Hi,

Thanks for developing such a flexible tool. I'm a bit stuck at the moment because my expected values in the detailed view aren't matching what I would expect.

In my early years of retirement, I am not withdrawing from the tax deferred or tax free accounts, so I would expect them to grow at the rate of approximately Return - Average minus Inflation - Average. For me that would be 5.2% - 2.5%, i.e. a real return of 2.7%. I am getting close to that in my first year of retirement, but the years after that it is significantly lower. Here are the numbers.

Sorry about the formatting being hard to read when this is pasted in....

Year Tax Def. Portfolio Value Real Tax Def Return Tax Free Portfolio Value Approx Tax Free Return

2019 (Age: 55-R) $2,247,286 2.62% $43,098 2.61%

2020 (Age: 56) $2,288,474 1.83% $43,888 1.83%

2021 (Age: 57) $2,329,608 1.80% $44,677 1.80%

2022 (Age: 58) $2,353,821 1.04% $45,141 1.04%

2023 (Age: 59) $2,397,197 1.84% $45,973 1.84%

The first, second, and fourth columns are directly from an export of the detailed view.

The third and fifth are columns I added to a sheet to calculate the approximate real return. i.e. end of year value minus start of year value divided by start of year value, shown as a percentage.

In the first year, the starting balance for tax deferred is $2,190,000 and tax free $42,000. i.e. these are the numbers entered in the summary view of the tool (my year 0 is the year I retire) and are not shown in the detailed view, the detailed view starts with one year later. As you can see, there are returns of around 2.6%, which is close to what is expected.

The years after that, the real returns decrease to 1.83%, then 1.80%, etc.

I even ran the numbers for a few more years than are shown above (being careful not to use a year where money is withdrawn from these accounts) and it never went above something like 2.02% real return.

Am I missing something about how these values are calculated?

I realize the tool is used as more than a calculator and actual returns are never average and the tool tries to account for that. I could see if the return was varying based on the standard deviation (mine are 15% on returns and 1% on inflation) but in that case I would expect returns to sometimes be higher than the average of 5.2% average return minus 2.5% average inflation i.e. 2.7%.

Thanks for any clarification you can provide.

Best regards.

## Returns in detailed view don't match expected values

### Re: Returns in detailed view don't match expected values

My guess is that what you're seeing is an artifact that results from reporting of median values in that table, coupled with the way these values interact with the sequence of returns chosen by the simulation through each of the 10,000 simulation iterations or paths. This effect is usually only noticeable with higher standard deviations and is usually much less pronounced when using lower returns and standard deviations.

What value are you using for standard deviation?

As a test, you might try setting the standard deviation to 0% to see if that causes the results to be more like what you expect.

If you are using a higher standard deviation, it's likely that is what's causing the portfolio values to track the way you're seeing them track. The portfolio values reported in the detailed output table are median values. That means for each year, all the portfolio values from each of the 10,000 simulation iterations are sorted and then the 5000th value is pulled from the sorted list. An interesting phenomena from this is that the median portfolio value for one year is likely to be from a completely different simulation iteration than the portfolio value of the previous year or the one chosen for the following year.

Another interesting phenomena for portfolio returns is that the median value of a variable that's growing geometrically can be very very far below the average of the lowest value and the highest value from the series. This is due to the nature of geometric growth.

To see this in action, create a new data file, set the inflation rate to 2.5%, the tax free portfolio to $42,000, the investing style to custom, the average return to 5.2, and the standard deviation to 15%. Also, zero out the annual retirement spending (we're intentionally leaving a lot of stuff out to isolate the phenomena). Next, run the simulation and hover the mouse over the right-most bar in the bar graph. You should see a pop up that shows the bottom 10% portfolio value of around $24k, the top 10% portfolio value around $400k, and the median portfolio value around $100k (note you can see this visually by clicking the show portfolio value bands checkbox). As you can see, the $100k median value is substantially below the halfway point between $24k and $400k.

Does any of this make sense? Please don't hesitate to follow up with more questions...

What value are you using for standard deviation?

As a test, you might try setting the standard deviation to 0% to see if that causes the results to be more like what you expect.

If you are using a higher standard deviation, it's likely that is what's causing the portfolio values to track the way you're seeing them track. The portfolio values reported in the detailed output table are median values. That means for each year, all the portfolio values from each of the 10,000 simulation iterations are sorted and then the 5000th value is pulled from the sorted list. An interesting phenomena from this is that the median portfolio value for one year is likely to be from a completely different simulation iteration than the portfolio value of the previous year or the one chosen for the following year.

Another interesting phenomena for portfolio returns is that the median value of a variable that's growing geometrically can be very very far below the average of the lowest value and the highest value from the series. This is due to the nature of geometric growth.

To see this in action, create a new data file, set the inflation rate to 2.5%, the tax free portfolio to $42,000, the investing style to custom, the average return to 5.2, and the standard deviation to 15%. Also, zero out the annual retirement spending (we're intentionally leaving a lot of stuff out to isolate the phenomena). Next, run the simulation and hover the mouse over the right-most bar in the bar graph. You should see a pop up that shows the bottom 10% portfolio value of around $24k, the top 10% portfolio value around $400k, and the median portfolio value around $100k (note you can see this visually by clicking the show portfolio value bands checkbox). As you can see, the $100k median value is substantially below the halfway point between $24k and $400k.

Does any of this make sense? Please don't hesitate to follow up with more questions...

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