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Quantum physicist explains the surprising arithmetic of FIRE

Quantum physicist explains the surprising arithmetic of FIRE


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This article was posted January 1, 2023.

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I recently came across the writings of a fellow member of the FIRE Class of 1994 on Quora.com -- quantum physicist w.w. Lenzo. Dr. Lenzo earned a PhD in Quantum Physics from Stanford in 1990, worked for an industrial company in Japan for 37 months, and accumulated a retirement nest egg of $125,000 over that period of time. He then retired in 1994 at age 33 on the assumption that he could live on $1,000/month and that his retirement expenses would decline over time as he became more cost efficient in his spending. Certainly a 9.6% initial annual retirement withdrawal rate from a 100% stock portfolio is a bold plan, but he lives in Canada, so US health care price gouging isn't a retirement issue.

Dr. Lenzo's study of Quantum Mechanics no doubt informs his view of investment risk (i.e., we can't know the future, and even our perception of the present may be in question (see Schrödinger's cat)). You can't live your life in fear. There's no amount of money you can save that eliminates all risk.

With that assumption in mind, Dr Lenzo advises, "estimate your retired monthly needs and multiply by 125. Invest it directly in twenty diverse stocks. It's good, of course, to have a little more than the bare minimum, perhaps up to double. Beyond that, in all honesty, you are fooling yourself." A retirement nestegg of 125 times monthly expenses is a 9.6% annual withdrawal rate, 250 times is a 4.8% withdrawal. Even the upper bound is a large discount to the 25 years' worth of living expenses implied by "the 4% rule".

Is Dr. Lenzo's approach for you?

Your spending is likely to decline in retirement?

Based on his then 27 years of early retirement living on a lakefront property about 20 miles South of Saskatoon, Saskatchewan, Canada, Dr Lenzo reports that spending in retirement can be much less than what you spent during your working years for the same quality of life.

In retirement, you're not going to need to dry clean your work attire. Without the demands of a job, you'll have more time to cook meals at home rather than opt for frequent meals at a restaurant. You'll have more time to shop for better prices. If you're good with hand tools, maybe you can fix things yourself rather than call a repair technician. The list goes on, it's entirely possible that retirement spending could be half what your living expenses were while working.

Also, if you're living on a lake in Canada's boreal forest, you won't have the grocery or fuel bills of a city dweller. You can cut and store firewood for the winter, and there's fish in the lake and large game (moose, deer, and bear) for the hunting. Plus on a low monthly income, you're Canadian health insurance premiums (in the form of taxation) are no doubt reasonable.

How safe is a 9.6% withdrawal rate from a 100% stock portfolio?

It isn't -- 1994 was a magical year to begin your early retirement. Over the next 6 years, the S&P 500 grew by 200% and the NASDAQ by 400%. Depending on how you were invested, you likely had 2 to 5 times your 1994 starting balance when the dot.com bubble burst in 2000 and the stock market suffered 50%+ declines. Life would be very different for the year 2000 early retiree adopting the same strategy with a 100% stock portfolio on the eve of a big stock market decline. The table below compares the survivability and portfolio balances for 100% stock and 60%/40%, stock/bond asset allocations for both 1994 and 2000 start dates at various withdrawal rates.

Retirement Portfolio Survivability
($100,000 starting balance, inflation-adjusted annual withdrawal)
Asset
Allocation
Note (1)
Starting
Year
Initial Annual
Withdrawal
Rate
Note (2)
Starting Balance Year End 2021
Balance
100% Stock 1994 10% $100,000 $0 (Busted in 2017)
60/40 1994 10% $100,000 $0 (Busted in 2012)
100% Stock 1994 8% $100,000 $189,562
60/40 1994 8% $100,000 $12,644
100% Stock 1994 6% $100,000 $470,555
60/40 1994 6% $100,000 $234,670
100% Stock 1994 4% $100,000 $751,547
60/40 1994 4% $100,000 $456,496
100% Stock 1994 2% $100,000 $1,032,530
60/40 1994 2% $100,000 $678,322
100% Stock 1994 1% $100,000 $1,173,835
60/40 1994 1% $100,000 $789,236
100% Stock 2000 10% $100,000 $0 (Busted in 2006)
60/40 2000 10% $100,000 $0 (Busted in 2008)
100% Stock 2000 8% $100,000 $0 (Busted in 2008)
60/40 2000 8% $100,000 $0 (Busted in 2011)
100% Stock 2000 6% $100,000 $0 (Busted in 2011)
60/40 2000 6% $100,000 $0 (Busted in 2017)
100% Stock 2000 4% $100,000 $25,682
60/40 2000 4% $100,000 $94,819
100% Stock 2000 2% $100,000 $200,326
60/40 2000 2% $100,000 $236,010
100% Stock 2000 1% $100,000 $287,649
60/40 2000 1% $100,000 $305,606

Note (1) -- 100% stock Vanguard's VFINX, 60% stock/40% bond VBINX

Note (2) -- Annual withdrawal as a percent of initial portfolio balance, with initial dollar
amount indexed for inflation in subsequent years.


What to conclude from these results?

Everyone has a different view of investment risk, but hopefully it's an informed view.

The "4% rule" is simply a description of the maximum, inflation-adjusted withdrawal rate that survived all 30-year payout periods examined for a given asset allocation. You can assume things will be better or worse in the future, but a useful check would be to investigate how your retirement plan would have performed in the past. As the table above demonstrates, a retiree taking a 9.6% withdrawal from a 100% stock portfolio in 1994 would likely need to appreciably reduce his annual withdrawal to survive a 30-year pay out period.

One thing that appealed to me when I investigated William P. Bengen's method using a larger data set from Yale economist Robert Shiller was the distribution of the terminal value of the portfolio after 30 years. As you can see from the table below, in 95% of the one hundred 30-year payout periods examined you ended that 30 year period with a higher balance than you started -- a higher balance despite 30 years of annual withdrawals. There's about a 50/50 chance you'll have 4X your starting balance and a 10% chance you'll end 30 years with nearly 8X. As long as you don't happen to retire on the eve of the next Crash of 1929 and the Great Depression, there's a good chance that the 4% rule will make you rich.



Retire Early Safe Withdrawal Study - (1871-2000)
Pay Out Period 10 Yrs 20 Yrs 30 Yrs 40 Yrs 50 Yrs 60 Yrs
Optimal Stock Allocation 48% 66% 74% 77% 82% 85%
Investment Expenses 0.20% 0.20% 0.20% 0.20% 0.20% 0.20%
Inflation Index PPI PPI PPI PPI PPI PPI
Max. Initial Inflation Adjusted
Withdrawal Rate
8.47% 4.78% 3.81% 3.54% 3.35% 3.24%
Survivability 100% 100% 100% 100% 100% 100%
Pay Out Periods
Examined
120 110 100 90 80 70
Terminal Values (Initial Portfolio Value = $1,000)
Max $ 1,826 $ 8,301 $ 11,133 $ 38,759 $ 181,388 $ 231,174
95% $ 1,416 $ 4,477 $ 8,836 $ 29,080 $ 118,388 $ 184,882
90% $ 1,277 $ 3,465 $ 7,834 $ 24,664 $ 75,186 $ 120,288
75% $ 970 $ 2,055 $ 5,403 $ 18,738 $ 39,217 $ 78,830
Median $ 690 $ 1,509 $ 3,977 $ 7,777 $ 16,434 $ 42,697
25% $ 440 $ 1,050 $ 2,591 $ 5,132 $ 10,833 $ 23,898
10% $ 181 $ 702 $ 1,607 $ 2,856 $ 9,099 $ 16,609
5% $ 79 $ 493 $ 1,313 $ 2,465 $ 6,311 $ 13,926
Min $ 0 $ 1 $ 1 $ 44 $ 9 $ 27


Resources for more information

How much do you really need to retire?, Quora.com post from w.w. Lenzo Ph.D Quantum Physics, Stanford University 1990

Life Expectancy vs. Income in the United States -- Opportunity Insights Harvard University

PortfolioCharts.com - site that shows lowest cost ETF/mutual fund choices for a retirement portfolio

Bengen, William P, Determining Withdrawal Rates Using Historical Data, Journal of Financial Planning, October 1994, pp 171-180, Volume 7, Number 4.

Investment Company Factbook 2019, ICI.org

You�ll Spend Less As You Age -- Time Magazine, Feb 26, 2014


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