# SWR - Amortize your portfolio

#### RgrGd

One way to look at the question of SWRs, asset allocation, how much do I need to get all FIRE'd up and stuff like that is to break the problem down into simple pieces, understand the basic mechanisms, then add complexity and real world considerations. The tool for doing this is the formula used to determine the periodic payment for a loan or an investment: PMT(principal, rate, term), where (in this case) principal is the portfolio value in \$; rate is the net rate of return in decimal form, i.e., 0.05; term is the length of time in years. The formula can be found on the Excel spreadsheet under Tools, Easy Calc, Other, Financial. The net rate of return is the average portfolio return minus the average inflation rate, both on a yearly basis. For this illustration, principal and PMT are expressed in thousands of dollars; to relate to a portfolio of, say one million, multiply results by 1000, a pay out of 50 is \$50,000.

Very important consideration; the term is the point where the principal is zero. If you want your investment to last 40 years, the term is 40. If you want something left at 40 years, make the term much larger.

Let's determine several initial payout amounts 'payments'. In all cases principal = 1000 and term = 40.

Rate = 0; PMT(1000,0,40) = 25. So for a million \$ portfolio, the initial payout is \$25,000. This is the case for either zero rate of return and zero inflation or equal rates for both. We can check this because 1000/40 = 25.

100% bond case; coupon = 0.05, inflation = 0.03, rate = 0.02 (the difference), PMT = 36.6. Note here that we are not taking all the coupon amount, the inflation part must be re-invested for the yearly payment increase at the 3% inflation rate.

100% equity case: For the years 1941-2006, the DJIA was 0.086, inflation was 0.041, rate = 0.045, PMT = 54.3.

60/40 equity/bond ratio case: PMT is 60% up from the difference, (54.3-36.6)*0.6 = 10.6. PMT = 36.6+10.6 = 47.2. LAB (Lo And Behold), this 47.2/1000 = 4.72% is within the 4 to 5 percent initial SWR currently in vogue.

In those cases where you are re-investing the inflation part; if you look at the balance over time, it will increase for roughly half the term, then fall to zero. The excess balance is the inflation part compounding to pay for future 'inflated' payments. Remember this in the real world, if you are concerned about conserving spending power, don't eat up an increasing portfolio balance indiscriminately. Part of that MAY be market return (which is fair game), but part IS banked inflation monies.

Also, if you can express the advantages of re-balancing, for example, in terms of improved portfolio return, you can judge whether it is worth it or not. You can easily evaluate any scheme that improves, or not, portfolio return and see the effect on SWR.

So the question of how much one needs to FIRE can be estimated. If your portfolio in one million, time span, 40 years, your return is 4.5% above inflation, bonds at 5% with a 60/40 mis and you can live with \$47.2K/yr adjusted for inflation, go for it. Adjust the numbers for your case. Change the term value for different time spans.

So you do it! At the end of the year, you re-do the calculation (do I have to go back to work?). The differences are: principal is your new portfolio balance and term is one year less (in this case 39). PMT will tell you the inflation adjusted amount to take out, assuming the rate is still valid. It turns out the precise rate value is not critical in the short term. PMT is self-adjusting, if you take out too much one year, the balance will decrease calling for a lower PMT the following year. The one year difference between, say, 4 and 5 % payout is meaningless when you can be slammed with a 20% market jerk in either direction. An updated averaged rate difference between your portfolio return and inflation is more mathematically correct, but probably not worth the trouble. Being as accurate as you can is important, it does have an effect on the payout spread.

So every year we re-do the calculation. All we need is the updated portfolio balance for principal and to reduce term by one year. The advantage of all this is that (1) it deals with you portfolio performance and time periods, (2) it gives you every year the best payout advice taking into account all the variables. It does not predict future market performance, but it does know that the end of term, you want to have spent down the portfolio balance. This payout advice is bases on the most likely future, i.e., your average return over inflation from the most current balance and time to go, and not a worst case. It also gives flexibility if you want to vary the payout, maybe take more up front and less when you are older. Every year you get an update and can judge the 'damages'. In the testing I have done so far, it is amazing how much you can ask of the portfolio without it going belly-up. Part of that is because we are not asking for anything left after the 'party'. Even with no portfolio return and 3% inflation (rate = -0.03), the initial payout is 12.6; not much, but it increases 3 % every year for 40 years.

As an example, I took the 1996-2005 time period using the DJIA as the portfolio. Avg. market return = 0.074, avg. inflation = 0.047, giving a rate of 0.027. However, I used the 0.045 rate in the PMT formula. This was a time period where in the 1st year, the market dropped 19%, in the 4th year, 15% and the 8&(th years 17 and 28%, with only two +15% years in between. For the 16 years between 1966 and 1981, the market return was 0.0075 (nearly flat), inflation was 0.068. The initial rate was, as calculated, 54.3 (100% stocks). This time period also included the good years from 1995-1997 as well as the bad ones 2000-2002. The initial run was made using the calculated payouts every year. The results: total payout \$ = 2321 (2.3 million from a 1 million start). There were 4 years with payouts less than 25 and 7 years with payouts over 100. To test changes, I added 10 to each yearly payout for the 5 years 2-6 (from roughly 40 to 50). Further, I set a minimum (floor) payout of 25. The results: total payout \$ = 2142, 8 years at the 25 cutoff and 6 years with payouts over 100.

I didn't wade through all of your post but I beleive that you have forgotten about portfolio volatility.

Yes if the world stays flat as it now is and interest rates, inflation and stocks neither really take off or nosedive then you can model it as you did.

However what if after being retired for 5 years we do a 1970's style stagflation. Just how long would your now much lower portfolio last. That would be a real bummer if you spend all of your money by the time you hit 70 years old !

http://www.efficientfrontier.com/ef/998/hell.htm

The thing about Firecalc is that using historical data you can test run a withdrawal scheme and hopefully never go broke.

Masterblaster said:
I beleive that you have forgotten about portfolio volatility.

Yes if the world stays flat as it now is and interest rates, inflation and stocks neither really take off or nosedive then you can model it as you did.

Exactly. It mystifies me when someone does calculations based on future average investment returns and future average inflation. Only if the future numbers hover closely around the mean (very low variation) will there be any accuracy. If the historically typical wide swings take place, then calcualtions based on averages will be very inaccurate, even if the wide swings turn out to average exactly what was projected.

Actually this method reminds me of the fixed percentage WD method.  This amortize method has the advantage of taking life expectancy into account in determining each year's WD.  However the problem as written is you are not updating your life expectancy as you get older, instead you are always using the initial life expectancy.

At first I also thought using an average real ROR in the calculation was a problem but upon further considersation I realized that using that average would moderate  the fluctuations in yearly WD brought about by the change in portfolio value.  Another reason the average ROR is appropriate is that this method is amortizing the portfolio over a long period of time.  The portfolio volatility is taken into account by the actual portfolio volatility since you recalculate every year with the actual portfolio value.

This method does have the advantage that if your portfolio starts to drop your annual WDs drop as well thus limiting the risk that you will exhaust your portfolio. However this method also appears to allow large changes in your yearly WDs which in and of itself might be a problem.

drigooch, you state that you ran an example
drigooch said:
As an example, I took the 1996-2005 time period using the DJIA as the portfolio.  Avg. market return = 0.074, avg. inflation = 0.047, giving a rate of 0.027.  However, I used the 0.045 rate in the PMT formula.  This was a time period where in the 1st year, the market dropped 19%, in the 4th year, 15% and the 8&(th years 17 and 28%, with only two +15% years in between. For the 16 years between 1966 and 1981, the market return was 0.0075 (nearly flat), inflation was 0.068.  The initial rate was, as calculated, 54.3 (100% stocks).  This time period also included the good years from 1995-1997 as well as the bad ones 2000-2002.  The initial run was made using the calculated payouts every year.  The results: total payout \$ = 2321 (2.3 million from a 1 million start).  There were 4 years with payouts less than 25 and 7 years with payouts over 100.  To test changes, I added 10 to each yearly payout for the 5 years 2-6 (from roughly 40 to 50).  Further, I set a minimum (floor) payout of 25.  The results:  total payout \$ = 2142, 8 years at the 25 cutoff and 6 years with payouts over 100.

I would be interested in seeing the input data used and the WDs on a yearly basis.  BTW I hope that your stated time frame of "1996-2005" was a typo and the actual period was 30 - 40 yrs long

On the life expectancy issue: I was assuming someone retiring at 60 & would live a max of 40 years. Pick your own #. I think you should pick the max. year and not change it.
On the large changes in WDs: The formula calculates the 'best' WD each year. You are free to change it (within reason). I would think that in real life if your portfolio has been battered for several years, you could set a high floor knowing the odds were high that reversion to the mean was forthcoming. In the example I used, it took 8 years for this to happen, but hopefully the 70s won't return. This method assures the portfolio will last to the end, no more, no less. If WDs come out in spurts, you don't have to spend it all; re-balance 'off campus'?

The DJIA data used from 1966-2005 are: -19, 15, 4, -15, 5, 6, 15, -17, -28, 38, 18, -17, -3, 4, 15, -9, 20, 20, -4, 28, 23, 2, 12, 27, -4, 20, 4, 14, 2, 33, 26, 23, 16, 25, -6, -7, -17, 25, 3, -1, 16.

The yearly WDs, without added changes: 54.3, 41.5, 45.9, 45.6, 36.6, 36.8, 37.4, 41.3, 32.3, 21.7, 24.0, 33.0, 25.8, 23.8, 23.7, 26.2, 22.6, 26.2, 30.4, 27.7, 34.4, 41.0, 40.0, 43.1, 53.2, 48.5, 56.3, 56.0, 61.7, 60.1, 78.5, 96.9, 116.6, 131.6, 162.5, 142.4, 122.4, 88.0, 114.5, 111.2

drigooch said:

I'll give you 10 shots a side. (Very rarely I would do that sight unseen. But in your case I'll make an exception).

Holy Mackeral

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