## Prob success (# failures)

### Prob success (# failures)

Hi. I couldn't find an answer to this in the documentation. In my plan results under details in the far right column it says for example for one of the years, 100(2). Does this mean that out of 10,000 simulations, 2 ran out of money? Is 'every' line the result of 10,000 runs?

So if I have a 40 year plan and all years but the one above is 100(0), my overall prob of success would be:

[2 / (39x10,000 + 1x9,998)] = 0.000005

x100 = 0.0005% failure rate

subtracted from 100 = 99.9995% success?

Also, if my Average Spending Shortfall shown is 12% for example, does that mean that these 2 failures came up short by 12% on average? And, is that 12% short of zero dollars left, or 12% short of my Minimum Expenses to Fund limit?

I'm just trying to understand the equation used. Thanks!

BTW, you program is excellent.

So if I have a 40 year plan and all years but the one above is 100(0), my overall prob of success would be:

[2 / (39x10,000 + 1x9,998)] = 0.000005

x100 = 0.0005% failure rate

subtracted from 100 = 99.9995% success?

Also, if my Average Spending Shortfall shown is 12% for example, does that mean that these 2 failures came up short by 12% on average? And, is that 12% short of zero dollars left, or 12% short of my Minimum Expenses to Fund limit?

I'm just trying to understand the equation used. Thanks!

BTW, you program is excellent.

### Re: Prob success (# failures)

Hi,

Thanks for your kind words about the planner and for posting two great questions.

Each simulation run will iterate through all 40 years of your plan 10,000 times. So there are a total of 10k simulation runs, not 10k times number of years. So 2 failures out of 10k runs means the plan had a 9998/10000 likelihood of success or a 99.98% probability of success.

The 'number of failures' shown in that last column tells you how many times the simulation ran out of money in the year associated with the given row. In your case, there were a total of 2 failures out of 10k runs and it sounds like they both occurred in the same year. You can also graph this output by clicking the 'show failures' checkbox at the bottom of the graph.

For average spending shortfall, yes, it basically means that, on average, in the two times the simulation failed, the plan was unable to fulfill 12% of your total planned spending. The minimum expenses to fund limit isn't used in this calculation. The spending shortfall ratio is the amount not funded (assuming a 100% funding goal)/total amount of spending needed throughout your retirement (also assuming 100% funding goal).

Please post again if this didn't fully answer your questions.

Jim

Thanks for your kind words about the planner and for posting two great questions.

Each simulation run will iterate through all 40 years of your plan 10,000 times. So there are a total of 10k simulation runs, not 10k times number of years. So 2 failures out of 10k runs means the plan had a 9998/10000 likelihood of success or a 99.98% probability of success.

The 'number of failures' shown in that last column tells you how many times the simulation ran out of money in the year associated with the given row. In your case, there were a total of 2 failures out of 10k runs and it sounds like they both occurred in the same year. You can also graph this output by clicking the 'show failures' checkbox at the bottom of the graph.

For average spending shortfall, yes, it basically means that, on average, in the two times the simulation failed, the plan was unable to fulfill 12% of your total planned spending. The minimum expenses to fund limit isn't used in this calculation. The spending shortfall ratio is the amount not funded (assuming a 100% funding goal)/total amount of spending needed throughout your retirement (also assuming 100% funding goal).

Please post again if this didn't fully answer your questions.

Jim

### Re: Prob success (# failures)

Ok. Thanks for all that. I think I mostly understand now.

So in this example above, the 12% shortfall can also be thought of as making it 88% (100-12) of the way through my 40 years before a possible failure occurrs (total nestegg going below zero dollars). If I graph it by checking the box below the graph, I would see the spike(s) appearing at year 35 of 40 (40 x 0.88). If the two failures happened in different years, then the average of the two failed years would be year 35. I would not expect to see the average spike in year 25 for example. Does that sound right?

From your explanation, it sounds like the 'Probability of Success' and the 'Average Spending Shortfall' shown under it are based only on the nestegg amount (staying positve), and has nothing to do with 'Percent of Expenses Funded' staying satisfied. I think I was getting those two things mixed up.

So if I have a 100% probability of success showing in my example, I really wouldn't care too much about the 12% average spending shortfall amount, because that 12% is only a breakdown of the extremely small percentage (9998/10000) of failures present.

I have used FireCalc also, and if all are equal, my example above would show 10,000 graphed lines over 40 years with only two lines straying below the horizontal axis (zero nestegg amount). And those two lines would cross at an average year of 35. Does all this sound like I understand correctly? I really appreciate your help.

Thanks!

So in this example above, the 12% shortfall can also be thought of as making it 88% (100-12) of the way through my 40 years before a possible failure occurrs (total nestegg going below zero dollars). If I graph it by checking the box below the graph, I would see the spike(s) appearing at year 35 of 40 (40 x 0.88). If the two failures happened in different years, then the average of the two failed years would be year 35. I would not expect to see the average spike in year 25 for example. Does that sound right?

From your explanation, it sounds like the 'Probability of Success' and the 'Average Spending Shortfall' shown under it are based only on the nestegg amount (staying positve), and has nothing to do with 'Percent of Expenses Funded' staying satisfied. I think I was getting those two things mixed up.

So if I have a 100% probability of success showing in my example, I really wouldn't care too much about the 12% average spending shortfall amount, because that 12% is only a breakdown of the extremely small percentage (9998/10000) of failures present.

I have used FireCalc also, and if all are equal, my example above would show 10,000 graphed lines over 40 years with only two lines straying below the horizontal axis (zero nestegg amount). And those two lines would cross at an average year of 35. Does all this sound like I understand correctly? I really appreciate your help.

Thanks!

### Re: Prob success (# failures)

I think so. A plan with uneven or lumpy retirement cashflows could mess with those assumptions, but in general that sounds about right.Willie wrote:So in this example above, the 12% shortfall can also be thought of as making it 88% (100-12) of the way through my 40 years before a possible failure occurrs (total nestegg going below zero dollars). If I graph it by checking the box below the graph, I would see the spike(s) appearing at year 35 of 40 (40 x 0.88). If the two failures happened in different years, then the average of the two failed years would be year 35. I would not expect to see the average spike in year 25 for example. Does that sound right?

Yes. Technically I could have adjusted the total unfulfilled spending in failure cases by the spending floor, but I didn't do it that way. In general, the shortfall percent is most useful as a relative measure to use for comparing two different retirement scenarios.From your explanation, it sounds like the 'Probability of Success' and the 'Average Spending Shortfall' shown under it are based only on the nestegg amount (staying positve), and has nothing to do with 'Percent of Expenses Funded' staying satisfied.

For example, you might have two scenarios that both have a 90% probability of success. However, one may have a spending shortfall of 15%, while the other has a spending shortfall of 35%. Plans with lumpy cash flows are particularly susceptible to this. Say for instance, one variation of your plan is to sell a larger home at age 75 and move to a less expensive condo. To model this, you add the difference in home prices to your portfolio at age 75. In this case, you may have some failures at age 73-74, but none after that until near the end of the plan. Spending shortfall should capture this difference in robustness when comparing this case to one where all the failures are close to the end of the plan.

I have used FireCalc also, and if all are equal, my example above would show 10,000 graphed lines over 40 years with only two lines straying below the horizontal axis (zero nestegg amount). And those two lines would cross at an average year of 35. Does all this sound like I understand correctly?[/quote]So if I have a 100% probability of success showing in my example, I really wouldn't care too much about the 12% average spending shortfall amount, because that 12% is only a breakdown of the extremely small percentage (9998/10000) of failures present.

Yes. That sounds about right.

### Re: Prob success (# failures)

Thanks Jim for all your usefull feedback. I tried applying this to my actual plan and the numbers aren't working.

Retirement age 56

End of plan 100

Stable scenario expenses are $45000/yr (doesn't change)

100% prob of success

6% shortfall

100(1) at 83

100(3) at 99

So 44 years in retirement = 44x45000 = $1,980,000 total to fund

1 failure at 83 = 100-83 = 17 years unfunded x 45000/yr = $765000 unfunded

3 failures at 99 = 100-99 = 1 x 3 x 45000/yr = $135000 unfunded

Total unfunded = $900,000.

divide by 4 failures = $225000 average unfunded.

Shortfall then = 225000/1980000 = 0.1136 or 11%

You mentioned that a plan with uneven or lumpy retirement cashflows could influence this number. By cashflow are you referring to retiement income and expenses or just expenses? If it includes income then that's probably where the discrepancy is.

Thanks.

Retirement age 56

End of plan 100

Stable scenario expenses are $45000/yr (doesn't change)

100% prob of success

6% shortfall

100(1) at 83

100(3) at 99

So 44 years in retirement = 44x45000 = $1,980,000 total to fund

1 failure at 83 = 100-83 = 17 years unfunded x 45000/yr = $765000 unfunded

3 failures at 99 = 100-99 = 1 x 3 x 45000/yr = $135000 unfunded

Total unfunded = $900,000.

divide by 4 failures = $225000 average unfunded.

Shortfall then = 225000/1980000 = 0.1136 or 11%

You mentioned that a plan with uneven or lumpy retirement cashflows could influence this number. By cashflow are you referring to retiement income and expenses or just expenses? If it includes income then that's probably where the discrepancy is.

Thanks.

### Re: Prob success (# failures)

The situation can occur when net retirement withdrawals are not steady from year to year. Even with steady expenses, if you have lumpy or uneven retirement income in your plan, that could make your portfolio withdrawals uneven, and may account for what you're seeing.Willie wrote:By cashflow are you referring to retiement income and expenses or just expenses? If it includes income then that's probably where the discrepancy is.

Jim

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