is 45 years. As increasing the horizon from 36 to 45 years required reducing the initial disbursement by half a percentage point to achieve comparable sustainability, it appears that a further half point reduction should be considered when the horizon becomes unlimited. For an unlimited horizon a key issue becomes finding a limit on the cumulative probability distribution of the disbursements as the years increase. It turns out that a limit on this probability distribution can be found, but it is so far in the future as to be of little practical consequence. The chances of a decline do not increase after about 100 years, and the chances of running out of funds do not increase after about 300 years. Nevertheless, the shorter-term results are of concern in such situations, and the long-term results are of theoretical interest. Technically, for the perpetual case, the limit each year, C*(t), becomes equal simply to RDR*V(t)/(1+RDR).
Charts 9.5 and 9.6 show the cumulative probability distributions in future years of initial disbursements of respectively 2.5% and 3.0% when the future disbursements are expected to be perpetual. It appears that many would be willing to accept the increase in sustainability risk in going from an initial disbursement of 2.5% to 3.0% to get an additional half percentage point of funds. Moreover, the risk of a decline by year 36 is similar for either the 3.5% initial disbursement with the 45-year horizon or the 3.0% initial disbursement for the unlimited horizon. Thus, the sustainability risk of a 3.0% initial disbursement with a perpetual horizon appears comparable to those considered earlier despite the much higher risks at later years.
Of theoretical interest in these charts is what happens in the far distant future. Suppose that disbursements that are less than a quarter percentage point of initial portfolio value are considered to be essentially the same as running out of funds. For perpetual disbursements running out of funds is then possible even when a limit is being put on the annual disbursements to prevent that from happening. Note in either chart for the perpetual disbursements that for year 72 the curve is at a zero probability for a disbursement of a quarter percentage point. Thus, in either case, there is a chance of running out of funds by year 72. At years after 72 the chances of running out of funds increase until they reach .22 in Chart 9.5 and .34 in Chart 9.6. These are the probabilities on the vertical axis of a quarter percentage point disbursement when these latter disbursements are at their limits about 300 years in the future. These probabilities are at their limits because doubling the number of years does not change the probabilities. At the limit, however, there are higher chances of smaller declines. The limit on the chances that there will be a decline are shown by the probabilities on the far right of the upper curves, which are .34 in Chart 9.5 and .54 in Chart 9.6.
Increaases considers the possibility of increasing the disbursement when the margin protecting the disbursement from exceeding its limit increases above the initial value of that margin. As the initial margin for the 4.0% initial disbursement in that case was about 35%, the disbursement was increased when it became less than 65% of its limit. For perpetual disbursements, the limit is a percentage of the value of the portfolio. The disbursement will be less than the initial margin when the disbursement is less than its initial percentage of the portfolio of 3.0%. Thus, for the perpetual case, comparable increases are made in the disbursement when it falls below 3.0% of the value of the portfolio. The procedure for making such increases in the simulations is the same as in the note for Increases, except that .03*V(t) replaces .65*C*(t).
When making such increases Chart 9.7 shows the probability that the disbursement will be greater than or equal to the values on the horizontal axis. Chart 9.7 is similar to Chart 8.1 in Increases that showed the increases that could be obtained with a 4.0% initial disbursement for a 36-year horizon when disbursements are made when the current disbursement is less than its limit by more than the initial margin. When the horizon becomes longer relatively more must be held in reserve to protect the disbursement from worse than expected investment returns. Thus, as the horizon increases the chances of a given increase might be expected to be less, and this is what happens, but the difference is fairly small. Chart 9.7 shows for the perpetuity that the chances of a one percentage point increase or more in the disbursement by year 24 are about a third. In Chart 8.1 for the 36-year horizon these chances are about .40.
As well as showing the benefits of increasing the disbursements with a 36-year initial horizon, Increases also considered the costs of making these increases. One cost is the increased chances of declines below the initial disbursement. For the perpetuity this cost is shown in Chart 9.8 where the dashed curves show the chances of these declines when the increases are not made. As for the 36-year horizon, the cost in terms of the increased chances of these declines is small at years 12 and 24. Later on, however, this cost becomes more appreciable. The beneficiaries of perpetual disbursements, however, may be willing to discount these distant costs to take advantage of the increases
.
Another cost considered in Increases for the 36 year horizon is the possibility of declines in the increased disbursements. For the perpetuity case, such declines are evident in Chart 9.7 because the chances of very small increases are less at later years. Thus, some increases are getting larger over time, but others are getting smaller, and some sufficiently so as to no longer be increases. For the 36 year horizon, tests indicated that possible declines from the increases were unlikely to dissuade beneficiaries from miaking such increases. For perpetual disbursements similar tests give similar results at least through year 36. For a 36 year horizon, a likely factor dissuading beneficiaties from making increases is the possible need for extra funds to cover emergencies. The beneficiaries of perpetual disbursements seem more likely to favor making the increases.
Conclusions
An important factor affecting the sustainability of an initial disbursement is the length of the initial horizon. Most of the illustrations assume a 36 year initial horizon, which would be the horizon for someone starting at 65 and planning to make a last disbursement at age 100. If the initial horizon is reduced by a half under otherwise the same cnditions the iinital disbursement with similar sustainability risk increases from 4.0% to 6.5%. If the initial horizon is increased by a quarter the initial disbursment declines from 4.0% to 3.5%. When the disbursements are perpetual there is a further decline from 3.5% to 3.0%. For perpetual disbursements there is the possibility of essentially running out of funds by year 72. There is also a limit on the chances of declines of any size. The limit on the chances of a deccline occurs after about 100 years, and is equal to about a half. The limit on the chances of running out of funds occurs after about 300 years, and is equal to about a third. Increasing future perpetual disbursements when the disbursement becomes less than 3.0% of the value of the portfolio provides meaningful chances of future increases at what may be an acceptable cost.
Horizons
Horizons
The length of the horizon is a major factor affecting the sustainability of an initial disbursement, and warrants significant attention. The simulations so far have assumed an initial horizon of 36 years. That would be the horizon of someone just reaching 65 and planning to make a last disbursement upon reaching 100. Many, however, have health issues, and a far shorter horizon. Others may be making disbursements from a retirement portfolio starting well before 65, or want to plan on making disbursements longer than to 100. The original 4% Rule study assumed a 30-year horizon. Thus, of interest is the initial disbursement that would give comparable sustainability if the initial horizon is half as long or 25% longer than 36 years. Also, sometimes disbursements are being made from a portfolio by a trust or an organization with no limit on how long they will last. In such cases, the disbursements can be considered as perpetual. Moreover, for perpetual disbursements, the possibility of increases in the disbursements is of particular interest. Beneficiaries may be willing to let excess funds accumulate in case they are needed for an emergency, realizing that if not needed for that purpose the funds will be available to increase bequests. For perpetual disbursements, however, there is not an estate.
Shorter Horizons
Beneficiaries with serious health issues will surely not want to plan on making disbursements initially with a 36-year horizon. Cutting the horizon by half to 18 years in some such cases may be reasonable. Suppose that other than the shorter horizon the conditions are the same as for the New 4% Rule, except the stock allocation is reduced somewhat due to the shorter horizon. For an 18-year initial horizon years 6 and 12 are respectively a third and two- thirds of the way through the period, the same as years 12 and 24 for a 36-year horizon. Charts 9.1 and 9.2 show the cumulative probability distributions at years 6 and 12 for initial disbursements of 6.0% and 6.5% when there is an 18-year initial horizon. Compare these curves with those for the 3.5% and 4.0% initial disbursements in Charts 5.13 and 5.14 at page, BID, for a 36-year horizon. The curves are virtually the same except that the curves in Charts 9.1 and 9.2 are shifted to the right on the horizontal axis by 2.5 percentage points. Thus, the sustainability risk is similar in either case. The 50% reduction in the horizon, however, has allowed a somewhat more than 50% increase in the initial disbursement.
Another possibility to consider is that a significant deterioration in health occurs after the disbursements begin. In this latter case, the horizon being used to calculate the limit can be significantly reduced to reflect the new situation. The past budget can be ignored given the additional need for assistance, and the additional spending can be accommodated by the new higher limit based on the shorter horizon. In effect, basing initial plans on a long horizon provides insurance for assistance if that should become necessary. The case just considered shows that significant funds may be available if a turn for the worse in health occurs early in the disbursement period. The value of the portfolio may be little changed, and if the horizon has been reduced by a half, the funds available to cover assistance may have increased by more than half of current spending.
Longer Horizons
Suppose now instead of being 50% shorter that the initial disbursement period is 25% longer, and equal to 45 instead of 36 years. This initial disbursement period would, for instance, cover starting at age 58 and making a final disbursement at age 102, which seems reasonable. For a 45-year initial horizon, years 15 and 30 are respectively a third and two-thirds of the way through the disbursement period. Charts 9.3 and 9.4 show the cumulative probability distributions at years 15 and 30 when starting at initial disbursements of 3.0% and 3.5% for the 45-year horizon. The curves are virtually the same as those starting at 3.5% and 4.0% in Charts 5.13 and 5.14 in page, BID, for a 36-year horizon except that they are shifted to the left by half a percentage point. Thus, the stainability risk is similar when the initial disbursement is reduced by half a percentage point for the longer horizon.
Perpetuity
Suppose now that the beneficiary of the disbursements is not an individual, but an organization, or a trust that has been set up to pursue a specified objective. In either case, there is not any limit on how long the disbursements may continue, and they can be considered as perpetual. Suppose furthermore that the conditions are otherwise the same as those just considered when the initial horizon is 45 years. As increasing the horizon from 36 to 45 years required reducing the initial disbursement by half a percentage point to achieve comparable sustainability, it appears that a further half point reduction should be considered when the horizon becomes unlimited. For an unlimited horizon a key issue becomes finding a limit on the cumulative probability distribution of the disbursements as the years increase. It turns out that a limit on this probability distribution can be found, but it is so far in the future as to be of little practical consequence. The chances of a decline do not increase after about 100 years, and the chances of running out of funds do not increase after about 300 years. Nevertheless, the shorter-term results are of concern in such situations, and the long-term results are of theoretical interest. Technically, for the perpetual case, the limit each year, C*(t), becomes equal simply to RDR*V(t)/(1+RDR).
Charts 9.5 and 9.6 show the cumulative probability distributions in future years of initial disbursements of respectively 2.5% and 3.0% when the future disbursements are expected to be perpetual. It appears that many would be willing to accept the increase in sustainability risk in going from an initial disbursement of 2.5% to 3.0% to get an additional half percentage point of funds. Moreover, the risk of a decline by year 36 is similar for either the 3.5% initial disbursement with the 45-year horizon or the 3.0% initial disbursement for the unlimited horizon. Thus, the sustainability risk of a 3.0% initial disbursement with a perpetual horizon appears comparable to those considered earlier despite the much higher risks at later years.
Of theoretical interest in these charts is what happens in the far distant future. Suppose that disbursements that are less than a quarter percentage point of initial portfolio value are considered to be essentially the same as running out of funds. For perpetual disbursements running out of funds is then possible even when a limit is being put on the annual disbursements to prevent that from happening. Note in either chart for the perpetual disbursements that for year 72 the curve is at a zero probability for a disbursement of a quarter percentage point. Thus, in either case, there is a chance of running out of funds by year 72. At years after 72 the chances of running out of funds increase until they reach .22 in Chart 9.5 and .34 in Chart 9.6. These are the probabilities on the vertical axis of a quarter percentage point disbursement when these latter disbursements are at their limits about 300 years in the future. These probabilities are at their limits because doubling the number of years does not change the probabilities. At the limit, however, there are higher chances of smaller declines. The limit on the chances that there will be a decline are shown by the probabilities on the far right of the upper curves, which are .34 in Chart 9.5 and .54 in Chart 9.6.
Increaases considers the possibility of increasing the disbursement when the margin protecting the disbursement from exceeding its limit increases above the initial value of that margin. As the initial margin for the 4.0% initial disbursement in that case was about 35%, the disbursement was increased when it became less than 65% of its limit. For perpetual disbursements, the limit is a percentage of the value of the portfolio. The disbursement will be less than the initial margin when the disbursement is less than its initial percentage of the portfolio of 3.0%. Thus, for the perpetual case, comparable increases are made in the disbursement when it falls below 3.0% of the value of the portfolio. The procedure for making such increases in the simulations is the same as in the note for Increases, except that .03*V(t) replaces .65*C*(t).
When making such increases Chart 9.7 shows the probability that the disbursement will be greater than or equal to the values on the horizontal axis. Chart 9.7 is similar to Chart 8.1 in Increases that showed the increases that could be obtained with a 4.0% initial disbursement for a 36-year horizon when disbursements are made when the current disbursement is less than its limit by more than the initial margin. When the horizon becomes longer relatively more must be held in reserve to protect the disbursement from worse than expected investment returns. Thus, as the horizon increases the chances of a given increase might be expected to be less, and this is what happens, but the difference is fairly small. Chart 9.7 shows for the perpetuity that the chances of a one percentage point increase or more in the disbursement by year 24 are about a third. In Chart 8.1 for the 36-year horizon these chances are about .40.
As well as showing the benefits of increasing the disbursements with a 36-year initial horizon, Increases also considered the costs of making these increases. One cost is the increased chances of declines below the initial disbursement. For the perpetuity this cost is shown in Chart 9.8 where the dashed curves show the chances of these declines when the increases are not made. As for the 36-year horizon, the cost in terms of the increased chances of these declines is small at years 12 and 24. Later on, however, this cost becomes more appreciable. The beneficiaries of perpetual disbursements, however, may be willing to discount these distant costs to take advantage of the increases
.
Another cost considered in Increases for the 36 year horizon is the possibility of declines in the increased disbursements. For the perpetuity case, such declines are evident in Chart 9.7 because the chances of very small increases are less at later years. Thus, some increases are getting larger over time, but others are getting smaller, and some sufficiently so as to no longer be increases. For the 36 year horizon, tests indicated that possible declines from the increases were unlikely to dissuade beneficiaries from miaking such increases. For perpetual disbursements similar tests give similar results at least through year 36. For a 36 year horizon, a likely factor dissuading beneficiaties from making increases is the possible need for extra funds to cover emergencies. The beneficiaries of perpetual disbursements seem more likely to favor making the increases.
Conclusions
An important factor affecting the sustainability of an initial disbursement is the length of the initial horizon. Most of the illustrations assume a 36 year initial horizon, which would be the horizon for someone starting at 65 and planning to make a last disbursement at age 100. If the initial horizon is reduced by a half under otherwise the same cnditions the iinital disbursement with similar sustainability risk increases from 4.0% to 6.5%. If the initial horizon is increased by a quarter the initial disbursment declines from 4.0% to 3.5%. When the disbursements are perpetual there is a further decline from 3.5% to 3.0%. For perpetual disbursements there is the possibility of essentially running out of funds by year 72. There is also a limit on the chances of declines of any size. The limit on the chances of a deccline occurs after about 100 years, and is equal to about a half. The limit on the chances of running out of funds occurs after about 300 years, and is equal to about a third. Increasing future perpetual disbursements when the disbursement becomes less than 3.0% of the value of the portfolio provides meaningful chances of future increases at what may be an acceptable cost.
Prosted September 2022 Revised October 2024