Tuesday, June 19, 2012

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.

1 comment:

  1. Reading this it hard to not want to become an asset manager.

    ReplyDelete