Friday, August 26, 2011

How Long Might Retirees Spend with No Remaining Wealth?

What the following figure shows for a couple both aged 65, is the probability that at least one of them will experience at least so many years at the end of their retirements with no remaining wealth. A note about the methodology and data is included at the end. This information is more detailed than just knowing the probability of failure, which is actually just the probability of spending at least 1 year of retirement with no wealth.  Now we can see further than that. For instance, using a 5% withdrawal rate, a couple can expect that at least one of them will spend at least 1 year at the end of retirement with no remaining wealth in 15% of cases, at least 4 years of retirement with no wealth in 10% of cases, at least 8 years with no wealth in 5% of cases, and so on. I do realize that real retirees would start cutting back on spending before their wealth is gone, but at least we can see about the patterns for the necessity of accepting a lower standard of living later in retirement.  Though using life expectancies did start pointing to the possibilities of using a higher withdrawal rate, these figures suggest caution about doing this because it may result in a long period of time with no wealth. 

Single males and single females would have lower probabilities for having no wealth, since they do not live as long. I forgot to save the figure for females, but the results for females would be somewhere in the middle between those for males and those for joint couples. Here is the figure for males:

Note: In the real world, actual results might be more pessimistic than this, either because people continue living longer and longer in the future (which is great of course, but in this context it will increase the failures), or because future market returns will not be as high as in the past, or because retirees will also have fees deducted from their portfolios. The above results really should be interpreted as a best case scenario.

Methodology: These figures are made using a 40% stock and 60% bond asset allocation strategy built from random combinations of the historical returns data. Simulations are bootstrapped using real annual 1926-2010 data from SBBI for large-cap stocks and intermediate-term government bonds. Withdrawals are taken at the start of year and are adjusted for inflation. The portfolio is rebalanced annually and there are no taxes or fees.  Mortality data is from the 2007 Social Security Administration Period Life Tables.


  1. The area under these graphs is a measure of the riskiness of the retirement that takes account of both the probability of failure and the magnitude of failure. You could now optimise the asset allocation, for a given WR, such that this area is minimised. The calculation could be repeated for different retirements (male/female/couple, ages) thus providing advice on asset allocation for retirees for their situation and chosen initial WR.

  2. Thank you for this good idea! When I tried this out, it does tend to shift toward 10 or 20 percentage points of less stocks, the asset allocations that minimize this measure. That is compared, to the asset allocations that minimize just the probability of failure. I might use this at some point. If you'd like to send me your name via email, I'd like to acknowledge you should I end up using it in a paper. Thanks!