Sunday, February 19, 2012

Retirement Planning Guidelines: An Alternative to the Trinity Study

Recently I wrote about the famous Trinity Study for developing guidelines about sustainable withdrawal rates to avoid outliving your wealth. I wrote about their portfolio success rates concept. Their approach results in tables like this:

Today, I'd like to suggest an alternative table for prospective retirees to use instead. The alternative is Table 3 from my article, "Capital Market Expectations, Asset Allocation, and Safe Withdrawal Rates," from the January 2012 Journal of Financial Planning. This table is based on the same data as the Trinity study table, but uses Monte Carlo simulations instead of historical simulations. The table looks like this:

I think this table has several advantages:

* It uses Monte Carlo simulations which count each year of the historical data equally. It is not subject to the bias against bonds in the historical simulations resulting from an overweighting of the middle historical years. (For more on this, see the section "Bias against Bonds in Historical Simulations" here.)
* I think the information is more directly useful: it connects withdrawal rates to acceptable failure rates and shows the optimal asset allocation.
* The results fit better with real world expectations. Stock allocation recommendations tend to be lower than the 50-75% outcome in the Trinity study. The table also shows how a wide range of asset allocations work nearly as well as the optimal. This gives relief for retirees worried about high stock allocations.
* Since it is based on Monte Carlo simulations, the table can be easily customized to a change in capital market expectations. That is, the historical portfolio success rates in the Trinity study may not matter now that bond yields and dividend yields are so much lower than their historical averages. By modifying these return assumptions, users can get results that may better fit their own expectations about the future. For example, here is the same table, but with the real return expectations for each asset class being two percentage points lower than their historical averages:





  1. Npt sure how to read these tables. What are the columns "For Withdrawal Rates within .1% of Maximum"? Is that the range of how much someone could withdraw? It would be helpful if you could give an example. Thanks.

  2. Thanks for the important question, because the table is dead on arrival if no one can understand it.

    Let me give an example for a 30 year retirement and for accepting a 10% chance for failure. The third column then tells you that the maximum sustainable withdrawal rate is 4.3% with these conditions. Then, the next set of columns show the optimal asset allocation to achieve this 4.3% withdrawal rate. It is 45% stocks, 55% bonds, and 0% cash. This is a fixed asset allocation held throughout retirement with annual rebalancing.

    The last six columns are meant to point out how that there are a range of allocations in which one could expect to do nearly as well (a withdrawal rate of 4.2%, which is within 0.1 of the maximum withdrawal rate. Any stock allocation between 28% and 68%, combined then with any bond allocation between 72% and 32% (with some slight rounding error as less than 0.5% must be in cash too) would support a withdrawal rate of 4.2%.

    Does this help?

  3. Dr, Pfau

    Yes it does. Very interesting set of tables. One of the conclusions I draw is that the emphasis on periodic rebalancing one reads about is largely missplaced given the very wide ranges of stock /bond allocations that seem to have minimal impact on the safe withdrawal rates. Is this a valid conclusion?

  4. I'm the initial anonymous poster above, and yes, your explanation was very helpful. Thanks.

  5. Good.

    About rebalancing, that isn't something I've looked at much yet. I personally like rebalancing, but I suppose an implication of these results is that you can have rather wide rebalancing bands. Though I didn't specifically test about not rebalancing, since I assumed annual rebalancing in all cases, I don't see any reason why your conclusion is not valid.

  6. This is extremely helpful, thanks for sharing your work.

    Going back to your example for explanation, am I correct in thinking based on this data (saying that any allocation from 28% to 68% stocks is within 0.1 of the w/d rate) that asset allocation upon which we advisors typically put so much focus is largely irrelevant within a prudent range?

    Meaning, client wants to be more aggressive and have a 60/40 portfolio - fine. Wants to me more conservative with a 30-70 portfolio? Fine again. Both have the same expected success rate as long as we're planning to be a click or two below the stated w/d rate.

    Thanks for your comments - John

  7. Dear John,

    Thank you. Yes, what you are explaining sounds correct. Please also see this blog post about William Bengen's research:

    Two relevant points here:

    (1) Figure 2.3 shows that I am not making this stuff up. That is a famous result from William Bengen that the worst-case withdrawal rates varied very little across a wide range of stock allocations.

    (2)So while stock allocation doesn't matter so much for safe withdrawal rates, Figure 2.4 does show it matters a whole lot for the expected bequest value. Higher stock holdings will result in higher average bequest values.

    Mentioning this does make me think of one more relevant point. The table I showed here is based on probability of failure, as is standard practice. But the magnitude of failure (i.e. running out of wealth sooner) could be a bit higher as the stock allocation increases.

    I think that is the trade off: though the probability of failure is about the same, higher stock allocations will lead to higher bequest values on average but also worst failures when the failures do happen.

    I should actually do more work to add both of these factors.

  8. Thanks for your excellent work ,as always. Hopefully you will be able to provide some thoughts on non inflation adjusted withdrawals in the future. I greatly appreciate all your work to date.

  9. Thank you for your great work and sharing! I really enjoy the different approaches and the thorough results you share. Do you happen to have data for a retirement duration of 50 years? I know that is not the norm but some couples retire "early" and have a family history of living past 100 may want to take the long view. Looking forward to more of your work!

  10. Thanks.

    I'm working a bit on non-inflation adjusted withdrawals. I'm planning to write my next Advisor Perspectives column about some different approaches related to that.

    As for 50 years, I never ran those numbers. Withdrawal rates continue decreasing as the time horizon lengthens, but at a decreasing rate. So 50 years would call for a bit lower than 40 years.

  11. Why are we so hung-up on a withdrawal rate when it is the withdrawal amount that pays the bills? Further, it is widely known that the withdrawal amount goes down adjusted for inflation as people age in retirement. This entire way of looking at retirement income is flawed.

    Rick Ferri

  12. Rick,

    Of course withdrawal amounts are what matters. But the idea is to divide your desired withdrawal amount by your financial assets and see what the implied withdrawal rate is. Then you can compare it to the withdrawal rates in tables such as these to get some idea about the potential sustainability of your plans.

    Actually, I'm working on a column now about whether inflation-adjusted withdrawal amounts is a good baseline assumption. So let me hold off talking about that for now.

    There are other approaches to retirement income planning besides safe withdrawal rates. You are right to say there are some important flaws with safe withdrawal rates, but I'm not sure that the flaws are related to the reasons you mention.

  13. Very interesting work and a very helpful tool for understanding the probability of the outcomes. Thank you for sharing on my site Wade.

    1. Thank you! As you are investigating Monte Carlo and thinking about withdrawal rates, the assumptions you use for mean and standard deviation are very important. Since we don't know what those will be going forward, it is useful to remain flexible and use conservative assumptions as you are doing with your choice of 3%. Hopefully, though, you will find that your wealth grows more and more with only a 3% withdrawal rate.