## Question regarding the calculation logic

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sunilsflexplanner
Posts: 2
Joined: Fri Jul 10, 2020 9:50 am

### Question regarding the calculation logic

I've been using this program for several years and find it one of more useful financial planning tools available. I ran a little experiment to understand the calculation logic better, and was confused about the results. I set up a simple set of 2 scenarios as follows:
Scenario 1:
• Current age 66, Retirement age 66, Life expectancy 95
• Inflation ave 3.0%, STD 0.0%
• Tax rates 21% and 31%
• Taxable portfolio value \$1,000,000
• Risk averse Investing style
• Income \$25,000 starting age 71, expenses \$50,000 every year
• Spending policy flexible
This scenario has a 100% success rate with a median ending value of \$590k

Scenario 2 is identical except that I enter the initial balance as an additional cash flow instead of on the main input screen. I show it as \$1M beginning and ending at Start of Plan. I expected to see a similar if not identical result (possibly shifted by a year). However, this scenario gives me a 0% success rate. The annual withdrawals are higher and the portfolio get's used up at age 88. What am I missing?

The reason for doing this was to create separate cash flows that I could tie back to the individual accounts for the assets my wife and I have. Thanks in advance for any enlightenment you can provide.
jimr
Posts: 720
Joined: Thu Feb 28, 2008 6:48 pm

### Re: Question regarding the calculation logic

The answer to your question depends on the type of cash flow you're using in additional inputs. Depending on how you do it, there are two reasons you might see a zero percent probability of success.

Case 1 - Using a "Taxable Savings" Cash flow in additional inputs.

The 0% probability you'd see in this case has to do with the order that the planner logic processes the cash flows. Logically, spending for the year is deducted from the portfolio on the first day of the year, while portfolio growth and savings are added in on the last day of the year.

This means that because the portfolio balance is zero when the logic tries to deduct the annual expenses, the plan always fails in the first year of the plan.

To correct this, you could adjust the start of plan to age 65 instead of age 66 and leave everything else as is. One snag though is that your income and expense amounts will be inflated by an extra 3% due to an extra year of inflation being taken into account (from the start moving from age 66 to 65).

Case 2 - Using a "Misc Income" cash flow (with taxes set to 0%)

In this case, the 0% probability of success results from failures later in the plan due to the way the "flexible" spending policy makes decisions about how to adjust spending as the plan progresses through the years. The flexible and conservative spending policy logic makes decisions about whether to increase or reduce spending based on the current portfolio value versus the portfolio value at retirement. In the case of using a misc income cash flow, the spending policy logic sees the portfolio value at retirement as \$0. This causes the spending policy logic to not realize that the plan isn't working because it always sees the "current portfolio value" as being much higher than the zero dollar portfolio value at retirement.

You can actually see the spending policy logic run amuck in the year-by-year detailed view tab. Here you'll see the "percent of expenses funded" blissfully get increased each year by the spending policy logic, even as the portfolio value continues to decrease.

You could go into settings and set the "maximum percent of expenses to fund" to 100% from the default of 500%, which makes the results much better, but doing this basically makes the flexible spending policy mimic the stable spending policy.
sunilsflexplanner
Posts: 2
Joined: Fri Jul 10, 2020 9:50 am

### Re: Question regarding the calculation logic

Thanks, Jim. I left the initial scenario unchanged, and modified the second per your suggestion: set start of plan at age 65, keep retirement age as 66 and have the additional cash flow at start of plan, with income and expenses starting at retirement.

The initial scenario has a median asset value at the end of year 66 of \$965,422, while the modified has a median asset value of \$965,589. That's a de minimis difference I can certainly ignore.

Just to clarify, the order of processing is:
• Income and expense are considered to occur at the beginning of the period
• Growth and savings at the end of the period
• Funding of any shortfalls
Are taxes on income and growth considered to occur when the income or growth are recognized, or always at the end of the period?

Thanks again for the help and for FRP in general - it's a great tool!
jimr
Posts: 720
Joined: Thu Feb 28, 2008 6:48 pm

### Re: Question regarding the calculation logic

sunilsflexplanner wrote: Sun Feb 28, 2021 2:28 pmAre taxes on income and growth considered to occur when the income or growth are recognized, or always at the end of the period?
I'd say they are considered to occur when the income and growth are recognized.

For income, the taxes are deducted from the gross amount and the net amount is subtracted from the planned expenses. If the after tax income is less than expenses, additional funds are withdrawn from the portfolio to make up the difference. If after tax income exceeds expenses, an extra amount is added to the taxable portfolio.

For growth, gains or losses on the portfolios are computed and taxed if appropriate and the portfolio balance is adjusted based on the net amount of the gain or loss.
Paul O
Posts: 9
Joined: Tue Oct 30, 2018 5:22 pm

### Re: Question regarding the calculation logic

I have a quick question regarding the flexible and conservative spending policies. The documentation giving several conditions and the corresponding spending adjustment that I interpret are as follows:

Balance year change: down
Relative to retirement start: smaller

Balance year change: up
Relative to retirement start: smaller

Balance year change: DOWN
Relative to retirement start: GREATER

Balance year change: up
Relative to retirement start: greater
Adjustment: increase by some COLA multiple

The documentation for the conservative spending policy documentation states "Otherwise, if the portfolio is bigger than it was at the start of retirement, some extra purchasing power that was lost in previous years is restored." The flexible spending policy does not address the situation when the yearly change in total balance decreases but the total balance is still greater than the balance at the start of retirement.

I would appreciate any clarification as to what the magnitude of the "extra purchasing power" is when the yearly change in total balance decreases but the total balance is still greater than the balance at the start of retirement.

Thank you Jim.

Paul O
jimr
Posts: 720
Joined: Thu Feb 28, 2008 6:48 pm

### Re: Question regarding the calculation logic

First, the code for the flexible and conservative spending policies is identical, except that with the conservative policy, the percent of expenses funded can't go over100%.

When I first envisioned these spending policies, I thought there would be a big difference between the flexible and conservative algorithms, with tweaks in the code between them to justify having two different spending policies.When I was testing out these algorithms, it became clear relatively early on that changes to the multipliers and thresholds in the code (see below) didn't impact the results very much at all compared to changes in the spending policy floor and the spending policy multiplier. Once I realized this I probably should have just eliminated the conservative spending policy and left Flexible and Stable to keep things simpler.

Not sure if this is helpful, but here's the code:
- adjustmentRate is the inflation rate times the spending multiplier.
- Balances are in inflation adjusted dollars

Code: Select all

``````    if ( (currentBalance < previousBalance) && (currentBalance < startBalance))
else {
if (currentBalance > startBalance) {
if (currentBalance > (2 * startBalance))
else
percentOfExpensesToFund = previousFundingPercent + (adjustmentRate / 4);
}  else
percentOfExpensesToFund = previousFundingPercent;
}
if (percentOfExpensesToFund > spendingPercentCeiling)
percentOfExpensesToFund = spendingPercentCeiling;
else if (percentOfExpensesToFund < spendingPercentFloor)
percentOfExpensesToFund = spendingPercentFloor;
``````
Paul O
Posts: 9
Joined: Tue Oct 30, 2018 5:22 pm

### Re: Question regarding the calculation logic

Thank you for the response. I believe I now understand how the code establishes the spending adjustment and incorrectly interpreted the documentation.
Paul O
Posts: 9
Joined: Tue Oct 30, 2018 5:22 pm

### Re: Question regarding the calculation logic

Jim,

After watching your recent Chicago Bogleheads presentation (excellent video for an overview of your planner capabilities), I was curious on the number of failures that you addressed. I looked at a different situation than you presented where the portfolio clearly started out too low or the spending target was set too high. I then manually conducted a sensitivity analysis reducing the return standard deviation and examined the resulting change in the average spending shortfall. For one particular run when the return standard deviation is set to zero, the portfolio balance is zero for 8 of the 14 years in retirement (e.g., zero failures for the first 6 years and 10k failures at 7 years into retirement). Based on my understanding, the average spending shortfall is 8 of 14 retirement years or a 57% spending shortfall. The planner output shows an average spending shortfall of 45% (zero return standard deviation). The average spending shortfall number of failures makes sense (looking only at summary data medians and number of failures) once the return standard deviation is greater than zero. My inquiry is why when the return standard deviation is zero does the average spending shortfall differ from my understanding of the approach that you discussed in your presentation?

Paul O
jimr
Posts: 720
Joined: Thu Feb 28, 2008 6:48 pm

### Re: Question regarding the calculation logic

Paul,

I think it'd be easiest if I could have a .frp file to investigate what might be happening.

Would it be possible to sent a file to me at info@flexibleretirementplanner.com with the numbers altered so no personal financial information is included?

Thanks,

Jim

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