I had some time on a couple of plane trips last week, so I managed to carefully go through this article and recreate some of his numbers. Like any paper, you have to take the formulas presented for what their worth, and not treat them as the final answer, but I am going to use his “short-cut” formula in my personal planning, and I would think that it would be very useful to everyone else as well.
The biggest reason that Milevesky comes up with SWR numbers lower than something like FIREcalc is that he uses different assumptions. The FIREcalc data uses years with equity returns that average almost 9% over inflation, with about a 19% standard deviation. If we use 75% equities and 25% TIPS at 2.5%, then we have an expected 7.4% and standard deviation 14.3%. Someone with a 30 year median life expectancy has about a 10% ruin probability using a 4.6% withdrawal rate with those assumptions. The number can get a lot lower if you make an assumption about future returns that don’t match the period used by FIREcalc. The result you state (94% safe at 3% WR) uses 5% / 12% for mean / standard deviation.
Of Milevesky's two simplifying assumptions (lognormal asset returns, and constant force of mortality), the force of mortality assumption is the most troubling to me. For an ER you might be working with a median lifespan of 45 years (say a 35 year old living to 80). This would give a constant force of mortality of 1.5%. However, your initial mortality will be something like 1/10th that. So Malkiel is dramatically overestimating the probability of death early in the plan. For example the constant force of mortality might give you a 85% probability of a 35 year old making it 10 years, while standard mortality would give you about a 98% chance. Dying young can “bail you out” of bad investment results. A constant force of mortality does show an unreasonably large probability of living to 150 or more, but that won’t upset your plan as often, since after you’ve made it 50-100 years you have most likely built up a large investment surplus. For this reason Malikiel’s formula tends to underestimate the probability of ruin, and will only overstate it when the withdrawal rate is very low (and you need a lot of years to blow out the plan).
So, it’s not perfect, but it is very interesting to think about, and the errors in his method really pale in comparison to the uncertainty around what the correct inputs are!
The biggest reason that Milevesky comes up with SWR numbers lower than something like FIREcalc is that he uses different assumptions. The FIREcalc data uses years with equity returns that average almost 9% over inflation, with about a 19% standard deviation. If we use 75% equities and 25% TIPS at 2.5%, then we have an expected 7.4% and standard deviation 14.3%. Someone with a 30 year median life expectancy has about a 10% ruin probability using a 4.6% withdrawal rate with those assumptions. The number can get a lot lower if you make an assumption about future returns that don’t match the period used by FIREcalc. The result you state (94% safe at 3% WR) uses 5% / 12% for mean / standard deviation.
Of Milevesky's two simplifying assumptions (lognormal asset returns, and constant force of mortality), the force of mortality assumption is the most troubling to me. For an ER you might be working with a median lifespan of 45 years (say a 35 year old living to 80). This would give a constant force of mortality of 1.5%. However, your initial mortality will be something like 1/10th that. So Malkiel is dramatically overestimating the probability of death early in the plan. For example the constant force of mortality might give you a 85% probability of a 35 year old making it 10 years, while standard mortality would give you about a 98% chance. Dying young can “bail you out” of bad investment results. A constant force of mortality does show an unreasonably large probability of living to 150 or more, but that won’t upset your plan as often, since after you’ve made it 50-100 years you have most likely built up a large investment surplus. For this reason Malikiel’s formula tends to underestimate the probability of ruin, and will only overstate it when the withdrawal rate is very low (and you need a lot of years to blow out the plan).
So, it’s not perfect, but it is very interesting to think about, and the errors in his method really pale in comparison to the uncertainty around what the correct inputs are!
