I wrote a Monte Carlo model to analysis how much money I should save before I can retire at 40 with a peace of mind. More exactly, the model shows me under a number of various macro and micro circumstances, what's the probability the money pile can survive me and my wife. It's a rigid statistical test of whether a certain amount of retirement fund balance is enough to support a happy early retirement life.
I'm making my model around the following key assumptions:
Assumption #1: I'll retire by the age of 40 by $1,000,000.
This is the goal I stated in the Backgrounder post of the site.
Assumption #2: For every retired year, I need to withdraw $45,000 every year in Year 2003 dollars (adjusted for inflation every year).
$45,000 is 100% of my estimated 2003 household expenses (everything from rent, grocery, entertainment, appliances, mortgage interest, etc., excluding one-time items like house-buying for 2003) so it is a safe bet. I assume 2% inflation from now to my retirement year, so it's around $59,000 in my first retirement year. Inflation rate after my retirement is part of Assumption #5.
Assumption #3: My life expectancy is a normal distribution of N(75,5). Same for my wife.
This is to say each of us has a 95% probability to live to an age within 65 to 85, which is a fair estimate.
Assumption #4: If one of us dies, we can expect to reduce annual withdrawal to 75% as before.
Assumption #5: Annual inflation rate will be a normal distribution N(4.43%,2.97%).
This is based on US inflation history since 1950. (Details)
Assumption #6: The market-average annual pre-tax return for a conservative strategy (like balanced portfolio strongly favoring fixed income) can deliver an above-inflation return as a normal distribution N(5.00%,3.00%).
Assumption #7: I can beat the market-average return by a margin of normal distribution of N(2.00%,5.00%).
Assumption #8: All capital gains will be taxed at an average rate of 10%.
10% is a fair assumption because I anticipate the capital gains will be taxed at 15% for long-term capital gain in brokerage firms, 0% for Roth IRA and up to 15% for 401(k). It also implies that capital gains will be taxed immediately each year, which is conservative. Also, there is reason to believe I don't have to pay capital gain tax if I live in China as a non-resident alien.
Assumption #9: If my return rate is below inflation in a certain year, I can reduce my withdrawal by 35% (in the first five years after retirement) and by 15% (after the first five years after retirement) by seeking some job income and by cutting discretionary expenses or in the same year.
Assumption #10: Exchange rate between USD and RMB is stable or the risk can be cheaply hedged.
Assumption #11: There will be no other income except for withdrawals and potential job income in the first 5 years after retirement (Assumption #9).
I'm using @Risk software from Palisade to conduct the stress test. The result:
- 80% chance I can live only by the withdrawals without any problem.
- 90% chance the plan will work for 27 to 43 years, although I need to take withdrawal cut (Assumption #9) between 2 to 9 years.
I'm very satisfied with the result, especially the fact that the plan works 80% of the time. With all conservative assumptions, I firmly believe $1,000,000 by 2016 (when I am 40) should lead to a comfortable and risk-free retirement life.