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 IBonds (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:
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:
RESULTS
I am presenting the following data:
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 nontrivial amount of time on this topic and came to the conclusion that MVIlike 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).