What is the largest periodic sustainable disbursement that can be made from a portfolio without too high a risk of much lower disbursements in the future? When should periodic sustainable disbursements from a portfolio be reduced? How much should be disbursed from a portfolio at the beginning of retirement when a retiree is faced with significant retrenchment? To answer these questions, this site investigates using the Retrenchment Rule.
The basic Retrenchment Rule says that the disbursement for the current year should be the same as the year before in real terms unless this disbursement exceeds the calculated value of a limit. This limit is the largest constant annuity that could be obtained each year for the longest that the disbursements might be needed. The value of this annuity is calculated assuming that the then current value of the portfolio is invested at a constant rate of return called the Retrenchment Discount Rate, or RDR.
The value to use for the RDR is determined by simulating the use of an increasing series of values to see which gives the best results. To make these simulations this site assumes the portfolio is some mix of stocks with returns resembling those on the S&P 500 and intermediate term fixed incomes with returns resembling those on U.S. government issues. For any simulation, the allocation of the portfolio is assumed to be the same at the beginning of each year over the disbursement period. Increasing the RDR improves the disbursements at the front of the disbursement period relative to the back. In the limit, when the RDR becomes infinite, the initial disbursement is always sustained until the portfolio runs out of funds. Simulations show that a good balance between the disbursements at the front and back of the period is obtained by setting the RDR equal to somewhat more than the expected return of the portfolio.
As the RDR depends on the expected return of the portfolio it depends on its allocation. To determine the optimal allocation, disbursements are simulated as the allocation to stocks is gradually increased. The best allocation has been found when the future disbursements stop improving and begin to deteriorate. The optimal stock allocation increases when the initial disbursement increases, and when less favorable returns are assumed for the investments in the portfolio.
An important use of the Retrenchment Rule is to see how increasing the initial disbursement affects future disbursements. As the initial disbursement increases, simulations show the changes that occur in the cumulative probability distributions of the disbursements in a series of future years. These probability distributions show the chances that there will be a decline in the disbursements by a future year, and the chances of cumulative declines of varying size. As the initial disbursement increases, these distributions also show the chances that disbursements in the future will be less than they would have been without the increase in the initial disbursement. The best initial disbursement has been found when the larger disbursements obtained by an increase are no longer worth the increased risk that it causes. In making this judgment it is important to differentiate as to whether the larger disbursements are funding an increase in spending by the beneficiary or avoiding further retrenchment as is sometimes the case when starting retirement. As avoiding further retrenchment has higher priority than increases in spending, larger increases in risk are acceptable when additional retrenchment is being avoided.
In general, ongoing disbursements are not increased in real terms because recipients are assumed to be more sensitive to the pain of decreases than the gain from increases. Increases in real terms in ongoing disbursements are therefore not desirable because they make later reductions more likely and larger if they occur. In the future, however, an emergency may arise requiring a significant increase in spending that cannot be avoided, and that is not fully covered by insurance. Suppose, for instance, that a serious deterioration in health requires significant expense for assisted living for a long time. In effect, the simulations include self-insurance for such a problem because they assume beforehand that the disbursements will continue for as long as they might possibly be needed. A serious deterioration in health reduces the longest that the disbursements might be needed, and increases the limit on disbursements given by the Retrenchment Rule. Simulations that reduce how long the disbursements might be needed at some future point show how much the disbursements might be increased to cover increased spending on health care.
Increased spending for an emergency that is unavoidable, however, is not confined to health issues. There are many possibilities the nature and size of which initially are unknown, and some may not even be dimly recognized. One possibility that might be recognized is the possible need to provide aid for a child. Another is water damage to a residence that is only partially covered by insurance, if at all. The chances of a large outlay for an emergency in any one year are very small, but over a long period the chances become significant and could have a comparable effect on the portfolio as large as a bear market for stocks. Such a possibility can be included in the simulations to assess the effect on the sustainability of the disbursements available for normal living expenses.
A disbursement initially is generally well below its limit, but when investment returns are less than expected the limit declines and in the future the disbursement can exceed its limit. In such cases the basic model resets the disbursement to the limit. Doing so, however, has the risk of very large annual declines in the disbursements, which will be disruptive. Moreover, there is a risk of very low disbursements in the future. To deal with these issues, the alternative is to reset an overlimit disbursement to far below its limit. A dilemma arises because of the very large costs and benefits of such a major retrenchment. There are significant reductions in the chances of low disbursements in the future, and in the risk of annual declines. These benefits, however, come at the cost of a significant curtailment of important habitual activities. Moreover, otherwise, many of these activities might never have to be curtailed for many years, and some might never have to be eliminated. To help in making a decision, simulations show the chances of future low disbursements with and without the major retrenchment. Simulations also show the risk of large annual declines if a major retrenchment is not undertaken.
An important use of the model at this site is to test the effect on disbursements of changes in investment returns. The assumptions generally used at this site to illustrate procedures reflect the investment returns realized prior to 2008. Since 2008, however the real returns on intermediate term issues have, of course, averaged far less. Moreover, if the expected return on intermediates in the future is much lower, presumably the expected return on stocks will be as well to maintain parity with respect to the equity premium. With lower expected returns there is likely to also be less volatility. Looking forward in the early 2020s, there is the prospect that for some time investment returns in real terms may be much lower than those in the illustration based on those realized prior to 2008. To help gauge how lower returns might affect the results obtained with this illustration, this site formulates a hypothetical set of low returns. These lower returns assume that the expected returns on both stocks and intermediates are three percentage points less, and that there is also some reduction in volatility. Simulations using the returns in the pre 2008 illustration are also run with these lower returns to provide some gauge as to what the effect of lower returns might be. With respect to allocation, there is no change for the lower returns when disbursements are sustainable, but much higher stock allocations become optimal for larger disbursements. Optimal initial disbursements are reduced by one percentage point of portfolio value with the lower returns significantly increasing the value of the portfolio necessary to generate a given stream.
The assumptions generally used at this site to illustrate procedures assume that investment returns are independently and identically distributed over time. Robert Shiller, however, famously argues that due to emotion stock prices in bull and bear markets tend to overshoot the levels warranted by future dividends and earnings. If stock prices overshoot, a period of much lower than normal returns in the past should be associated with higher than normal returns in the future. Reductions in the disbursements that otherwise might be needed will therefore tend to be less, and sustainability improved. These favorable hedging benefits tend to increase the optimal stock allocation. High prior average returns before the disbursements begin, however, could offset these favorable hedging benefits. There is evidence that stock returns are negatively related to very long moving averages of prior returns. Using Prior Average Dependent (PAD) stock returns in the simulations shows the extent to which negative PAD stock returns can improve sustainability.
Instead of investing all of the funds available initially in a portfolio of stocks and fixed income issues, retirees in good health could use some of the funds to purchase an immediate lifetime annuity. To evaluate this possibility the Retrenchment Rule must be modified to add the annual annuity benefit each year in the future to the portfolio, and to add the present value of these future benefits in real terms to the value of the portfolio in determining the current limit for a disbursement. Also, since almost all available annuities pay benefits that are fixed in nominal terms, provision must be made to adjust the future nominal benefits for inflation. As lifetime annuity benefits have some similarities to fixed income issues, purchasing an annuity might affect the optimal stock allocation of the remaining funds in the investment portfolio. Simulations show that annuitizing does increase somewhat the best stock allocation of the remaining funds.
The key issue is does annuitizing increase the Best Initial Disbursement (BID) enough to compensate for the loss of portfolio value to cover emergencies, or if not needed for that purpose to increase bequests? One test assumes the pre 2008 returns and an annuity rate that might have been obtained in the first half of 2007. Inflation follows a simple recursive random process with initial inflation and inflation expected in the long run both equal to 3%. Annuitizing half the portfolio increases the BID by about half a percentage point of initial portfolio value. By the back of the disbursement period on average the portfolio value reduction declines from 50% to about 30%. The annuitizing is desirable if the half percentage point increase in the BID is deemed to more than compensate for the loss of portfolio value. A similar tradeoff is obtained using the lower return assumptions in Model and an annuity rate available in the fall of 2022. For this test initial inflation is increased from 3% to 5%, but expected inflation in the long run remains at 3%.
Generally, the disbursements from a portfolio at this site are assumed to be funding the living expenses of an individual over a limited lifetime. Sometimes, however, a trust may be endowed with an investment to pursue a specified objective for an unlimited time. How are the results affected if the disbursements are assumed to be perpetual? For the pre 2008 returns with an initial horizon of 36 years the Best Initial Disbursement (BID) appears to be about 4.5% of portfolio value. To get comparable sustainability when the disbursements are perpetual the initial disbursement must be reduced from 4.5% to 3.25%. After 120 years there is a limit on the chances of a decline equal to .30, but there is not a limit on the chances of large declines. Suppose the disbursement is allowed to increase to keep it from becoming less than 2.5% of the current value of the portfolio. There is then a .30 chance that the disbursement has increased by 1.0 percentage points or more by year 24, and 2.0 percentage points or more by year 36. There is not an increased chance of declines earlier in the period, but no longer a limit on the chances of a decline in the very long run, but this increase is extremely small.
In addition to investigating how best to make periodic disbursements from a portfolio of risky assets, this site also looks at the best way to accumulate that portfolio. The assets in the portfolio are the same as when making the disbursements. Some key questions to answer: How should the portfolio be allocated over time when accumulating? How much more savings are required for the lower assumptions about investment return?
For the assumptions at this site, the optimal stock allocation for making sustainable disbursements is a moderate 30%. Very large stock allocations are optimal only when making large initial disbursements with the low assumptions about investment returns. In contrast, very large stock allocations are desirable early in the period when accumulating over a long period with either the low or higher investment return assumptions. Moreover, very large stock allocations can be desirable over much shorter periods when sizable additional contributions are being made to the portfolio in the future. Large stock allocations are desirable early in a long accumulation period due to the benefits of hedging over time. They are desirable when there will be sizable contributions in the future because these future contributions absorb some of the volatility. In either case, the higher volatility of the stocks tends to be suppressed making the higher expected return of the stocks more desirable.
Large stock allocations for accumulating are desirable even when the downside risk for accumulated value is strictly limited. In particular, for the analysis at this site the stock allocation for any year is determined by finding the largest stock allocation for that year whose lowest 5 percentile for the accumulated value is not less than the lowest 5 percentile value when the portfolio is entirely allocated to intermediates. When there is only one more year for accumulation the stock allocation with this property can be determined analytically. When there is more than one year simulations must be used with a backwards recursive process in which the future allocations are those that have already been determined to have this property. Suppose there are not any future contributions and that the pre 2008 investment returns are assumed. Suppose the years remaining for accumulation are 20, 15, 10, 5, and 1. The stock allocations obtained are respectively: 84%, 76.5%, 64%, 49%, and 28%.
Now suppose that there are contributions to the portfolio at the beginning of future years that are equal in real terms and that might represent the addition of more savings. In this case, an addition is made to the allocation each year that is a multiple of the ratio of the annual contribution to the initial portfolio value for that year. The values of these multiples are determined using a backwards recursive process in which the values of the future multiples are those that have already been determined to have the desired property. The desired value of a multiple is the largest for which the lowest 5 percentile for the accumulated value is not less than the lowest 5 percentile value when the portfolio is entirely allocated to intermediates.
Sometimes, however, the downside risk for accumulated value with 100% allocated to stocks is not greater than with 100% allocated to intermediates. In such cases, the stock allocation is set at 100% because leverage is not allowed, and it is not possible to allocate enough to stocks to cause as much risk as when allocating entirely to intermediates. Such situations commonly arise in the early years when the future contributions are equal to the initial value of the portfolio. Later on, however, the value of the portfolio rises substantially reducing the ratio of the contributions to portfolio value. A declining series of stock allocations can then be found over the remainder of the period with comparable downside risk for accumulated value to investing entirely in intermediates.
Assuming equal contributions in real terms to the portfolio each year over a long period provides a useful model for seeing how low returns might affect the savings needed for retirement. For the low returns, new allocations and multiples for the ratios must be determined using the backwards regressive processes. With the allocations determined simulations show the cumulative probability distributions for the funds accumulated with a constant stream of savings over 20 years. The probability of the funds accumulated as a percentage of contributed value can then be compared for the low and higher assumptions for investment returns. This comparison shows that the central tendency is for the accumulated value to be about 40% higher for the higher returns. For the assumptions about disbursements at this site, about 40% more is also required in the initial portfolio with the low returns to get a sustainable stream of disbursements of the same size. As 40% more savings is required to get a portfolio that is 40% larger, these increases are compounded. Savings must be almost twice as much to get the same sustainable stream of disbursements in retirement.
Overview
What is the largest periodic sustainable disbursement that can be made from a portfolio without too high a risk of much lower disbursements in the future? When should periodic sustainable disbursements from a portfolio be reduced? How much should be disbursed from a portfolio at the beginning of retirement when a retiree is faced with significant retrenchment? To answer these questions, this site investigates using the Retrenchment Rule.
The basic Retrenchment Rule says that the disbursement for the current year should be the same as the year before in real terms unless this disbursement exceeds the calculated value of a limit. This limit is the largest constant annuity that could be obtained each year for the longest that the disbursements might be needed. The value of this annuity is calculated assuming that the then current value of the portfolio is invested at a constant rate of return called the Retrenchment Discount Rate, or RDR.
The value to use for the RDR is determined by simulating the use of an increasing series of values to see which gives the best results. To make these simulations this site assumes the portfolio is some mix of stocks with returns resembling those on the S&P 500 and intermediate term fixed incomes with returns resembling those on U.S. government issues. For any simulation, the allocation of the portfolio is assumed to be the same at the beginning of each year over the disbursement period. Increasing the RDR improves the disbursements at the front of the disbursement period relative to the back. In the limit, when the RDR becomes infinite, the initial disbursement is always sustained until the portfolio runs out of funds. Simulations show that a good balance between the disbursements at the front and back of the period is obtained by setting the RDR equal to somewhat more than the expected return of the portfolio.
As the RDR depends on the expected return of the portfolio it depends on its allocation. To determine the optimal allocation, disbursements are simulated as the allocation to stocks is gradually increased. The best allocation has been found when the future disbursements stop improving and begin to deteriorate. The optimal stock allocation increases when the initial disbursement increases, and when less favorable returns are assumed for the investments in the portfolio.
An important use of the Retrenchment Rule is to see how increasing the initial disbursement affects future disbursements. As the initial disbursement increases, simulations show the changes that occur in the cumulative probability distributions of the disbursements in a series of future years. These probability distributions show the chances that there will be a decline in the disbursements by a future year, and the chances of cumulative declines of varying size. As the initial disbursement increases, these distributions also show the chances that disbursements in the future will be less than they would have been without the increase in the initial disbursement. The best initial disbursement has been found when the larger disbursements obtained by an increase are no longer worth the increased risk that it causes. In making this judgment it is important to differentiate as to whether the larger disbursements are funding an increase in spending by the beneficiary or avoiding further retrenchment as is sometimes the case when starting retirement. As avoiding further retrenchment has higher priority than increases in spending, larger increases in risk are acceptable when additional retrenchment is being avoided.
In general, ongoing disbursements are not increased in real terms because recipients are assumed to be more sensitive to the pain of decreases than the gain from increases. Increases in real terms in ongoing disbursements are therefore not desirable because they make later reductions more likely and larger if they occur. In the future, however, an emergency may arise requiring a significant increase in spending that cannot be avoided, and that is not fully covered by insurance. Suppose, for instance, that a serious deterioration in health requires significant expense for assisted living for a long time. In effect, the simulations include self-insurance for such a problem because they assume beforehand that the disbursements will continue for as long as they might possibly be needed. A serious deterioration in health reduces the longest that the disbursements might be needed, and increases the limit on disbursements given by the Retrenchment Rule. Simulations that reduce how long the disbursements might be needed at some future point show how much the disbursements might be increased to cover increased spending on health care.
Increased spending for an emergency that is unavoidable, however, is not confined to health issues. There are many possibilities the nature and size of which initially are unknown, and some may not even be dimly recognized. One possibility that might be recognized is the possible need to provide aid for a child. Another is water damage to a residence that is only partially covered by insurance, if at all. The chances of a large outlay for an emergency in any one year are very small, but over a long period the chances become significant and could have a comparable effect on the portfolio as large as a bear market for stocks. Such a possibility can be included in the simulations to assess the effect on the sustainability of the disbursements available for normal living expenses.
A disbursement initially is generally well below its limit, but when investment returns are less than expected the limit declines and in the future the disbursement can exceed its limit. In such cases the basic model resets the disbursement to the limit. Doing so, however, has the risk of very large annual declines in the disbursements, which will be disruptive. Moreover, there is a risk of very low disbursements in the future. To deal with these issues, the alternative is to reset an overlimit disbursement to far below its limit. A dilemma arises because of the very large costs and benefits of such a major retrenchment. There are significant reductions in the chances of low disbursements in the future, and in the risk of annual declines. These benefits, however, come at the cost of a significant curtailment of important habitual activities. Moreover, otherwise, many of these activities might never have to be curtailed for many years, and some might never have to be eliminated. To help in making a decision, simulations show the chances of future low disbursements with and without the major retrenchment. Simulations also show the risk of large annual declines if a major retrenchment is not undertaken.
An important use of the model at this site is to test the effect on disbursements of changes in investment returns. The assumptions generally used at this site to illustrate procedures reflect the investment returns realized prior to 2008. Since 2008, however the real returns on intermediate term issues have, of course, averaged far less. Moreover, if the expected return on intermediates in the future is much lower, presumably the expected return on stocks will be as well to maintain parity with respect to the equity premium. With lower expected returns there is likely to also be less volatility. Looking forward in the early 2020s, there is the prospect that for some time investment returns in real terms may be much lower than those in the illustration based on those realized prior to 2008. To help gauge how lower returns might affect the results obtained with this illustration, this site formulates a hypothetical set of low returns. These lower returns assume that the expected returns on both stocks and intermediates are three percentage points less, and that there is also some reduction in volatility. Simulations using the returns in the pre 2008 illustration are also run with these lower returns to provide some gauge as to what the effect of lower returns might be. With respect to allocation, there is no change for the lower returns when disbursements are sustainable, but much higher stock allocations become optimal for larger disbursements. Optimal initial disbursements are reduced by one percentage point of portfolio value with the lower returns significantly increasing the value of the portfolio necessary to generate a given stream.
The assumptions generally used at this site to illustrate procedures assume that investment returns are independently and identically distributed over time. Robert Shiller, however, famously argues that due to emotion stock prices in bull and bear markets tend to overshoot the levels warranted by future dividends and earnings. If stock prices overshoot, a period of much lower than normal returns in the past should be associated with higher than normal returns in the future. Reductions in the disbursements that otherwise might be needed will therefore tend to be less, and sustainability improved. These favorable hedging benefits tend to increase the optimal stock allocation. High prior average returns before the disbursements begin, however, could offset these favorable hedging benefits. There is evidence that stock returns are negatively related to very long moving averages of prior returns. Using Prior Average Dependent (PAD) stock returns in the simulations shows the extent to which negative PAD stock returns can improve sustainability.
Instead of investing all of the funds available initially in a portfolio of stocks and fixed income issues, retirees in good health could use some of the funds to purchase an immediate lifetime annuity. To evaluate this possibility the Retrenchment Rule must be modified to add the annual annuity benefit each year in the future to the portfolio, and to add the present value of these future benefits in real terms to the value of the portfolio in determining the current limit for a disbursement. Also, since almost all available annuities pay benefits that are fixed in nominal terms, provision must be made to adjust the future nominal benefits for inflation. As lifetime annuity benefits have some similarities to fixed income issues, purchasing an annuity might affect the optimal stock allocation of the remaining funds in the investment portfolio. Simulations show that annuitizing does increase somewhat the best stock allocation of the remaining funds.
The key issue is does annuitizing increase the Best Initial Disbursement (BID) enough to compensate for the loss of portfolio value to cover emergencies, or if not needed for that purpose to increase bequests? One test assumes the pre 2008 returns and an annuity rate that might have been obtained in the first half of 2007. Inflation follows a simple recursive random process with initial inflation and inflation expected in the long run both equal to 3%. Annuitizing half the portfolio increases the BID by about half a percentage point of initial portfolio value. By the back of the disbursement period on average the portfolio value reduction declines from 50% to about 30%. The annuitizing is desirable if the half percentage point increase in the BID is deemed to more than compensate for the loss of portfolio value. A similar tradeoff is obtained using the lower return assumptions in Model and an annuity rate available in the fall of 2022. For this test initial inflation is increased from 3% to 5%, but expected inflation in the long run remains at 3%.
Generally, the disbursements from a portfolio at this site are assumed to be funding the living expenses of an individual over a limited lifetime. Sometimes, however, a trust may be endowed with an investment to pursue a specified objective for an unlimited time. How are the results affected if the disbursements are assumed to be perpetual? For the pre 2008 returns with an initial horizon of 36 years the Best Initial Disbursement (BID) appears to be about 4.5% of portfolio value. To get comparable sustainability when the disbursements are perpetual the initial disbursement must be reduced from 4.5% to 3.25%. After 120 years there is a limit on the chances of a decline equal to .30, but there is not a limit on the chances of large declines. Suppose the disbursement is allowed to increase to keep it from becoming less than 2.5% of the current value of the portfolio. There is then a .30 chance that the disbursement has increased by 1.0 percentage points or more by year 24, and 2.0 percentage points or more by year 36. There is not an increased chance of declines earlier in the period, but no longer a limit on the chances of a decline in the very long run, but this increase is extremely small.
In addition to investigating how best to make periodic disbursements from a portfolio of risky assets, this site also looks at the best way to accumulate that portfolio. The assets in the portfolio are the same as when making the disbursements. Some key questions to answer: How should the portfolio be allocated over time when accumulating? How much more savings are required for the lower assumptions about investment return?
For the assumptions at this site, the optimal stock allocation for making sustainable disbursements is a moderate 30%. Very large stock allocations are optimal only when making large initial disbursements with the low assumptions about investment returns. In contrast, very large stock allocations are desirable early in the period when accumulating over a long period with either the low or higher investment return assumptions. Moreover, very large stock allocations can be desirable over much shorter periods when sizable additional contributions are being made to the portfolio in the future. Large stock allocations are desirable early in a long accumulation period due to the benefits of hedging over time. They are desirable when there will be sizable contributions in the future because these future contributions absorb some of the volatility. In either case, the higher volatility of the stocks tends to be suppressed making the higher expected return of the stocks more desirable.
Large stock allocations for accumulating are desirable even when the downside risk for accumulated value is strictly limited. In particular, for the analysis at this site the stock allocation for any year is determined by finding the largest stock allocation for that year whose lowest 5 percentile for the accumulated value is not less than the lowest 5 percentile value when the portfolio is entirely allocated to intermediates. When there is only one more year for accumulation the stock allocation with this property can be determined analytically. When there is more than one year simulations must be used with a backwards recursive process in which the future allocations are those that have already been determined to have this property. Suppose there are not any future contributions and that the pre 2008 investment returns are assumed. Suppose the years remaining for accumulation are 20, 15, 10, 5, and 1. The stock allocations obtained are respectively: 84%, 76.5%, 64%, 49%, and 28%.
Now suppose that there are contributions to the portfolio at the beginning of future years that are equal in real terms and that might represent the addition of more savings. In this case, an addition is made to the allocation each year that is a multiple of the ratio of the annual contribution to the initial portfolio value for that year. The values of these multiples are determined using a backwards recursive process in which the values of the future multiples are those that have already been determined to have the desired property. The desired value of a multiple is the largest for which the lowest 5 percentile for the accumulated value is not less than the lowest 5 percentile value when the portfolio is entirely allocated to intermediates.
Sometimes, however, the downside risk for accumulated value with 100% allocated to stocks is not greater than with 100% allocated to intermediates. In such cases, the stock allocation is set at 100% because leverage is not allowed, and it is not possible to allocate enough to stocks to cause as much risk as when allocating entirely to intermediates. Such situations commonly arise in the early years when the future contributions are equal to the initial value of the portfolio. Later on, however, the value of the portfolio rises substantially reducing the ratio of the contributions to portfolio value. A declining series of stock allocations can then be found over the remainder of the period with comparable downside risk for accumulated value to investing entirely in intermediates.
Assuming equal contributions in real terms to the portfolio each year over a long period provides a useful model for seeing how low returns might affect the savings needed for retirement. For the low returns, new allocations and multiples for the ratios must be determined using the backwards regressive processes. With the allocations determined simulations show the cumulative probability distributions for the funds accumulated with a constant stream of savings over 20 years. The probability of the funds accumulated as a percentage of contributed value can then be compared for the low and higher assumptions for investment returns. This comparison shows that the central tendency is for the accumulated value to be about 40% higher for the higher returns. For the assumptions about disbursements at this site, about 40% more is also required in the initial portfolio with the low returns to get a sustainable stream of disbursements of the same size. As 40% more savings is required to get a portfolio that is 40% larger, these increases are compounded. Savings must be almost twice as much to get the same sustainable stream of disbursements in retirement.
Posted November, 2020 Revised July, 2022 February, 2023