Dear Jim and FRP users,

I'm very new to all this but find this program to be an amazing, one-of-a-kind tool to run detailed financial simulations without digging into

the Monte Carlo methodology.

I did a very simple setup and don't really understand the results. I set a 65 yr old user to retire at 65 with a $1,000 taxable portfolio, chose the moderate risk portfolio, (8.0 % with 9.9% SD). I made spending stable at 1 dollar per year and retirement income at 1 dollar per year, and ended the plan at 95 (30 year run). Inflation was 0.

So I copied the 10%, median and 90% portfolio values into excel for each year and then back-calculated the annual return for each year (from the year before) for 10, 50 and 90 percentile. I figured this would give me 30 samples of the 10, 50 and 90% annual returns.

My problem is I don't understand why the average of the median portfolio growth is 6.5 percent when FRP says it was sampling 8% with 9.9% SD.

I'm sure I have done something stupid, or I don't understand how the program works (I understand it is monte carlo...i.e. not every return is a constant, but why isn't the mean return of median portfolio not centered around 8% ?).

Here's more of the data:

median Portfolio annual returns (31 years): 6.0% - 6.9 % mean of 6.5%

10 percentile portfolio ann. returns (31 yr): -4.3% to 6.1 % mean of 4.5 %

90 percentil portfolio ann. returns : 7.1% to 17.3 % mean of 8.4 %

I'm running the downloaded version of the program if that matters.

I look forward to learning from you guys, and hope this isn't too big a waste of your time.

Thanks for any insights !

Lindsay Hough

## FRP mechanics and returns

### Re: FRP mechanics and returns *taxes*

I'm still looking at this question... so even though income and expenses were $1 / year, taxes were not zeroed out. When I give 0 income and investment tax rates, my median return on an "8%" return portfolio is 7.6 % - much closer ! Like I said - this is a learning curve for me.

Any other thoughts or comments would be appreciated. Lindsay

Any other thoughts or comments would be appreciated. Lindsay

### Re: FRP mechanics and returns * SD *

Well - when I remove the standard deviation and run a custom 8.0% return on the above portfolio I get 8% return every year - on the nose.

So there are two things I would like to understand about the program at this point:

1) when I say my age is 65 and retirement starts at 65 my portfolio of 1,000 has one year's return in it. so the program starts at the first of year of 65 and the value in the table for that year are end-of-year values ?

2) I'm not sure I understand why 8.0% with SD=9.9% gives average of 7.6% but with SD=0 gives 8.0 %. Maybe I won't be able to understand the answer.

Thanks for any assistance. Lindsa

So there are two things I would like to understand about the program at this point:

1) when I say my age is 65 and retirement starts at 65 my portfolio of 1,000 has one year's return in it. so the program starts at the first of year of 65 and the value in the table for that year are end-of-year values ?

2) I'm not sure I understand why 8.0% with SD=9.9% gives average of 7.6% but with SD=0 gives 8.0 %. Maybe I won't be able to understand the answer.

Thanks for any assistance. Lindsa

### Re: FRP mechanics and returns

For question1, if I understand the question, the answer is yes. Logically, the simulation does portfolio withdrawals at the beginning of the year and then computes portfolio returns at the end of the year.

For question 2, from what you describe I'd guess the confusion has to do with the difference between average return and geometric return. Geometric return takes into account the sequencing of portfolio returns and measures the average rate of portfolio growth rather than simply averaging the year-to-year rate of return. The basic concept is that if you have a return of -50% followed by a return of +50%, you'll get an average return of 0%, but the geometric return will be -25%. The initial 50% loss has a much bigger impact on the value of the portfolio than the 50% gain that follows.

If you click the "show all runs" button, there's a table that shows the average return and the geometric return for each run.

For question 2, from what you describe I'd guess the confusion has to do with the difference between average return and geometric return. Geometric return takes into account the sequencing of portfolio returns and measures the average rate of portfolio growth rather than simply averaging the year-to-year rate of return. The basic concept is that if you have a return of -50% followed by a return of +50%, you'll get an average return of 0%, but the geometric return will be -25%. The initial 50% loss has a much bigger impact on the value of the portfolio than the 50% gain that follows.

If you click the "show all runs" button, there's a table that shows the average return and the geometric return for each run.

### Re: FRP mechanics and returns

Thank you Jim - A little late getting back to this but your answer helped a lot understanding the (BIG) difference between geometric and arithmetic returns. In the popular press we hear a lot about how a 'balanced' portfolio would have an 8% average return. But to a layman, we might think that is what you would expect if you averaged 30 different one-yr returns. Now it seems clear to me that when you say portfolio X has an average annual return of 8%, it means that over the lifetime of the investment the ending value is equivalent to 8% every year ---- the geometric mean. If I understand this correctly, a portfolio with an average return of 8% and some standard deviation will give a geometric mean return (over the retirement lifetime) within the mean and SD. So I should be able to calculate the geometric return from each year's return and see how it stacks up. If this is too technical (or incorrect) feel free to take it down !

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