The basic model assumes that overlimit disbursements are reset to the limit, and this assumption is followed in determining the Best Initial Disbursement in the page, BID. If future investment returns are poor enough to put the BID above its limit, however, there is also another possibility to consider. Instead of simply reducing the disbursement to its limit, a decision could be made to undertake a major retrenchment, and reset the next disbursement to far below its limit. The reason for doing so would be to reduce the risk of large annual declines in the disbursements, and the chances of very low disbursements in the future. Whether to undertake such a major retrenchment instead of continuing to reset overlimit disbursements to the limit, however, is a sufficiently difficult decision so as to pose a dilemma. It is one of the most important and difficult decisions that may have to be made when making disbursements. It should not be made hypothetically in advance, but only when faced with the actual immediate consequences of the major curtailment of important habitual activities that will be required. Substantially reducing the risk of large annual declines and the chances of low disbursements in the future are clearly very valuable benefits. Are they worth, however, the cost of a major curtailment of important habitual activities? Moreover, otherwise, many of these activities could be continued for many years, and some might never have to be curtailed.
Results from simulations are of significant help in making this decision. Simulations can show how large a retrenchment will be required to significantly reduce the chances of another decline in the disbursements. Simulations can also show the chances of large annual declines in the disbursements if such a major retrenchment is not undertaken, and how much higher the chances might be of very low disbursements in the future. To obtain such results, suppose the New 4% Rule developed in page, BID, is being followed with the same allocation and RDR. Suppose also over the first 12 years that a disbursement of 4% has been made at the beginning of each year, as it has not been over its limit. At the beginning of the last 24 years, however, the value of the portfolio has now declined to 55.5% of its initial value. A calculation shows that a disbursement equal to 4.0% of initial portfolio value over the remaining 24 years is now just about equal to its limit. Consider two possibilities. In one case, any overlimits in the future are reset to the limit. In the other, there is a major retrenchment of 30% and the next disbursement is reduced from 4.0% to 2.8% of initial portfolio value. The distributions of the disbursements at years 12 and 24 of the remaining 24 years are shown for these two possibilities in Charts 6.1 and 6.2.
The retrenchment requires immediately giving up for sure important habitual activities worth 1.2% of initial portfolio value. The cost of this loss, however, depends on when these activities would need to have been curtailed anyway, if overlimits were being reset to the limit. The solid curve in Chart 6.1 shows that if the overlimits were being reset to the limit that by year 12 there is a .37 chance all of the spending lost due to the retrenchment would be lost anyway. This probability is found on the vertical axis where the solid curve is equal to a disbursement of 2.8%, which is what was available after the retrenchment. One less .37, or .63, is the chance that the disbursement is still larger at year 12 than after the retrenchment. Moreover, there are smaller chances that the disbursement at year 12 is much larger than after the retrenchment. In particular, note that there is a .08 chance that there has not been any decline at all, as shown by the solid curve at 4.0% on the horizontal axis. There is a .25 chance that the disbursement is only less by no more than 0.5 percentage points of initial portfolio value. This .25 chance is one less the probability on the vertical axis where the disbursement on the horizontal axis is equal to 3.5%. Thus, there are significant chances that much of he spending lost due to the retrenchment would otherwise be continuing.
Note also at year 12 that the dashed curve begins to turn to the left at a probability of .20 indicating that after the retrenchment there is a .20 chance by year 12 that the disbursement is again at its limit. Nevertheless, comparing the dashed curve to the solid curve for disbursements less than 2.8% shows that there are significant chances that the retrenchment provided significant benefits. The disbursements with the retrenchment are as much as 0.4 percentage points larger, and on average larger by about 0.2 percentage points. Moreover, these improvements are especially beneficial because they are from diminished values of the disbursement. The chances that there will be such benefits as a result of the retrenchment are equal to the .37 probability on the vertical axis where the solid curve becomes equal to 2.8%
When overlimits are reset to the limit Chart 6.1 shows that much of the spending that would have been curtailed by the retrenchment is still continuing at year 12. After year 12, however, some of this continuing spending is further curtailed. The extent to which this further curtailment occurs can be gauged by looking at the results at the end of the disbursement period at year 24 shown in Chart 6.2. At year 24, the solid curve is now equal to a disbursement of 2.8% at a probability of .60 instead of .37. Thus, the chances have declined from .63 to .40 that some spending is continuing that would have been curtailed by the retrenchment if overlimits instead were reset to the limit. Moreover, the chances that there has not been any decline at all are now .06 instead of .08. Also, there is now a .15 chance instead of .25 chance that the disbursement is only less by no more than 0.5 percentage points as indicated by the probability on the vertical axis for a disbursement of 3.5%.
Note also at year 24 that the dashed curve begins to turn to the left at a probability of .30 instead of .20 indicating by the end of the period that there is a .30 instead of a .20 chance that the disbursement is again at its limit. Note, however, that comparing the dashed curve to the solid curve for the disbursements less than 2.8% also shows that the retrenchment is now providing significant increased benefits. The disbursements with the retrenchment are now as much as 0.8 percentage points larger, and on average larger by about 0.4 percentage points. Moreover, the chances that there will be such benefits has significantly increased from .37 to .60 because the solid curve now becomes equal to 2.8% at this higher probability on the vertical axis.
The results in Chart 6.2 are much more favorable for retrenchment than those in Chart 6.1. The results in chart 6.2, however, must be discounted for decreasing life expectancy and the small chance that these benefits will be relevant. Moreover, retrenching to reduce the chances of future lower disbursements will be difficult for beneficiaries who would generally prefer to defer painful actions as long as possible. On the other hand, Charts 6.1 and 6.2 ignore the risk of uncertain annual budgets caused by resetting overlimits to the limit. The substantial reduction in this risk provided by undertaking a major retrenchment deserves further consideration.
Annual Budget Risk
Prior to reaching its limit the annual budget has been protected each year from unfavorable returns by a cushion. Once the limit is reached, however, this cushion no longer exists and annual budgets each year are at risk to a substantial cut. A major retrenchment eliminates annual budget risk unless in the future the disbursement once again reaches its limit. Annual budget declines that do not exceed a few percent should not be too difficult to accommodate. On the other hand, declines of 5%, and especially 10%, will be disruptive. When the disbursement is at its limit, and overlimits are being reset to the limit, the model can be modified to show the risk of large declines. Modifications of the model to do so are discussed in a note. The risk of large annual budget declines for the same conditions as for Charts 6.1 and 6.2 are shown in Charts 6.3 and 6.4.
Chart 6.3 shows the chances that there will be annual declines of over 5%, or over 10%, during the first 12 of the 24 years. In particular, the vertical axis shows the probability that the number of such declines will exceed the number shown on the horizontal axis. Thus, for instance, the probability for the upper curve at zero on the horizontal axis is .84. This shows that there is a .84 chance that there will be one or more annual declines of over 5% during the first 12 of the 24 years. Of much more concern, the lower curve shows that there is a .62 chance of an annual decline of over 10%, and a .30 chance of more than one such decline. There is a .12 chance of more than two. Especially as they are unexpected, annual declines of this size will clearly be very disruptive. The retrenchment does not eliminate any chance of such a large annual decline. Nevertheless, Chart 6.1 does show that the chances of any decline at all over the 12 years have been reduced to .20, which indicates that the risk of large annual declines has been significantly reduced.
Chart 6.4 shows the further increase in the chances of large annual declines when viewed over all of the remaining 24 years. Doubling the length of the period has little effect on the chances of one or two large declines, but much more than doubles the chances of many large declines. Chart 6.2 shows that over the 24 year period the chances of reaching the limit increase to .30 from .20 over the 12 year period. Based on Charts 6.1 and 6.2, beneficiaries who heavily discount the future will not want to undertake the retrenchment. Charts 6.3 and 6.4 show, however, that even if the future is heavily discounted, that the retrenchment can be desirable to eliminate short term budget risk. Nevertheless, for many what to do will be a dilemma.
Shorter Horizons
Suppose instead of first reaching the limit in 12 years that the 4.0% disbursement does so after 24 years, with 12 more years of disbursements possibly remaining to be made. Does the shorter horizon have any effect on the desirability of undertaking a major retrenchment instead of resetting overlimits to the limit? In view of the shorter horizon suppose a retrenchment of 20% is considered instead of 30%. Charts 6.5 and 6.6 show the results in this case versus continuing to reset any overlimits to the limit. With both a smaller retrenchment and shorter periods the charts show there has been little change in key results. In Charts 6.5 and 6.6 the dashed curves turn to the left at the same probabilities on the vertical axis as in Charts 6.1 and 6.2 indicating in either case there are the same chances of being back at the limit either half way or at the end of the remaining period. Moreover, the solid curves cross the dashed curves at about the same probabilities in both sets of charts indicating the same chances in either case that the disbursement will be larger without the retrenchment either half way or at the end of the remaining period. Moreover, annual budget risk will be comparably reduced in either case by the retrenchment. A smaller retrenchment is required in the latter case to get these effects, but curtailing activities may be more difficult later in the period. Thus, in general it appears that the retrenchment dilemma may be very similar whenever it occurs over the disbursement period.
Conclusions
When a disbursement is over its limit the model calls for the disbursement to be reset to its limit. There is an alternative, however, that poses a dilemma due to the very high costs and benefits involved. A major retrenchment can be undertaken that significantly reduces the chances of low disbursements at the back of the remaining disbursement period, and the risk of annual budget declines. Such a decision should be made only after the activities that will have to be curtailed have been clearly identified so that the consequences of doing so can be properly judged. Without the retrenchment, many of these activities could continue for many years and some might never have to be curtailed. The immediate and certain cost of the retrenchment must be weighed against significantly reduced chances of low disbursements at the back of the remaining period, and the likely avoidance of any further annual declines.
Note
The objective is to find the chances of the number of annual declines over a given period that exceed the proportion q. If, for instance, q=.05 these are the number of declines that exceed 5%. The probability that the number of such declines exceeds a given number can be found by adding a couple of columns to the spreadsheet of the model. One column sets the value of L(t) equal to one if such a decline occurs at t, and to zero otherwise:
L(t)=If[C(t)<(1–q)*C(t–1),1,0] t = 2, 3, … T
The other column calculates the sum of the L(t) up through t’, t’’, T:
N(t)=Sum[L(2):L(t)] t = t’, t’’, T
For a given value of q and a given period of time, simulations are used to find the portion of the total iterations for which the number of such declines exceeds any given number.
Posted November 2018 Revised July 2022 October 2024
Retrench
Retrenchment Dilemma
The basic model assumes that overlimit disbursements are reset to the limit, and this assumption is followed in determining the Best Initial Disbursement in the page, BID. If future investment returns are poor enough to put the BID above its limit, however, there is also another possibility to consider. Instead of simply reducing the disbursement to its limit, a decision could be made to undertake a major retrenchment, and reset the next disbursement to far below its limit. The reason for doing so would be to reduce the risk of large annual declines in the disbursements, and the chances of very low disbursements in the future. Whether to undertake such a major retrenchment instead of continuing to reset overlimit disbursements to the limit, however, is a sufficiently difficult decision so as to pose a dilemma. It is one of the most important and difficult decisions that may have to be made when making disbursements. It should not be made hypothetically in advance, but only when faced with the actual immediate consequences of the major curtailment of important habitual activities that will be required. Substantially reducing the risk of large annual declines and the chances of low disbursements in the future are clearly very valuable benefits. Are they worth, however, the cost of a major curtailment of important habitual activities? Moreover, otherwise, many of these activities could be continued for many years, and some might never have to be curtailed.
Results from simulations are of significant help in making this decision. Simulations can show how large a retrenchment will be required to significantly reduce the chances of another decline in the disbursements. Simulations can also show the chances of large annual declines in the disbursements if such a major retrenchment is not undertaken, and how much higher the chances might be of very low disbursements in the future. To obtain such results, suppose the New 4% Rule developed in page, BID, is being followed with the same allocation and RDR. Suppose also over the first 12 years that a disbursement of 4% has been made at the beginning of each year, as it has not been over its limit. At the beginning of the last 24 years, however, the value of the portfolio has now declined to 55.5% of its initial value. A calculation shows that a disbursement equal to 4.0% of initial portfolio value over the remaining 24 years is now just about equal to its limit. Consider two possibilities. In one case, any overlimits in the future are reset to the limit. In the other, there is a major retrenchment of 30% and the next disbursement is reduced from 4.0% to 2.8% of initial portfolio value. The distributions of the disbursements at years 12 and 24 of the remaining 24 years are shown for these two possibilities in Charts 6.1 and 6.2.
The retrenchment requires immediately giving up for sure important habitual activities worth 1.2% of initial portfolio value. The cost of this loss, however, depends on when these activities would need to have been curtailed anyway, if overlimits were being reset to the limit. The solid curve in Chart 6.1 shows that if the overlimits were being reset to the limit that by year 12 there is a .37 chance all of the spending lost due to the retrenchment would be lost anyway. This probability is found on the vertical axis where the solid curve is equal to a disbursement of 2.8%, which is what was available after the retrenchment. One less .37, or .63, is the chance that the disbursement is still larger at year 12 than after the retrenchment. Moreover, there are smaller chances that the disbursement at year 12 is much larger than after the retrenchment. In particular, note that there is a .08 chance that there has not been any decline at all, as shown by the solid curve at 4.0% on the horizontal axis. There is a .25 chance that the disbursement is only less by no more than 0.5 percentage points of initial portfolio value. This .25 chance is one less the probability on the vertical axis where the disbursement on the horizontal axis is equal to 3.5%. Thus, there are significant chances that much of he spending lost due to the retrenchment would otherwise be continuing.
Note also at year 12 that the dashed curve begins to turn to the left at a probability of .20 indicating that after the retrenchment there is a .20 chance by year 12 that the disbursement is again at its limit. Nevertheless, comparing the dashed curve to the solid curve for disbursements less than 2.8% shows that there are significant chances that the retrenchment provided significant benefits. The disbursements with the retrenchment are as much as 0.4 percentage points larger, and on average larger by about 0.2 percentage points. Moreover, these improvements are especially beneficial because they are from diminished values of the disbursement. The chances that there will be such benefits as a result of the retrenchment are equal to the .37 probability on the vertical axis where the solid curve becomes equal to 2.8%
When overlimits are reset to the limit Chart 6.1 shows that much of the spending that would have been curtailed by the retrenchment is still continuing at year 12. After year 12, however, some of this continuing spending is further curtailed. The extent to which this further curtailment occurs can be gauged by looking at the results at the end of the disbursement period at year 24 shown in Chart 6.2. At year 24, the solid curve is now equal to a disbursement of 2.8% at a probability of .60 instead of .37. Thus, the chances have declined from .63 to .40 that some spending is continuing that would have been curtailed by the retrenchment if overlimits instead were reset to the limit. Moreover, the chances that there has not been any decline at all are now .06 instead of .08. Also, there is now a .15 chance instead of .25 chance that the disbursement is only less by no more than 0.5 percentage points as indicated by the probability on the vertical axis for a disbursement of 3.5%.
Note also at year 24 that the dashed curve begins to turn to the left at a probability of .30 instead of .20 indicating by the end of the period that there is a .30 instead of a .20 chance that the disbursement is again at its limit. Note, however, that comparing the dashed curve to the solid curve for the disbursements less than 2.8% also shows that the retrenchment is now providing significant increased benefits. The disbursements with the retrenchment are now as much as 0.8 percentage points larger, and on average larger by about 0.4 percentage points. Moreover, the chances that there will be such benefits has significantly increased from .37 to .60 because the solid curve now becomes equal to 2.8% at this higher probability on the vertical axis.
The results in Chart 6.2 are much more favorable for retrenchment than those in Chart 6.1. The results in chart 6.2, however, must be discounted for decreasing life expectancy and the small chance that these benefits will be relevant. Moreover, retrenching to reduce the chances of future lower disbursements will be difficult for beneficiaries who would generally prefer to defer painful actions as long as possible. On the other hand, Charts 6.1 and 6.2 ignore the risk of uncertain annual budgets caused by resetting overlimits to the limit. The substantial reduction in this risk provided by undertaking a major retrenchment deserves further consideration.
Annual Budget Risk
Prior to reaching its limit the annual budget has been protected each year from unfavorable returns by a cushion. Once the limit is reached, however, this cushion no longer exists and annual budgets each year are at risk to a substantial cut. A major retrenchment eliminates annual budget risk unless in the future the disbursement once again reaches its limit. Annual budget declines that do not exceed a few percent should not be too difficult to accommodate. On the other hand, declines of 5%, and especially 10%, will be disruptive. When the disbursement is at its limit, and overlimits are being reset to the limit, the model can be modified to show the risk of large declines. Modifications of the model to do so are discussed in a note. The risk of large annual budget declines for the same conditions as for Charts 6.1 and 6.2 are shown in Charts 6.3 and 6.4.
Chart 6.3 shows the chances that there will be annual declines of over 5%, or over 10%, during the first 12 of the 24 years. In particular, the vertical axis shows the probability that the number of such declines will exceed the number shown on the horizontal axis. Thus, for instance, the probability for the upper curve at zero on the horizontal axis is .84. This shows that there is a .84 chance that there will be one or more annual declines of over 5% during the first 12 of the 24 years. Of much more concern, the lower curve shows that there is a .62 chance of an annual decline of over 10%, and a .30 chance of more than one such decline. There is a .12 chance of more than two. Especially as they are unexpected, annual declines of this size will clearly be very disruptive. The retrenchment does not eliminate any chance of such a large annual decline. Nevertheless, Chart 6.1 does show that the chances of any decline at all over the 12 years have been reduced to .20, which indicates that the risk of large annual declines has been significantly reduced.
Chart 6.4 shows the further increase in the chances of large annual declines when viewed over all of the remaining 24 years. Doubling the length of the period has little effect on the chances of one or two large declines, but much more than doubles the chances of many large declines. Chart 6.2 shows that over the 24 year period the chances of reaching the limit increase to .30 from .20 over the 12 year period. Based on Charts 6.1 and 6.2, beneficiaries who heavily discount the future will not want to undertake the retrenchment. Charts 6.3 and 6.4 show, however, that even if the future is heavily discounted, that the retrenchment can be desirable to eliminate short term budget risk. Nevertheless, for many what to do will be a dilemma.
Shorter Horizons
Suppose instead of first reaching the limit in 12 years that the 4.0% disbursement does so after 24 years, with 12 more years of disbursements possibly remaining to be made. Does the shorter horizon have any effect on the desirability of undertaking a major retrenchment instead of resetting overlimits to the limit? In view of the shorter horizon suppose a retrenchment of 20% is considered instead of 30%. Charts 6.5 and 6.6 show the results in this case versus continuing to reset any overlimits to the limit. With both a smaller retrenchment and shorter periods the charts show there has been little change in key results. In Charts 6.5 and 6.6 the dashed curves turn to the left at the same probabilities on the vertical axis as in Charts 6.1 and 6.2 indicating in either case there are the same chances of being back at the limit either half way or at the end of the remaining period. Moreover, the solid curves cross the dashed curves at about the same probabilities in both sets of charts indicating the same chances in either case that the disbursement will be larger without the retrenchment either half way or at the end of the remaining period. Moreover, annual budget risk will be comparably reduced in either case by the retrenchment. A smaller retrenchment is required in the latter case to get these effects, but curtailing activities may be more difficult later in the period. Thus, in general it appears that the retrenchment dilemma may be very similar whenever it occurs over the disbursement period.
Conclusions
When a disbursement is over its limit the model calls for the disbursement to be reset to its limit. There is an alternative, however, that poses a dilemma due to the very high costs and benefits involved. A major retrenchment can be undertaken that significantly reduces the chances of low disbursements at the back of the remaining disbursement period, and the risk of annual budget declines. Such a decision should be made only after the activities that will have to be curtailed have been clearly identified so that the consequences of doing so can be properly judged. Without the retrenchment, many of these activities could continue for many years and some might never have to be curtailed. The immediate and certain cost of the retrenchment must be weighed against significantly reduced chances of low disbursements at the back of the remaining period, and the likely avoidance of any further annual declines.
Note
The objective is to find the chances of the number of annual declines over a given period that exceed the proportion q. If, for instance, q=.05 these are the number of declines that exceed 5%. The probability that the number of such declines exceeds a given number can be found by adding a couple of columns to the spreadsheet of the model. One column sets the value of L(t) equal to one if such a decline occurs at t, and to zero otherwise:
L(t)=If[C(t)<(1–q)*C(t–1),1,0] t = 2, 3, … T
The other column calculates the sum of the L(t) up through t’, t’’, T:
N(t)=Sum[L(2):L(t)] t = t’, t’’, T
For a given value of q and a given period of time, simulations are used to find the portion of the total iterations for which the number of such declines exceeds any given number.
Posted November 2018 Revised July 2022 October 2024