Retirement Income and the Tyranny of Compounding Fees

Clearly, the wonderful magic of compounding returns has been overwhelmed by the powerful tyranny of compounding costs.

-          John Bogle, Enough, p. 42

Another optimistic assumption of classic safe withdrawal rate studies is that investors are able to earn precisely the underlying index returns, even after accounting for any portfolio management fees, risks that active management does not precisely match the underlying benchmarks, or behavioral and timing mistakes of buying high and selling low. In reality, many investors will find that their investment returns will lag behind the annually rebalanced and indexed portfolios enjoyed by the hypothetical retiree in the safe withdrawal rate studies.

Here, I will look at the impact of fees and/or account underperformance. When discussing a 1% fee, what I mean is that at the end of each year the remaining account balance is reduced by 1%. This could result from actual fees or from other types of investor underperformance compared to the indices. I simplify by just referring to it as a fee.

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, and inflation-adjusted withdrawal amounts. The two cases are for no portfolio fees, and for a 1% annual fee. Data is from the SBBI Yearbook.

First, Table 4.1 shows the maximum sustainable withdrawal rates for the baseline case with and without fees. In both cases, 1966 retirees are the source of our SAFEMAX. Without fees, a 1966 retiree could sustain withdrawals over 30 years using a 4.04% withdrawal rate. With a 1% fee, the SAFEMAX fell by 0.48 percentage points to 3.56%. From the perspective of the SAFEMAX, a 1% fee would have resulted in reduction of potential spending power by 11.9%. Across the historical period, fees caused the maximum sustainable withdrawal rates to fall on average by 0.63 percentage points or 11% of spending power.

Despite common misconceptions, there is not a one-to-one tradeoff between fees and withdrawal rates. As the portfolio decreases in size, fee amounts decline while real withdrawal amounts do not change.

Table 4.1 Maximum Sustainable Withdrawal Rates (MWRs) Cases: (1) No Fees,  (2) 1% Annual Fee For 50/50 Asset Allocation, 30-Year Retirement Duration, Inflation Adjustments Using SBBI Data, 1926-2011, S&P 500 and Intermediate-Term Government Bonds
Year	MWR (No Fees)	MWR (1% Fee)	Difference	Year	MWR (No Fees)	MWR (1% Fee)	Difference
1926	7.28	6.47	0.81	1955	5.59	4.9	0.69
1927	7.03	6.24	0.79	1956	5.03	4.4	0.63
1928	6.03	5.35	0.68	1957	5.18	4.53	0.65
1929	5.12	4.54	0.58	1958	5.62	4.91	0.71
1930	5.39	4.79	0.6	1959	4.91	4.29	0.62
1931	5.81	5.16	0.65	1960	4.87	4.25	0.62
1932	7.13	6.34	0.79	1961	4.82	4.21	0.61
1933	6.78	6.02	0.76	1962	4.38	3.83	0.55
1934	5.63	5	0.63	1963	4.64	4.07	0.57
1935	5.79	5.14	0.65	1964	4.35	3.82	0.53
1936	4.91	4.36	0.55	1965	4.11	3.62	0.49
1937	4.35	3.87	0.48	1966	4.04	3.56	0.48
1938	5.55	4.95	0.6	1967	4.41	3.91	0.5
1939	4.75	4.24	0.51	1968	4.18	3.71	0.47
1940	4.8	4.3	0.5	1969	4.2	3.73	0.47
1941	5.19	4.65	0.54	1970	4.83	4.31	0.52
1942	6.26	5.62	0.64	1971	4.81	4.3	0.51
1943	6.47	5.81	0.66	1972	4.64	4.16	0.48
1944	6.15	5.52	0.63	1973	4.44	4	0.44
1945	5.93	5.32	0.61	1974	5.27	4.76	0.51
1946	5.28	4.73	0.55	1975	6.89	6.24	0.65
1947	6.69	6	0.69	1976	6.4	5.8	0.6
1948	7.42	6.64	0.78	1977	5.99	5.44	0.55
1949	7.76	6.93	0.83	1978	6.93	6.3	0.63
1950	7.29	6.49	0.8	1979	7.64	6.95	0.69
1951	6.97	6.18	0.79	1980	8.31	7.56	0.75
1952	6.89	6.09	0.8	1981	8.51	7.73	0.78
1953	6.59	5.8	0.79	1982	9.77	8.87	0.9
1954	6.85	6.01	0.84	1983 +	30 Years of Data Not Yet Available
Note: SAFEMAXs are boxed. All MWRs below 4% are bold-faced.

The tyranny of compounding fees is shown even more starkly in Table 4.2. This table shows the remaining real value of wealth after 30 years for someone who retired with wealth of 100 and used a 4% withdrawal rate. Over the 30-year period, annual real withdrawal amounts are 4. With the other standard assumptions, this table shows the remaining wealth for the cases of no fees and a 1% fee. About these calculations, when wealth falls below zero, fees are no longer deducted. Real wealth is shown as negative to reflect the total desired real withdrawal amounts which could not be taken from the portfolio.

The difference in wealth amounts between the two columns shows the combined impact on wealth of a 1% annual fee. The combined impact of the fees include both the actual fee paid and the loss of subsequent capital gains and interest that would have been earned if the fee amounts had stayed in the investment portfolio.

With a 4% withdrawal rate and a 30-year retirement period, the total withdrawals enjoyed by the retiree add to 120. Clearly, when the portfolio grows, the fees paid are larger. In some cases, which are both lucky and shocking, the retiree ends up paying more through the 1% fee than they do for their retirement spending on everything else. That can be seen clearly for the 1982 retiree who had real wealth of 465 after 30 years in the no fee case.  Note that compared to a withdrawal of 4, 1% of that wealth amount is 4.65. In total, fees for the 1982 retiree led to a total reduction in potential wealth of 145.2.

Though the 4% withdrawal rate was sustainable in every rolling period from this historical data, a 1% fee would have fully depleted the wealth for 8 of the 57 retirees. Though the total lifetime fees paid by these unlucky retirees tend to be less, this is only because they experienced rapid wealth depletion which limited fee collections. For a further example, a 1970 retiree would have maintained the real value of their principal when not paying fees, but the real value of their principal would only be about 30% of its initial value when fees are included. Since timing the market and actively selecting investments is quite difficult, this table strongly suggests that retirees should consider whether low-cost index funds may better suit their needs.

I do not mean to suggest that the services of a financial planner may not be helpful. If a planner helps a retiree to choose a reasonable asset allocation and to stay the course and avoid behavioral mistakes, then the overall gains from these actions could more than make up for the impacts of fees. My attack on fees is more directed at overpriced mutual funds than anything else. 

Table 4.2 Remaining Wealth After 30 Years (Measured in Real  Terms) Using a 4% Withdrawal Rate and Retirement Date Wealth=100 50/50 Asset Allocation, Inflation Adjustments for Withdrawals Case: (1) No Fees, (2) 1% Annual Fee Using SBBI Data, 1926-2011, S&P 500 and Intermediate-Term Government Bonds
Year	Real Wealth (No Fee)	Real Wealth (1% Fee)	Total Cost of Lifetime Fees (Fees and Missing Capital Gains)	Year	Real Wealth (No Fee)	Real Wealth (1% Fee)	Total Cost of Lifetime Fees (Fees and Missing Capital Gains)
1926	255	160	95	1955	74	35	39
1927	227	140	87	1956	56	18	38
1928	138	76	62	1957	71	27	44
1929	85	34	51	1958	96	46	50
1930	106	50	56	1959	55	15	40
1931	138	74	64	1960	60	15	45
1932	257	160	97	1961	54	12	42
1933	210	127	83	1962	28	-8	36
1934	129	66	63	1963	48	5	43
1935	147	78	69	1964	27	-10	37
1936	75	25	50	1965	8	-20	29
1937	27	-8	35	1966	3	-24	26
1938	125	64	61	1967	38	-6	44
1939	61	16	44	1968	19	-18	37
1940	57	17	39	1969	23	-17	41
1941	85	38	46	1970	103	32	71
1942	164	97	67	1971	95	30	65
1943	184	111	73	1972	68	15	54
1944	140	81	58	1973	43	0	43
1945	99	56	43	1974	134	66	68
1946	69	33	36	1975	306	194	112
1947	155	95	60	1976	238	146	92
1948	174	111	63	1977	198	116	81
1949	178	115	63	1978	291	186	105
1950	150	94	56	1979	288	190	98
1951	135	83	52	1980	358	240	117
1952	114	69	45	1981	376	253	122
1953	112	66	47	1982	465	320	145
1954	131	78	53	1983 +	30 Years of Data Not Yet Available
Note: All wealth values below 100 are bold-faced. When wealth reaches zero, real withdrawal amounts are deducted to show the degree of underfunding from the spending goal. No further fees are collected.