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 30^th 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 30^th 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 30^th year, or maintaining the real value of retirement date wealth at the end of the 30^th 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 30^th 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 30^th 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.