Ben Mathew wrote: Sat Aug 09, 2025 11:48 am
Fairfox wrote: Fri Aug 08, 2025 3:55 pm
The fact that TPAW shows the 5th percentile line as though it’s an actual trajectory of withdrawals is leading to confusion here. None of the lines shown in TPAW (5th, median, or 95th) are an actual trajectory. Actually trajectories in the Monte Carlo are MUCH NOISIER than these. And they go up and down past these lines. I plotted the trajectory with the 5th percentile of lifetime spending in my own spinoff recreation of TPAW’s basic algorithm, and the spending is well under the 5th percentile in some years, bounded up to the median, comes back down, etc. An actual trajectory that stuck to the 5th percentile line all along would be both worse and better than the actual noisy spending trajectory that would come if you followed your TPAW instructions for years. I know Ben has said that putting sample trajectories on the website is on the list – I’m just going to state again that I think that would be really helpful and help users not be confused about what the tool is offering in terms of spending stability.
Yes, individual trajectories would be jagged, and not smooth like the percentile lines. Surfacing individual trajectories on the graph is still on the to-do list. We are prioritizing duration matching and taxes, so won’t be able to get to it in the near future. But we understand the usefulness, and will implement it eventually.
I wanted to add to this, with some more reasons why it would be helpful to show some individual Monte Carlo trajectories, or do something else to help visualize how risky the different risk tolerances actually are.
Elsewhere in this thread, you have recommended that people discover their risk tolerance number by adjusting the risk tolerance and spending tilt sliders while looking at the spending graph, until you find the spending graph that you most prefer. The problem I’ve found with this is that, if I were to try to decide what my risk tolerance was solely by looking at the spending chart, I would conclude that my risk tolerance was the highest, 24, regardless of how risk-averse I actually am.
Here are some screenshots to illustrate why I say this. These are based on this simple test plan.
https://tpawplanner.com/link?params=dM9 … a66VJAWa6r
This is a basic plan, where the person saves until they retire at 55, then starts taking SS at 70, up to a max age of 100.
Below are screenshots of the spending graph with 3 different risk tolerances: 0, 12, and 24. Risk tolerance 0 results in a 100% bonds portfolio, and risk tolerance 24 results in a 100% stocks portfolio. For each risk tolerance level, I adjust the spending tilt to make the 5% percentile spending roughly level, to make it easy to make an apples-to-apples comparison.
Risk tolerance 0, spending tilt 0.4
Risk tolerance 12, spending tilt -0.3
Risk tolerance 24, spending tilt -2.6
Based only on the spending graphs shown above, it appears that there is almost no downside to going 100% stocks, and quite a big upside. So even if I was an extremely risk-averse person, I would conclude that I should choose risk tolerance 24, and go with 100% stocks.
I’m pretty sure though that if I could see the individual Monte Carlo trajectories, this would change my opinion. I suspect what I’d see is that with the higher risk portfolio, some of the individual trajectories would show much more wildly varying spending over the years, compared to the lower risk portfolios. A more risk-averse person would presumably be willing to trade off some of the potential upside of a risky portfolio in exchange for a greater likelihood of a more level spending trajectory.
I think it would be useful to rank the MC trajectories by some metric, and show different percentile trajectories based on that metric. A couple of ideas for how they could be ranked are
- For each trajectory, find the minimum spending in any month, and then sort the trajectories by that number. So a trajectory whose low point was $4,000 would rank lower than a trajectory whose low point was $5,000, regardless of how high the spending was in other parts of the trajectory. This one makes the most sense to me, since the main risk I’m trying to mitigate when choosing how risky my portfolio should be is the risk of having to reduce my living standard unacceptably low at some point. If I see that Risk Tolerance level 24 means 5% of the MC trajectories dipped below $X at some point, I might decide that’s too risky for me.
- Sum up the total spending for each trajectory, and sort by that.
