Here are some comparisons. These tables show the 5-year rolling averages of what you could withdraw at years 5, 10, 15, 20, 25 and 30 if you remove 25% of a portfolio's year-to-year gains (but not losses). Other tables show what the withdrawal rates are when none of the gains are removed. In addition, the TIPS Equivalent Safe Withdrawal Rate shows what a 100% TIPS portfolio can deliver with no risk at all.
Conditions
$100000 initial balance.
50% stocks and 50% TIPS at 2% interest.
0.20% expenses.
25% of year-to-year gains (but not losses) were removed.
A percentage of the initial balance (plus inflation) was withdrawn each year as well. The reported results are the highest percentages that would have survived for a full 30 years. If this percentage were increased by 0.1%, the portfolio would have failed within the first 30 years.
Other conditions were at their standard settings. Inflation adjustments were made each year in accordance with the CPI. The portfolio was rebalanced each year to maintain a fixed allocation. Withdrawal amounts (not including expenses) were determined at the beginning of each year. Half was withdrawn at the beginning of the year. The other half was withdrawn at the end of the year.
The 0.20% expenses are included in the reported withdrawal amounts. This is a limitation of the calculator. The alternative was to set expenses equal to zero.
Tables
Withdrawal amounts averaged over the preceding 5 years, starting with an initial portfolio balance of $100000 and removing 25% of all portfolio gains (but not losses) from the previous year, 50% stocks and 50% TIPS at a 2% interest rate.
Year, Percentage Earnings Yield 100E10/P, Maximum Surviving Withdrawal Rates in terms of the initial balance, Amounts at 5 years, Amounts at 10 years, Amounts at 15 years
Code: Select all
1921 19.61 6.4 7078 8024 7068
1922 15.87 6.7 7722 8224 7983
1923 12.20 6.4 7136 7927 7914
1924 12.35 6.4 7752 7413 8034
1925 10.31 6.2 8174 7061 7203
1926 8.85 5.6 7122 6409 6568
1927 7.58 5.5 7039 6952 5859
1928 5.32 4.9 5913 6455 5008
1929 3.69 4.2 4360 5638 4306
1930 4.48 4.2 4923 5103 4313
1931 5.99 4.5 5287 5499 4638
1932 10.75 5.5 7296 5977 5881
1933 11.49 6.4 8948 6576 6900
1934 7.69 5.6 7024 5842 5991
1935 8.70 6.0 7595 6343 6392
1936 5.85 5.2 5959 5522 5532
1937 4.63 4.7 4881 5268 4864
1938 7.41 5.5 5714 6236 5729
1939 6.41 5.3 5620 5900 5546
1940 6.10 5.5 5956 6027 5775
1941 7.19 6.6 7238 7168 7153
1942 9.90 7.2 8454 7655 7642
1943 9.80 6.9 7954 7373 7401
1944 9.01 6.6 7439 7085 7145
1945 8.33 6.4 7106 6912 7232
1946 6.41 6.7 6878 7725 7256
1947 8.70 7.4 8067 8312 7963
1948 9.62 7.3 8067 8245 7936
1949 9.80 7.1 7890 8088 7793
1950 9.35 7.4 8286 9086 7746
1951 8.40 6.8 7916 7793 7184
1952 8.00 6.3 7422 7083 6736
1953 7.69 6.1 7251 7061 6465
1954 8.33 6.1 7320 7136 6591
1955 6.25 5.3 6503 5847 5588
1956 5.46 4.9 5696 5525 5176
1957 5.99 5.0 5832 5694 5268
1958 7.25 5.2 6325 5777 5529
1959 5.56 4.6 5004 5298 4858
1960 5.46 4.5 5194 5023 4772
1961 5.41 4.4 5223 4861 4695
1962 4.72 4.2 4851 4592 4732
1963 5.18 4.4 5106 4911 4901
1964 4.63 4.1 4748 4540 4469
1965 4.29 3.9 4474 4297 4304
1966 4.15 3.9 4363 4305 4361
1967 4.90 4.1 4656 4869 4389
1968 4.65 4.0 4494 4660 4313
1969 4.72 4.1 4644 4598 4475
1970 5.85 4.4 5011 5046 4783
1971 6.06 4.4 4966 5174 4708
1972 5.78 4.4 5282 4871 4582
1973 5.35 4.5 5149 5013 4770
1974 7.41 5.2 5984 6009 5481
1975 11.24 5.9 7011 6743 6261
1976 8.93 5.3 5984 5948 5752
1977 8.77 5.4 6301 5970 5781
1978 10.87 6.0 7077 6949 6465
1979 10.75 6.2 7487 7006 6819
1980 11.24 6.1 7318 7034 6743
Code: Select all
1921 19.61 6.4 7094 6446 6403
1922 15.87 6.7 6971 6748 6702
1923 12.20 6.4 6505 6446 6402
1924 12.35 6.4 6500 6445 6401
1925 10.31 6.2 6291 6240 6201
1926 8.85 5.6 5680 5650 5600
1927 7.58 5.5 5619 5528 5500
1928 5.32 4.9 5023 4922 4900
1929 3.69 4.2 4341 4222 4200
1930 4.48 4.2 4349 4218 4200
1931 5.99 4.5 4638 4518 4500
1932 10.75 5.5 5563 5525 5500
1933 11.49 6.4 6473 6429 6400
1934 7.69 5.6 5688 5626 5600
1935 8.70 6.0 6128 6030 6000
1936 5.85 5.2 5324 5223 5200
1937 4.63 4.7 4780 4722 4700
1938 7.41 5.5 5649 5531 5500
1939 6.41 5.3 5482 5332 5300
1940 6.10 5.5 5726 5532 5500
1941 7.19 6.6 6730 6636 6600
1942 9.90 7.2 7423 7248 7201
1943 9.80 6.9 7173 6950 6902
1944 9.01 6.6 6908 6650 6602
1945 8.33 6.4 6500 6449 6402
1946 6.41 6.7 6810 6754 6703
1947 8.70 7.4 7528 7462 7405
1948 9.62 7.3 7445 7367 7306
1949 9.80 7.1 7275 7164 7104
1950 9.35 7.4 7544 7469 7405
1951 8.40 6.8 6932 6862 6805
1952 8.00 6.3 6442 6360 6305
1953 7.69 6.1 6273 6157 6105
1954 8.33 6.1 6226 6155 6105
1955 6.25 5.3 5409 5379 5303
1956 5.46 4.9 5032 5026 4904
1957 5.99 5.0 5245 5038 5002
1958 7.25 5.2 5506 5237 5202
1959 5.56 4.6 4837 4631 4667
1960 5.46 4.5 4772 4532 4502
1961 5.41 4.4 4698 4431 4402
1962 4.72 4.2 4274 4228 4202
1963 5.18 4.4 4495 4427 4401
1964 4.63 4.1 4228 4125 4101
1965 4.29 3.9 4046 3926 3901
1966 4.15 3.9 4016 3923 3900
1967 4.90 4.1 4175 4127 4101
1968 4.65 4.0 4089 4025 4001
1969 4.72 4.1 4154 4122 4100
1970 5.85 4.4 4480 4425 4400
1971 6.06 4.4 4506 4424 4400
1972 5.78 4.4 4489 4418 4400
1973 5.35 4.5 4554 4518 4500
1974 7.41 5.2 5268 5229 5201
1975 11.24 5.9 6034 5939 5903
1976 8.93 5.3 5445 5347 5306
1977 8.77 5.4 5597 5453 5406
1978 10.87 6.0 6183 6099 6009
1979 10.75 6.2 6577 6388 6211
1980 11.24 6.1 6908 6193 6113
Year, Percentage Earnings Yield 100E10/P, Historical Surviving Withdrawal
Code: Select all
1921 19.61 7.1
1922 15.87 7.5
1923 12.20 7.2
1924 12.35 7.2
1925 10.31 7.0
1926 8.85 6.3
1927 7.58 6.2
1928 5.32 5.5
1929 3.69 4.6
1930 4.48 4.6
1931 5.99 4.9
1932 10.75 6.1
1933 11.49 7.2
1934 7.69 6.1
1935 8.70 6.6
1936 5.85 5.5
1937 4.63 4.9
1938 7.41 5.8
1939 6.41 5.6
1940 6.10 5.9
1941 7.19 7.0
1942 9.90 7.8
1943 9.80 7.5
1944 9.01 7.1
1945 8.33 6.9
1946 6.41 7.1
1947 8.70 7.8
1948 9.62 7.8
1949 9.80 7.6
1950 9.35 8.0
1951 8.40 7.3
1952 8.00 6.8
1953 7.69 6.6
1954 8.33 6.7
1955 6.25 5.7
1956 5.46 5.3
1957 5.99 5.4
1958 7.25 5.6
1959 5.56 4.9
1960 5.46 4.9
1961 5.41 4.8
1962 4.72 4.5
1963 5.18 4.8
1964 4.63 4.4
1965 4.29 4.2
1966 4.15 4.2
1967 4.90 4.5
1968 4.65 4.4
1969 4.72 4.4
1970 5.85 4.8
1971 6.06 4.8
1972 5.78 4.8
1973 5.35 4.8
1974 7.41 5.7
1975 11.24 6.5
1976 8.93 5.8
1977 8.77 5.9
1978 10.87 6.6
1979 10.75 6.9
1980 11.24 6.9
Year, HSWR with no gains removed, Withdrawal Amounts (with 25% of gains removed) at 5 years, 10 years, 20 years and 30 years.
Code: Select all
1921 7.1 7078 8024 7094 6403
1922 7.5 7722 8224 6971 6702
1923 7.2 7136 7927 6505 6402
1924 7.2 7752 7413 6500 6401
1925 7.0 8174 7061 6291 6201
1926 6.3 7122 6409 5680 5600
1927 6.2 7039 6952 5619 5500
1928 5.5 5913 6455 5023 4900
1929 4.6 4360 5638 4341 4200
1930 4.6 4923 5103 4349 4200
1931 4.9 5287 5499 4638 4500
1932 6.1 7296 5977 5563 5500
1933 7.2 8948 6576 6473 6400
1934 6.1 7024 5842 5688 5600
1935 6.6 7595 6343 6128 6000
1936 5.5 5959 5522 5324 5200
1937 4.9 4881 5268 4780 4700
1938 5.8 5714 6236 5649 5500
1939 5.6 5620 5900 5482 5300
1940 5.9 5956 6027 5726 5500
1941 7.0 7238 7168 6730 6600
1942 7.8 8454 7655 7423 7201
1943 7.5 7954 7373 7173 6902
1944 7.1 7439 7085 6908 6602
1945 6.9 7106 6912 6500 6402
1946 7.1 6878 7725 6810 6703
1947 7.8 8067 8312 7528 7405
1948 7.8 8067 8245 7445 7306
1949 7.6 7890 8088 7275 7104
1950 8.0 8286 9086 7544 7405
1951 7.3 7916 7793 6932 6805
1952 6.8 7422 7083 6442 6305
1953 6.6 7251 7061 6273 6105
1954 6.7 7320 7136 6226 6105
1955 5.7 6503 5847 5409 5303
1956 5.3 5696 5525 5032 4904
1957 5.4 5832 5694 5245 5002
1958 5.6 6325 5777 5506 5202
1959 4.9 5004 5298 4837 4667
1960 4.9 5194 5023 4772 4502
1961 4.8 5223 4861 4698 4402
1962 4.5 4851 4592 4274 4202
1963 4.8 5106 4911 4495 4401
1964 4.4 4748 4540 4228 4101
1965 4.2 4474 4297 4046 3901
1966 4.2 4363 4305 4016 3900
1967 4.5 4656 4869 4175 4101
1968 4.4 4494 4660 4089 4001
1969 4.4 4644 4598 4154 4100
1970 4.8 5011 5046 4480 4400
1971 4.8 4966 5174 4506 4400
1972 4.8 5282 4871 4489 4400
1973 4.8 5149 5013 4554 4500
1974 5.7 5984 6009 5268 5201
1975 6.5 7011 6743 6034 5903
1976 5.8 5984 5948 5445 5306
1977 5.9 6301 5970 5597 5406
1978 6.6 7077 6949 6183 6009
1979 6.9 7487 7006 6577 6211
1980 6.9 7318 7034 6908 6113
Mathematically, owning TIPS is similar to granting a mortgage. The same formula applies.
The TIPS Equivalent Safe Withdrawal Rate (TESWR) is in terms of inflation adjusted (i.e., real) dollars. Two subtleties enter into the equations. One is the time mismatch between an inflation index report and the adjustment to the TIPS principal. I assume that you spend in accordance to coupon payments received as opposed to matching inflation as it occurs. The other subtlety is that some TIPS must be sold. I assume that there are no gains or losses from these transactions.
The TIPS Equivalent Safe Withdrawal Rate (TESWR) is the percentage of the original balance that can be withdrawn in equal (inflation adjusted, real) dollar amounts over the entire time period (of 30 years) with a final balance of zero.
The formula for the TIPS Equivalent Safe Withdrawal Rate (TESWR) is:
TESWR = r / [1 - (1 / [1+r] )^N ], where r is the interest rate as a decimal fraction and N is the number of years. In this case, r = 0.02 and N = 30.
Using these numbers, the TIPS Equivalent Safe Withdrawal Rate (TESWR) is 4.465%. If the initial balance is $100000, the annual withdrawal is $4465.
I will make an analysis of these data in the near future. I have already determined the regression equations when withdrawal amounts are plotted versus the percentage earnings yield 100E10/P (or 100% / [P/E10]).
Initial findings
Withdrawing 25% of the year-to-year gains generally results in larger withdrawals early and smaller withdrawals later. This extends to the comparisons with a conventional approach as well. Withdrawal amounts are (generally) larger than the conventional approach in the earlier years and smaller in later years.
There were some periods in which owning stocks reduced income relative to an all-TIPS portfolio (at a 2% interest rate). They seem to correspond to times of high valuations such as the 1960s. Today's valuations are very high, just a little bit above than P/E10 = 26 (using Professor Robert Shiller's P/E10 for the S&P500 index).
Have fun.
John R.