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OmegaNot (and volatility)

I'm making this available to M* readers for comments before integration into my website. This sounds really considerate but the truth is that I don't currently have time to do all four different asset allocations  and  I'm having some problems with Microsoft FrontPage and can't currently integrate this (easily) into my website. A study tuned to the conversations in "Investing During Retirement" (conversation #642) is easier. 

In OmegaNot (click here) I investigated a strategy where you divide your portfolio into two pieces (one equities and one fixed income) and I defined withdrawal rules that said either withdraw from equities or fixed income, but never rebalance between these two pieces of your portfolio. The analytical data presented indicated a significant performance  improvement over an annually rebalanced portfolio. But it used I-Bonds (real yield 3.4%) as the fixed income instrument which were not included in the analysis with which OmegaNot was compared. This naturally leads to the question "where did the improvement come from - an alternative withdrawal methodology or the use of IBonds?". I have repeated the OmegaNot analysis using the same asset classes (Intermediate Government Bonds for Fixed Income) in all cases and compared the OmegaNot withdrawal strategy with a 'normal' withdrawal strategy involving rebalancing to the target asset allocation at the end of each year.  The results of this analysis also led me to an investigation into the volatility implications, which I'll also discuss. 

The methodology simulated for the annual rebalancing case (I will refer to this as the 'base case') is:

  1. A starting $1,000,000 portfolio and an initial withdrawal of 4.4% (this was the 100% survivable portfolio withdrawal per the originating analysis)  
  2. Withdrawals were adjusted for inflation each year and taken as a lump sum at the beginning of each year 
  3. An asset allocation of 25% large company stocks, 25% small company stocks, and 50% intermediate government bonds was used. A 50% equity allocation was kind of the "sweet spot" of the discussions recently on "Investing During Retirement".
  4. After withdrawals were made the portfolio was rebalanced to the target allocation.
  5. Each simulation was for 30 years using the Ibbotson data. I used the 'starting years' 1926 through 1979 inclusively. As I had done previously for simulations that push you beyond the current date I simply 'rolled back to 1960'. This was an arbitrary choice on my part as I wanted to be sure that I included the mid-70's. If I were doing this all over again I'd probably roll back to 1969 (instead of 1960), but I've been using 1960 so I didn't change that. Portfolio performance at the end of the simulations isn't the big swinger that it is at the beginning. Even the starting year 1973 simulation using fixed 4.4% withdrawals has an inflation adjusted portfolio value of over $1.1M going into the first roll-over year. I can't envision a reasonable assumption here that would materially affect these results. 
  6. I did not make any accommodations/adjustments for taxes or investment fees.

The differences between previously published analyses and this one are (click here for documentation of the previously used methodology). 

1) I did not include a 5% allocation to Treasury Bills 

2) I did not take into account any returns that could be achieved on your annual withdrawal during the year

3) I have only analyzed a 50/50 equities/fixed income split

The OmegaNot withdrawal rules were: 

  1. I started with the same $1,000,000 portfolio with all withdrawals made at the beginning of the year. I ignored returns on the withdrawals and any fees/taxes as in the base case.
  2. The equity portion of was equally split between large company stocks and small company stocks and rebalanced each year (just like the earlier studies that I did and in the base case). 
  3. Withdrawals were adjusted for inflation and not reduced when portfolio values dropped (just like the Trinity and Jarrett studies and the base case). 
  4. Each year a 'new equity target' was calculated as the initial equity value adjusted upward (or downward) for inflation. For example if you started with a $1,000,000 portfolio with 50% equities (initial equity target of $500,000) and in year 5 the cumulative inflation to date is 20%, your equity target is now $500,000x1.2=$600,000.
  5. Withdrawals were taken from equities first but only to the extent that your final equity value did not drop below the 'new equity target' discussed in #4 above. In some cases the equity withdrawal could be zero.
  6. The remainder of the withdrawal was made from Intermediate Government Bonds. 
  7. If your Bond total value dropped to zero then all future withdrawals were made from equities. The Bond supply was never replenished.
  8. Each simulation was for 30 years using the Ibbotson data (1926 through 1999 - I haven't updated with 2000 data yet). I used the ' starting years' 1926 through 1979 inclusively. I used the same roll-over assumption as the base case. 
  9. I did not make any accommodations for taxes or investment fees.


I am presenting the following data:

  1. The median (half more/half less) inflation adjusted end portfolio value for the 54 different retirement  
  2. The number of times the "portfolio failed" (failed to provide the inflation adjusted income in all years)
  3. The lowest ending (inflation adjusted) portfolio value 
  4. The number of times that the ending portfolio value (inflation adjusted) dropped below the starting value. This 'rule' asserts that your ending portfolio value has the same purchasing power as at the start  (the "Withdrawals Forever" rule). This is more inline with the thinking of some M* contributors (assurance that you will never go broke).


  Median End Value (inflation adjusted) Number of portfolio failures Minimum End Value (inflation adjusted)


Cases where End Value <$1M (inflation adjusted)
Annual Rebalancing (base case) $1,524,000 1* 0 19%
OmegaNot $2,299,000 0 $909,000 2%

                     Fixed inflation adjusted $44,000 withdrawals from an initial $1M portfolio 

*1969 failed in the final year of withdrawals

WOW!!!!!! - the data certainly makes OmegaNot look like a real winner. In fact you can actually raise your withdrawal target from 4.4% to 4.9% without encountering a portfolio failure. This is a greater than 10% increase in income for simply changing your withdrawal strategy. Despite the fact that this is my data and my withdrawal strategy (although it originated as a misinterpretation of Scott Burns' Omega strategy), this doesn't pass my personal sniff test and looks suspiciously like a "free lunch" for these reasons:

As I have stated in M* (in Investing During Retirement) I find the the results of the simulations that I have done regarding the volatility of "MVI" most disconcerting. However, as I stated in Efficient Frontiers in Withdrawal (click here) I spent a non-trivial amount of time on this topic and came to the conclusion that MVI-like withdrawal strategies (click here), given the work that I had done to date, are relatively efficient.  It is also fair to observe that including international equity asset classes, REIT's, and a variety of alternative fixed income instruments such as IIS might well improve the volatility results significantly (the same could be said for the Trinity and Jarrett studies).

So I'm going to use "MVI" (as I understand it) to evaluate the volatility impacts of OmegaNot. For both the base case and OmegaNot the withdrawal amount will be 4.4% of your actual portfolio value, rather than 4.4% of your initial portfolio value (adjusted for inflation). As before I'll be expressing all results in inflation adjusted terms. 

Volatility is a reasonably difficult issue to express succinctly. What we have is 54 different 30 year retirement simulations. Each 30 year simulation has its own unique set of results which are:

1) Inflation adjusted end portfolio value

2) The 30 different inflation adjusted incomes that you achieved

And we have 54 different sets of the above 31 different results (1674 numbers). For each 30 year retirement simulation I will calculate the following.

1) Median ending portfolio value (half more/half less)

2) Median inflation adjusted income across all 30 years

3) The 75th percentile minimum inflation adjusted income across all 30 years (75% were better)

4) The 95th percentile minimum inflation adjusted income across all 30 years (95% were better)

5) The minimum inflation adjusted income across all 30 years

This has reduced 31 numbers to 5, but we still have 54 sets of these 5 numbers (54 median ending portfolio values, 54 minimum inflation adjusted income values, etc). So I will simply "do it again" to these 5 sets of 54 numbers. I'll find the median value of all 54 different median ending portfolio values, I'll find the 75th percentile minimum of all the median ending portfolio values, ....  I'll find the 95th percentile minimum of all the 54 different 75th percentile minimum inflation adjusted incomes .. It is easy to automate but tends to make your mind think in ways that it will probably object to. Mine does and it always takes me a minute or two to get it back after I leave this stuff for a while. "The 95th percentile minimum of 75th percentile minimum single year incomes" is not a concept that fits nicely in my mind for sure. Fortunately in this case a larger number is always a better number. So you don't necessarily have to have a complete grasp of this stuff to get a feel for how the numbers compare. I was using this analytical technique as a way to compare volatilities. Normal volatility measurements (e.g., mean and standard deviatio) always leave you with the question "which is better at a 95% certainty level - a mean income of $40,000 with a standard deviation of $5,000 or a mean income of $38,500 and a standard deviation of $4,000?"  

I'll be presenting this data in a table and each entry in the table will have the form BC#/ON# where BC# will be the base case result for that entry and ON# will be the OmegaNot result for that entry. For example an entry of '34,713/36,123' is a base case result of 34,713 and an OmegaNot result of 36,123. The table across the top represents the statistics of the individual 30 year retirement scenarios. For example if you were interested in investigating the minimum single year income achieved you would read across the top of the table to the 'Minimum Single Year Income' entry. Remember that there are 54 of these numbers. Then you go down the column and find the median, 75th percentile, 95th percentile, and absolute minimum from these 54 different numbers. Now for the data. It is all in units of $1,000.

  Median Single Year Income 75th Percentile Single Year Income 95th Percentile Single Year Income Minimum Single Year Income Ending Portfolio Value
Median 52,200/54,600 44,800/44,400 37,700/38,100 34,500/34,300 1,337K/1,742K
75th percentile 45,000/47,100 38,300/37,700 32,300/32,700 29,100/30,000 1,152K/1,306K
95th percentile 38,900/41,400 32,500/32,900 28,900/28,800 25,800/25,400 1,023K/1,089K
Minimum 35,700/36,300 28,700/28,700 25,000/25,200 22,200/22,400 741K/1,000K

                 Base Case Results/OmegaNot Results - 4.4% 'MVI' withdrawals from a starting $1M portfolio


These numbers also show OmegaNot to (in almost all cases) be 'better' than the Base Case, although I find this data to be somewhat less compelling (more like a free snack rather than a free lunch). Even though these simulations did not ever allow your bond portfolio to go to zero, I still find this aspect of OmegaNot troublesome.  I tend to agree with William Bernstein in that rebalancing between asset classes of dramatically differing mean returns is not particularly efficient. This  leads me to the conclusion that the improvement of OmegaNot is mostly due to not doing annual rebalancing between equities and bonds. And there are certainly ways saner than OmegaNot to achieve this. Some alternatives are:

1) Rebalancing every 'n' years where 'n' is greater than 1

2) Rebalancing when your portfolio is more than x% out of balance. You might chose x=15% where you would only rebalance if (for the 50/50 target allocation case) your equities rose above 65% or fell below 35% (and this still leaves you with the option of either rebalancing to the original target or to the upper/lower limit). 

3) Rebalance only when your equities are out of balance high 

4) Never rebalance directly between equities and fixed income instruments, simply draw from the asset class(es) that is out of balance high

5) Chose a maximum annual rebalancing amount (in percent of your portfolio)

6) Rebalance half way between your current allocation and the target (or 2/3's or 1/3 or .4287465 or whatever). 

7) Follow OmegaNot but set a lower limit to your bond allocation

The message that I am personally taking from all this is that I will continue to rebalance between various equity asset classes, but I'm going to be less likely than before to annually rebalance between equities and fixed income assets. My inclination is toward option #4 (and never say never).