Sunday, June 17, 2012

Leaving an Inheritance / Safety Margin and Safe Withdrawal Rates


One of the classical assumptions in the safe withdrawal rate literature is that retirees choose a withdrawal rate based on what would have left precisely no wealth after the withdrawal in the 30th year of retirement. Retirees do not deviate from the inflation-adjusted withdrawal amounts, which leaves them playing a game of chicken as their wealth may be plummeting toward zero. As well, retirees do not make any adjustments for the fact that as their 30th year of retirement approaches, they are increasingly likely to live longer than 30 years. As well, the classical assumptions are such that retirees do not have any particular desire to leave a bequest, an estate, an inheritance, or whatever you may like to call it. The objective of the classical studies is to get a handle on what is the maximum sustainable withdrawal rate from a portfolio of volatile assets over a 30 year retirement period.
That being said, as Michael Kitces notes on his blog, when we talk about using a safe withdrawal rate, we are really talking about a case in which no wealth will be left in the worst-case scenario. More often than not, wealth may continue to grow when using a 4% withdrawal rate rule.
Nonetheless, what I aim to investigate here is how withdrawal rate decisions may change when retirees specifically incorporate a desire to leave a bequest, which I will summarize here as either maintaining the nominal value of retirement date wealth at the end of the 30th year, or maintaining the real value of retirement date wealth at the end of the 30th year. The value of wealth may decline in the interim and then make a comeback, as I am only checking the value of wealth after the 30th year.
I am using the same assumptions as described in my entry on William Bengen’s SAFEMAX. These assumptions include withdrawals at the start of the year, annual rebalancing from a 50/50 portfolio of stocks and bonds, a 30-year retirement, inflation-adjusted withdrawal amounts, and no fees. Data is from the SBBI Yearbook.
As an aside, this is the first time I’ve shown results with data through the end of 2011. Now we know the outcome for the 1982 retiree, a new record setter! While that was a terrible year to retire in terms of pre-retirement bear markets, the 1982 retiree could have used a whopping 9.78% withdrawal rate with whatever wealth they had.
Table 4.2 shows the maximum sustainable withdrawal rates by retirement year for three scenarios: the classic case in which wealth is depleted after 30 years, the case in which the nominal value of retirement date wealth is preserved after 30 years, and the case in which the real inflation-adjusted value of retirement date wealth is preserved after 30 years.
With the classical wealth depletion assumption and a 50/50 asset allocation, the 1966 retiree experienced the worst-case scenario withdrawal rate (SAFEMAX), which was 4.04%. As Michael Kitces and Bill Bengen both emphasize, 4% also does pretty well with preserving the nominal value of retirement date wealth (though after 30 years of inflation that wealth may not have a whole lot of purchasing power left). There were only 4 cases when 4% did not preserve nominal wealth, and the SAFEMAX for this case was 3.78% for the 1937 retiree.
I think that when someone says they want to preserve the value of their wealth, they probably are implicitly thinking in terms of preserving the real purchasing power of their wealth, even if they do not fully articulate this. The next column shows the maximum sustainable withdrawal rates than will preserve the real value of wealth after the 30th year. The 4% withdrawal rate accomplishes this in 54% of the historical simulations (31 out of 57 rolling periods). The SAFEMAX for this case happened for a 1965 retiree who could only use 2.73% to preserve the real value of their retirement date wealth.
Table 4.2
Maximum Sustainable Withdrawal Rates (MWRs)
Cases: (1) Wealth Depletion,  (2) Preserve Nominal Value of Retirement Date Wealth,
and (3) Preserve Real Value of Retirement Date Wealth
For 50/50 Asset Allocation, 30-Year Retirement Duration, Inflation Adjustments, No Fees
Using SBBI Data, 1926-2011, S&P 500 and Intermediate-Term Government Bonds
Year

MWR
(Wealth Depletion)
MWR
(Preserve Nominal Wealth)
MWR
(Preserve Real Wealth)
Year
(1)
MWR
(Wealth Depletion)
MWR
(Preserve Nominal Wealth)
MWR
(Preserve Real Wealth)
1926
7.29
6.42
6
1955
5.6
5.03
3.45
1927
7.04
6.16
5.7
1956
5.04
4.57
3.21
1928
6.04
5.11
4.56
1957
5.19
4.77
3.51
1929
5.12
4.33
3.81
1958
5.62
5.19
3.93
1930
5.4
4.62
4.08
1959
4.92
4.5
3.27
1931
5.82
5.1
4.5
1960
4.87
4.52
3.42
1932
7.14
6.54
5.92
1961
4.82
4.46
3.3
1933
6.78
6.21
5.46
1962
4.39
4.08
3.03
1934
5.64
5.09
4.38
1963
4.65
4.35
3.31
1935
5.8
5.27
4.58
1964
4.35
4.07
3.06
1936
4.91
4.38
3.7
1965
4.12
3.82
2.73
1937
4.36
3.78
3.04
1966
4.04
3.8
2.89
1938
5.56
5.01
4.31
1967
4.42
4.19
3.34
1939
4.76
4.24
3.51
1968
4.19
3.98
3.23
1940
4.81
4.25
3.39
1969
4.2
4.02
3.36
1941
5.19
4.67
3.79
1970
4.84
4.65
4.03
1942
6.26
5.73
4.88
1971
4.81
4.61
3.96
1943
6.47
5.92
5.13
1972
4.64
4.42
3.71
1944
6.15
5.52
4.62
1973
4.45
4.2
3.42
1945
5.94
5.19
3.99
1974
5.27
5.03
4.33
1946
5.29
4.63
3.43
1975
6.9
6.63
5.95
1947
6.69
6.02
4.96
1976
6.4
6.11
5.4
1948
7.42
6.63
5.45
1977
5.99
5.7
4.99
1949
7.77
6.95
5.65
1978
6.93
6.62
5.93
1950
7.3
6.53
5.11
1979
7.65
7.24
6.38
1951
6.98
6.26
4.77
1980
8.32
7.88
7.11
1952
6.9
6.12
4.36
1981
8.51
8.03
7.31
1953
6.6
5.94
4.29
1982
9.78
9.25
8.54
1954
6.85
6.25
4.68
1983 +
30 Years of Data Not Yet Available
Note: SAFEMAXs are boxed. All MWRs below 4% are bold-faced.

Finally, to provide more detail, Table 4.3 identifies the amount of wealth remaining after 30 years in both nominal and real terms (retirement date wealth = 100) when using a 4% withdrawal rate with a 50/50 asset allocation and all of the other standard assumptions. The SAFEMAX of 4.04% happened with a 1966 retiree, and we can see that the real value of their wealth after 30 years is 3.3. Since a withdrawal of 4 will be taken in year 31, the 4% rule would fail over a 31 year horizon for the 1966 retiree. On the other end of the spectrum, as we can now calculate outcomes for the 1982 retiree as well, we can see the growth of their wealth had they used 4% withdrawals. In nominal terms, their wealth would have grown to more than 10 times its retirement date value, and even in real terms the value of their wealth grew by more than 4 times.

Table 4.3
Remaining Wealth After 30 Years (Measured in Nominal and Real  Terms)
Using a 4% Withdrawal Rate and Retirement Date Wealth=100
50/50 Asset Allocation, Inflation Adjustments for Withdrawals, No Fees
Using SBBI Data, 1926-2011, S&P 500 and Intermediate-Term Government Bonds
Year
Nominal
Wealth
Real
Wealth
Year
Nominal
Wealth
Real
Wealth
1926
380.2
254.9
1955
281.3
74.3
1927
345.6
227.4
1956
221.5
56.4
1928
219.9
137.7
1957
279.6
70.6
1929
141.1
85.0
1958
372.1
95.7
1930
178.8
106.0
1959
220.9
55.4
1931
251.6
138.1
1960
245.6
59.9
1932
525.5
257.1
1961
227.3
53.7
1933
481.2
209.8
1962
125.2
28.1
1934
298.6
129.3
1963
218.2
48.1
1935
338.4
147.0
1964
124.3
27.0
1936
169.5
75.0
1965
38.6
8.3
1937
60.8
26.7
1966
15.5
3.3
1938
284.7
124.7
1967
178.6
38.3
1939
146.4
60.5
1968
88.7
19.0
1940
144.1
56.6
1969
106.2
23.4
1941
226.3
84.6
1970
447.0
102.8
1942
420.9
163.6
1971
402.0
95.0
1943
448.6
184.4
1972
288.9
68.2
1944
341.1
139.9
1973
178.5
42.9
1945
257.3
99.0
1974
524.2
134.0
1946
196.7
69.0
1975
1086.8
305.9
1947
400.0
154.9
1976
817.3
238.4
1948
431.1
173.6
1977
669.3
197.9
1949
459.3
177.9
1978
945.4
291.1
1950
430.6
150.2
1979
893.8
288.2
1951
413.5
134.7
1980
979.7
357.6
1952
370.9
113.8
1981
940.7
375.8
1953
395.8
112.5
1982
1085.0
465.2
1954
475.8
131.0
1983 +
30 Years of Data Not Yet Available
Note: All wealth values below 100 are bold-faced.

5 comments:

  1. Follow this link to Jim Otar's website

    http://retirementoptimizer.com/

    Go to "whitepapers" and then to the paper "Perpetual Distribution Rates for..."

    In this paper, Otar presents an analysis similar to the theme of today's post. I am personally very interested in maintaining or perhaps even expanding my portfolio's real value over time.

    I think you might find his paper interesting.

    ReplyDelete
  2. Wade,

    Thanks for the data. Very good stuff. Interesting to look at Shiller PE for 1982 was 7.39 in contrast to the very poor years that had PE 10 at 21-24. Seems to me that now is not a great time for retirees with a PE 10 of 21-22. I am reallly enjoying your post and comments.

    Thanks,

    Charles

    ReplyDelete
  3. Hi,

    Thank you both. I still need to read Otar's work. Thank you for the reminder.

    Charles, I've got a new post up today which addresses your comment a bit in the context of a retiree in 2000.

    As for retirees today, markets are on the overvalued side, but what concerns me more is the fact that bond yields are at historic lows.

    Best wishes, Wade

    ReplyDelete
  4. Wade - very interesting.

    In the focus on SWR/MWR what is fascinating to me is that there is just a modest difference between MWR and real wealth preserved. Between no money and your capital is preserved at a minimum.

    A quick and dirty calculation finds an average of only a 1.48% difference between the 2 over the 57 years listed. Ranging from a high of 2.54% (1952)to 0.81% (1970). ANy errors are all mine.

    No wonder there are large amounts at the end of 30 years with "4%" SWR and MWR. A very small change in spending/withdrawals can make a large difference at the end of 30 years.

    THanks
    Matt

    ReplyDelete
  5. Matt,

    You are right about the concept (I didn't check your numbers, but they look reasonable).

    Small changes in withdrawal rates can make a big difference. It is all connected to the current withdrawal rate. Once wealth starts to diminish and current withdrawal rates (withdrawal amount / remaining wealth in later years) start to increase, the bar is set higher for returns. Returns have to be higher the the CWR just for wealth to stay the same level. At some point a threshold is reached where the CWR starts to increase rapidly and before long wealth will be gone.

    ReplyDelete