The basic model in Model assumes that overlimit disbursements are reset to the limit, and this assumption is followed in determining the Best Initial Disbursement (BID) in Increase. 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, assume the investment returns in the pre 2008 illustration, and that the initial disbursement is the Best Initial Disbursement (BID) found for this case in Increase of 4.5%. Suppose over the first 12 years that this disbursement is made at the beginning of each year, as it is not over its limit. At the beginning of the last 24 years, however, the value of the portfolio has declined to 57% of its initial value. A calculation shows that a disbursement equal to 4.5% of initial portfolio value is now just about equal to its limit. Consider two possibilities. In one case, any overlimits are reset to the limit. In the other, there is a major retrenchment of 30% and the next disbursement is reduced from 4.5% to 3.15%. Any subsequent overlimit is assumed to be reset to its limit. If another overlimit were to occur, however, a decision could be made to undertake another major retrenchment. The distributions of the disbursements at years 12 and 24 of the remaining 24 years are shown for these conditions in Charts R.1 and R.2.
There is no doubt that the retrenchment is not an improvement over the first few years. The retrenchment means there is virtually no chance of any annual declines, but that is scant compensation for the loss caused by a major retrenchment. The most favorable case for the retrenchment is at the end of the disbursement period in Chart R.2. The chances that the disbursement is larger with the retrenchment are given by the .60 probability on the vertical axis where the curve starting at 4.5% crosses the curve for the retrenchment. Note that if the disbursement is larger with the retrenchment, the expected amount by which it is larger is sizable. It is roughly equal to about half the distance between the curves on the horizontal axis at a probability equal to .30 on the vertical axis. Half of this distance is a little less than half a percentage point of initial portfolio value. Note also the chances that there has been a decline with the retrenchment is .30 as shown by the probability on the vertical axis where the curve for the retrenchment begins to move to the left. Thus, the retrenchment is not an improvement early in the period, but does appear to be an improvement at the end of the period. At year 24 there is a .60 chance that lower disbursements have been avoided, and that the disbursement on average is larger than it would have been without a retrenchment by a little less than half a percentage point of initial portfolio value. Moreover, the chances are .70 that there have not been any annual declines in the disbursements over the 24 years.
The end of the period, however, is a very long time to wait for benefits. Moreover, with the declining chances of survival, benefits anywhere near the end of the period are unlikely to even be applicable. Thus, for those who choose not to retrench, the benefits in Chart R.2 appear to be only a remote downside risk. The more relevant benefits of the retrenchment to weigh against the very large and certain cost of the retrenchment in the early years are those at year 12 in R.1. These benefits although still well in the future, have a reasonably good chance of being applicable. The benefits of the retrenchment in R.1 are similar to those in R.2, but far more muted. Instead of a .60 chance that the disbursement will be larger with the retrenchment, the chances at year 12 are .40. Instead of there being a .60 chance that the disbursement on average will be larger by a little less than a half percentage point, at year 12 there is a .40 chance on average it will be larger by a little less than a quarter percentage point. Nevertheless, reducing the chances of very low disbursements and very likely avoiding large annual declines are important. It appears questionable, however, how many will be willing to pay the high cost of these possible benefits, which is why such a retrenchment causes a dilemma.
Lower Returns
Suppose instead of running the simulations using the investment returns in the pre 2008 illustration that the hypothetical lower returns specified in Model to gauge the effect of lower returns are used. As discussed in Increase doing so reduces the Best Initial Disbursement (BID) from 4.5% to 3.5%. Also, the stock allocation increases to 60% and the RDR is reduced to .044. Suppose in this case that the initial disbursement of 3.5% is made over the first 12 years as this disbursement remains below its limit. At the beginning of the last 24 years, however, the value of the portfolio has declined to 53.5% of its initial value, and a calculation indicates that a disbursement equal to 3.5% of initial portfolio value is just about equal to its limit. Suppose in this case that a major retrenchment is undertaken by reducing the next disbursement by 30% from 3.5% to 2.45% of initial portfolio value. The results of doing so are compared to continuing to reset overlimits to the limit in Charts R.3 and R.4. Except for being one percentage point less on the horizontal axis, the curves for the lower returns are almost the same as for the higher returns in Charts R.1 and R.2. Thus, the lower returns have no effect on the desirability of undertaking a major retrenchment when the disbursement is at its limit. There is the same dilemma as with the higher returns when a disbursement is at its limit.
Shorter Horizons
Suppose instead of first being overlimit after 12 years with the pre 2008 illustration that the 4.5% initial disbursement is not overlimit until after 24 years. With a shorter horizon presumably a smaller percentage retrenchment will be sufficient to get similar results, and that turns out to be true. Suppose for the first 24 years that a 4.5% initial disbursement is not overlimit. At the beginning of the last 12 years, however, the portfolio is down to 39% of its initial value. A calculation shows that a disbursement of 4.5% of initial portfolio value is now just about equal to its limit. Charts R.5 and R.6 compare the results with and without a 20% retrenchment at years 6 and 12 of the remaining 12 years. At first glance, these charts look similar to the earlier ones, but there are some differences. Both the costs and benefits of the retrenchment are less with the shorter horizon. The cost of the retrenchment is less as the retrenchment is now 20% instead of 30%. The benefits are also less because the chances that the disbursement will be larger with the retrenchment half way through the period are now .30 instead of .40, At the end of the period the decline is from .60 to .50. The beneficiary in this case has survived for 24 years, but looking forward the chances of surviving to the end of the remaining period or halfway may not have changed that much. The wait time for the benefits, however, is much shorter. All things considered, the dilemma after 24 years appears very similar to the dilemma after 12 years.
Annual Declines
So far, the focus has been on how a major retrenchment will reduce the chances of low disbursements later in the disbursement period. The other benefit, however, is reducing the risk of large annual declines, and that benefit begins immediately after the major retrenchment occurs. The earlier charts show the chances that the retrenchment will avoid any chance of a decline. The major concern, however, is avoiding large declines, and the value of the retrenchment in this regard depends on the chances that large annual declines will occur without the retrenchment. Modification of the model to obtain the chances of large declines is discussed in a note. When simulations are run using this procedure, the results obtained are shown in Charts R.7 and R.8. In particular, these charts show the chances of large annual declines when a 4.5% initial disbursement with the returns in the pre 2008 illustration is first at its limit with 24 years of disbursements remaining.
Specifically, Chart R.7 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 .80. This shows that there is a .80 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 .60 chance of an annual decline of over 10%, and a .30 chance of more than one such decline. There is a .10 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 R.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 R.8 shows the further increase in the chances of large annual declines when viewed over all of the remaining 24 years. Chart R.2 shows that the retrenchment reduces to .30 the chances of any declines over the 24 years. Suppose instead of the illustration based on pre 2008 returns that the hypothetical lower returns are used. Earlier, using these lower returns caused no change in the effect of a large retrenchment on reducing the chances of low disbursements. The lower returns also have no effect on the chances of large annual declines.
Conclusions
When a disbursement is over its limit 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 any further annual 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. The most important factor in the decision is the willingness to discount the future, and it also depends on risk aversion.
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 in 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
Addendum
Increase considers the possibility that the initial disbursement may have to be increased above 4.5% to avoid retrenchment. Doing so by even a small amount, however, causes much more risk of future declines than is accepted by disbursing 4.5%. Nevertheless, taking into account the results just obtained in the text of Retrench, increasing the initial disbursement to as much as 7.5% may be justified to avoid curbing important habitual activities that might otherwise never have to be curtailed. The risk of future retrenchment in doing so is not much more than what is accepted when deciding not to undertake a major retrenchment when an initial disbursement of 4.5% reaches its limit in the future. Those who would not undertake a major retrenchment in such circumstances will surely want to consider the possibility of increasing the initial disbursement to as much as 7.5% to avoid very painful initial retrenchment if that decision were to arise.
To simulate the effect of disbursing 7.5% initially and resetting any subsequent overlimit disbursements to the limit, the best allocation and RDR for doing so are required. Increasing the initial disbursement increases the best stock allocation by 10 percentage points for each one percentage point increase of initial portfolio value. Thus, for a 7.5% initial disbursement, the best stock allocation increases to 70%. When the RDR is set .02 above the expected return of the portfolio the RDR for the 7.5% initial disbursement becomes .078. Using these results, the probability distributions of the disbursements when starting at 7.5% are compared to those for starting at 4.5% at years 12, 24, and 36 in Charts R.9, R.10, and R.11. These charts look very similar to Charts R.1 and R.2 that show probabilities for the disbursements over the remaining 12 and 24 years when a 4.5% initial disbursement reaches its limit after 12 years. Charts R.1 and R.2 compare the disbursements when subsequent overlimits are reset to the limit to instead undertaking a major retrenchment of 30% when the 4.5% initial disbursement reaches its limit.
The chances that the initial disbursement starting at 7.5% will be higher than 4.5% after 12 or 24 years are somewhat more than the chances that the 4.5% disbursement will be higher than its value after the major retrenchment when instead overlimits are reset to the limit. Note, however, that the results in Chart R.10 are for year 24 of 36, whereas for R.2 the results are for year 24 of 24, and at the end of the disbursement period. Thus, the results in Chart R.2 can be more heavily discounted as they are 12 years further from the beginning of the disbursements. Nevertheless, any who would decide not to undertake a major retrenchment when a 4.5% initial disbursement reaches its limit in 12 years will surely want to consider the possibility of initially disbursing as much as 7.5% to avoid very painful retrenchment if that decision were to arise.
Retrench
Retrenchment Dilemma
The basic model in Model assumes that overlimit disbursements are reset to the limit, and this assumption is followed in determining the Best Initial Disbursement (BID) in Increase. 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, assume the investment returns in the pre 2008 illustration, and that the initial disbursement is the Best Initial Disbursement (BID) found for this case in Increase of 4.5%. Suppose over the first 12 years that this disbursement is made at the beginning of each year, as it is not over its limit. At the beginning of the last 24 years, however, the value of the portfolio has declined to 57% of its initial value. A calculation shows that a disbursement equal to 4.5% of initial portfolio value is now just about equal to its limit. Consider two possibilities. In one case, any overlimits are reset to the limit. In the other, there is a major retrenchment of 30% and the next disbursement is reduced from 4.5% to 3.15%. Any subsequent overlimit is assumed to be reset to its limit. If another overlimit were to occur, however, a decision could be made to undertake another major retrenchment. The distributions of the disbursements at years 12 and 24 of the remaining 24 years are shown for these conditions in Charts R.1 and R.2.
There is no doubt that the retrenchment is not an improvement over the first few years. The retrenchment means there is virtually no chance of any annual declines, but that is scant compensation for the loss caused by a major retrenchment. The most favorable case for the retrenchment is at the end of the disbursement period in Chart R.2. The chances that the disbursement is larger with the retrenchment are given by the .60 probability on the vertical axis where the curve starting at 4.5% crosses the curve for the retrenchment. Note that if the disbursement is larger with the retrenchment, the expected amount by which it is larger is sizable. It is roughly equal to about half the distance between the curves on the horizontal axis at a probability equal to .30 on the vertical axis. Half of this distance is a little less than half a percentage point of initial portfolio value. Note also the chances that there has been a decline with the retrenchment is .30 as shown by the probability on the vertical axis where the curve for the retrenchment begins to move to the left. Thus, the retrenchment is not an improvement early in the period, but does appear to be an improvement at the end of the period. At year 24 there is a .60 chance that lower disbursements have been avoided, and that the disbursement on average is larger than it would have been without a retrenchment by a little less than half a percentage point of initial portfolio value. Moreover, the chances are .70 that there have not been any annual declines in the disbursements over the 24 years.
The end of the period, however, is a very long time to wait for benefits. Moreover, with the declining chances of survival, benefits anywhere near the end of the period are unlikely to even be applicable. Thus, for those who choose not to retrench, the benefits in Chart R.2 appear to be only a remote downside risk. The more relevant benefits of the retrenchment to weigh against the very large and certain cost of the retrenchment in the early years are those at year 12 in R.1. These benefits although still well in the future, have a reasonably good chance of being applicable. The benefits of the retrenchment in R.1 are similar to those in R.2, but far more muted. Instead of a .60 chance that the disbursement will be larger with the retrenchment, the chances at year 12 are .40. Instead of there being a .60 chance that the disbursement on average will be larger by a little less than a half percentage point, at year 12 there is a .40 chance on average it will be larger by a little less than a quarter percentage point. Nevertheless, reducing the chances of very low disbursements and very likely avoiding large annual declines are important. It appears questionable, however, how many will be willing to pay the high cost of these possible benefits, which is why such a retrenchment causes a dilemma.
Lower Returns
Suppose instead of running the simulations using the investment returns in the pre 2008 illustration that the hypothetical lower returns specified in Model to gauge the effect of lower returns are used. As discussed in Increase doing so reduces the Best Initial Disbursement (BID) from 4.5% to 3.5%. Also, the stock allocation increases to 60% and the RDR is reduced to .044. Suppose in this case that the initial disbursement of 3.5% is made over the first 12 years as this disbursement remains below its limit. At the beginning of the last 24 years, however, the value of the portfolio has declined to 53.5% of its initial value, and a calculation indicates that a disbursement equal to 3.5% of initial portfolio value is just about equal to its limit. Suppose in this case that a major retrenchment is undertaken by reducing the next disbursement by 30% from 3.5% to 2.45% of initial portfolio value. The results of doing so are compared to continuing to reset overlimits to the limit in Charts R.3 and R.4. Except for being one percentage point less on the horizontal axis, the curves for the lower returns are almost the same as for the higher returns in Charts R.1 and R.2. Thus, the lower returns have no effect on the desirability of undertaking a major retrenchment when the disbursement is at its limit. There is the same dilemma as with the higher returns when a disbursement is at its limit.
Shorter Horizons
Suppose instead of first being overlimit after 12 years with the pre 2008 illustration that the 4.5% initial disbursement is not overlimit until after 24 years. With a shorter horizon presumably a smaller percentage retrenchment will be sufficient to get similar results, and that turns out to be true. Suppose for the first 24 years that a 4.5% initial disbursement is not overlimit. At the beginning of the last 12 years, however, the portfolio is down to 39% of its initial value. A calculation shows that a disbursement of 4.5% of initial portfolio value is now just about equal to its limit. Charts R.5 and R.6 compare the results with and without a 20% retrenchment at years 6 and 12 of the remaining 12 years. At first glance, these charts look similar to the earlier ones, but there are some differences. Both the costs and benefits of the retrenchment are less with the shorter horizon. The cost of the retrenchment is less as the retrenchment is now 20% instead of 30%. The benefits are also less because the chances that the disbursement will be larger with the retrenchment half way through the period are now .30 instead of .40, At the end of the period the decline is from .60 to .50. The beneficiary in this case has survived for 24 years, but looking forward the chances of surviving to the end of the remaining period or halfway may not have changed that much. The wait time for the benefits, however, is much shorter. All things considered, the dilemma after 24 years appears very similar to the dilemma after 12 years.
Annual Declines
So far, the focus has been on how a major retrenchment will reduce the chances of low disbursements later in the disbursement period. The other benefit, however, is reducing the risk of large annual declines, and that benefit begins immediately after the major retrenchment occurs. The earlier charts show the chances that the retrenchment will avoid any chance of a decline. The major concern, however, is avoiding large declines, and the value of the retrenchment in this regard depends on the chances that large annual declines will occur without the retrenchment. Modification of the model to obtain the chances of large declines is discussed in a note. When simulations are run using this procedure, the results obtained are shown in Charts R.7 and R.8. In particular, these charts show the chances of large annual declines when a 4.5% initial disbursement with the returns in the pre 2008 illustration is first at its limit with 24 years of disbursements remaining.
Specifically, Chart R.7 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 .80. This shows that there is a .80 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 .60 chance of an annual decline of over 10%, and a .30 chance of more than one such decline. There is a .10 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 R.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 R.8 shows the further increase in the chances of large annual declines when viewed over all of the remaining 24 years. Chart R.2 shows that the retrenchment reduces to .30 the chances of any declines over the 24 years. Suppose instead of the illustration based on pre 2008 returns that the hypothetical lower returns are used. Earlier, using these lower returns caused no change in the effect of a large retrenchment on reducing the chances of low disbursements. The lower returns also have no effect on the chances of large annual declines.
Conclusions
When a disbursement is over its limit 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 any further annual 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. The most important factor in the decision is the willingness to discount the future, and it also depends on risk aversion.
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 in 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
Addendum
Increase considers the possibility that the initial disbursement may have to be increased above 4.5% to avoid retrenchment. Doing so by even a small amount, however, causes much more risk of future declines than is accepted by disbursing 4.5%. Nevertheless, taking into account the results just obtained in the text of Retrench, increasing the initial disbursement to as much as 7.5% may be justified to avoid curbing important habitual activities that might otherwise never have to be curtailed. The risk of future retrenchment in doing so is not much more than what is accepted when deciding not to undertake a major retrenchment when an initial disbursement of 4.5% reaches its limit in the future. Those who would not undertake a major retrenchment in such circumstances will surely want to consider the possibility of increasing the initial disbursement to as much as 7.5% to avoid very painful initial retrenchment if that decision were to arise.
To simulate the effect of disbursing 7.5% initially and resetting any subsequent overlimit disbursements to the limit, the best allocation and RDR for doing so are required. Increasing the initial disbursement increases the best stock allocation by 10 percentage points for each one percentage point increase of initial portfolio value. Thus, for a 7.5% initial disbursement, the best stock allocation increases to 70%. When the RDR is set .02 above the expected return of the portfolio the RDR for the 7.5% initial disbursement becomes .078. Using these results, the probability distributions of the disbursements when starting at 7.5% are compared to those for starting at 4.5% at years 12, 24, and 36 in Charts R.9, R.10, and R.11. These charts look very similar to Charts R.1 and R.2 that show probabilities for the disbursements over the remaining 12 and 24 years when a 4.5% initial disbursement reaches its limit after 12 years. Charts R.1 and R.2 compare the disbursements when subsequent overlimits are reset to the limit to instead undertaking a major retrenchment of 30% when the 4.5% initial disbursement reaches its limit.
The chances that the initial disbursement starting at 7.5% will be higher than 4.5% after 12 or 24 years are somewhat more than the chances that the 4.5% disbursement will be higher than its value after the major retrenchment when instead overlimits are reset to the limit. Note, however, that the results in Chart R.10 are for year 24 of 36, whereas for R.2 the results are for year 24 of 24, and at the end of the disbursement period. Thus, the results in Chart R.2 can be more heavily discounted as they are 12 years further from the beginning of the disbursements. Nevertheless, any who would decide not to undertake a major retrenchment when a 4.5% initial disbursement reaches its limit in 12 years will surely want to consider the possibility of initially disbursing as much as 7.5% to avoid very painful retrenchment if that decision were to arise.
Posted December 2022