Investing Roadmap Part 2: How much do you need to retire?

In my previous post, I spoke about having goals for investing. My goals fall into the second category, Investing to achieve some target and/or goal, and that goal is to not have to work.

Now, most people don’t want to work. Given the choice, I would rather sit on my balcony all day sipping an espresso reading books, researching companies, or in the living room watching a good film. However, work is a reality of life: we have to pay the bills somehow (how will I buy the espresso?). So, to be able to get to the point where I don’t have to work to make money, I need to have some inflow of cash which handles all of my regular expenses. This is a fairly mechanical exercise:

1. Identify your monthly expenses, and multiply by 12 to annualize
2. Add in any annual expenses (e.g. property tax on your residence, if you own a home)
3. Add inflation up to the point that you wish to retire
4. Factor in personal taxes

After the four steps above, you’ll have your required annual pre-tax income for when you wish to stop working.  Here is an example:

 Monthly Expenses Rent \$1,500.00 Groceries \$300.00 Entertainment \$400.00 Insurance \$100.00 Utilities \$200.00 Transportation \$200.00 Pet care \$75.00 Mobile phone \$85.00 Internet \$50.00 Netflix / TV \$10.00 Computer / Technology \$100.00 Maintenance Fees \$350.00 Emergency Funds \$200.00 Total Monthly \$3,570.00 Annualized \$42,840.00 Annual Expenses Vacation \$5,000.00 Property Taxes \$3,000.00 Total Annual Expenses \$8,000.00 Total Expenses \$50,840.00 Implied Tax Rate 40% Total Annual (Gross) \$84,733.33

From the example above, if I were to stop working today, I would need ~\$84.7M (\$M=000) in annual income to maintain my current lifestyle.

However, there is a small wrinkle in that this is in today’s dollars, and we need to factor in inflation (step #3 above).  For example, if we assume 2% inflation (i.e. on average costs will go up 2% next year), our pre-tax income shoots up to ~\$86.4M.  And to further complicate things, inflation is an unknown: we don’t know what inflation will be.  Say for example I wish to stop working in 10 years, in 2025.  What inflation rate do I use for 2016, 2017, 2018, etc.?

My own workplace uses a 2.25% inflation assumption for each year.  I would prefer to account for some variability, and one way to account for this variability is to run a simulation, using a range of acceptable inflation values.  Specifically, a Monte Carlo simulation, wherein I have run 100,000 trials using an inflation assumption of 2.25% +/- 1.00% per year for the next 27 years.  One iteration of the simulation gives results such as the following:

 Year Pre-tax income (Jan 1) Inflation Assumption Pre-tax income (Dec 31) 2015 \$85,000 3.21% \$87,729 2016 \$87,729 3.13% \$90,474 2017 \$90,474 2.68% \$92,899 2018 \$92,899 1.29% \$94,098 2019 \$94,098 1.89% \$95,876 2020 \$95,876 2.56% \$98,330 2021 \$98,330 2.13% \$100,425 2022 \$100,425 2.67% \$103,106 2023 \$103,106 3.15% \$106,354 2024 \$106,354 1.39% \$107,832 2025 \$107,832 1.87% \$109,849 2026 \$109,849 1.93% \$111,969 2027 \$111,969 2.64% \$114,925 2028 \$114,925 1.67% \$116,844 2029 \$116,844 2.60% \$119,882 2030 \$119,882 3.24% \$123,766 2031 \$123,766 2.79% \$127,219 2032 \$127,219 2.88% \$130,883 2033 \$130,883 1.88% \$133,344 2034 \$133,344 1.91% \$135,891 2035 \$135,891 1.79% \$138,323 2036 \$138,323 2.36% \$141,588 2037 \$141,588 2.85% \$145,623 2038 \$145,623 2.85% \$149,773 2039 \$149,773 2.67% \$153,772 2040 \$153,772 2.89% \$158,216 2041 \$158,216 2.17% \$161,649

As you can see, by the time we hit 2041, to live at my current lifestyle, I would require \$158.2M in annual income.  The inflation also bounces around a lot, as each year the inflation is estimates to be somewhere between 1.25% and 3.25%.

Now, if we run this simulation 100,000 times, we get the following for the required income in 2041 (only first 10 entries shown):

 Sequence # 2041 pre-tax income 1 \$158,216.33 2 \$160,945.75 3 \$142,668.57 4 \$160,712.46 5 \$160,133.85 6 \$160,235.08 7 \$146,449.32 8 \$150,616.91 9 \$161,482.05 10 \$152,456.35

But, what do we do with those numbers?  The answers is to perform some statistical analysis on each year, and come up with what we feel is a reliable number.  If we focus on 2041 as our example, here is the histogram:

For the above, we have a median required income of \$154,922.16, and a mean income of \$154,991.19.  However, the median and mean are the mid-point and average required incomes respectively.  Whilst the median is \$154,992.16, there is a chance that it will be above that.  What I am interested in is the required income with a certain level of confidence.  If we do some more analysis on the histogram, we can break up all of the salary ranges into buckets, and from there interpolate the expected required income in 2041 with 95% confidence:

 Bucket # Low High Count Cumulative Probability 1 \$134,510.51 \$135,685.09 1 0.0010% 2 \$135,685.09 \$136,859.67 0 0.0010% 3 \$136,859.67 \$138,034.25 1 0.0020% 4 \$138,034.25 \$139,208.83 6 0.0080% 5 \$139,208.83 \$140,383.41 12 0.0200% 6 \$140,383.41 \$141,557.99 55 0.0750% 7 \$141,557.99 \$142,732.57 156 0.2310% 8 \$142,732.57 \$143,907.15 338 0.5690% 9 \$143,907.15 \$145,081.73 682 1.2510% 10 \$145,081.73 \$146,256.31 1296 2.5470% 11 \$146,256.31 \$147,430.89 2098 4.6450% 12 \$147,430.89 \$148,605.47 3325 7.9700% 13 \$148,605.47 \$149,780.05 4653 12.6230% 14 \$149,780.05 \$150,954.63 6419 19.0420% 15 \$150,954.63 \$152,129.21 8000 27.0420% 16 \$152,129.21 \$153,303.79 9048 36.0900% 17 \$153,303.79 \$154,478.37 10070 46.1600% 18 \$154,478.37 \$155,652.94 10061 56.2210% 19 \$155,652.94 \$156,827.52 9678 65.8990% 20 \$156,827.52 \$158,002.10 8773 74.6720% 21 \$158,002.10 \$159,176.68 7376 82.0480% 22 \$159,176.68 \$160,351.26 5833 87.8810% 23 \$160,351.26 \$161,525.84 4249 92.1300% 24 \$161,525.84 \$162,700.42 3006 95.1360% 25 \$162,700.42 \$163,875.00 2057 97.1930% 26 \$163,875.00 \$165,049.58 1224 98.4170% 27 \$165,049.58 \$166,224.16 721 99.1380% 28 \$166,224.16 \$167,398.74 453 99.5910% 29 \$167,398.74 \$168,573.32 214 99.8050% 30 \$168,573.32 \$169,747.90 126 99.9310% 31 \$169,747.90 \$170,922.48 43 99.9740% 32 \$170,922.48 \$172,097.06 14 99.9880% 33 \$172,097.06 \$173,271.64 7 99.9950% 34 \$173,271.64 \$174,446.22 5 100.0000% 100000 100.0000%

Based on the above, our required income, at 95% confidence, is \$162,647.28.  In other words, I can say with a degree of confidence that my required income in 2041 will always be at, or less than, \$162,647.28; put another way: there is only a 5% chance that I will need more than \$162,647.28 in annual income to live comfortably in 2041.

However, that is only for the year 2041.  It would be nice to see a bunch of years, say, from 2026 to 2041.  I won’t display all of the histograms and such, but here is the summary table:

 Year Income Required at 95% confidence Mean Income Required Median Income Required 2026 \$114,667.71 \$111,013.30 \$110,991.02 2027 \$117,397.60 \$113,512.43 \$113,484.70 2028 \$120,183.67 \$116,061.47 \$116,037.66 2029 \$123,019.43 \$118,672.26 \$118,654.49 2030 \$125,975.59 \$121,345.28 \$121,319.06 2031 \$128,935.52 \$124,077.19 \$124,044.14 2032 \$131,995.18 \$126,871.97 \$126,845.13 2033 \$135,073.08 \$129,724.75 \$126,845.13 2034 \$138,286.34 \$132,644.87 \$129,688.96 2035 \$141,521.77 \$135,624.14 \$129,688.96 2036 \$144,833.57 \$138,672.78 \$138,639.86 2037 \$148,260.68 \$141,794.27 \$141,765.55 2038 \$151,705.86 \$144,983.10 \$144,948.96 2039 \$155,291.29 \$148,242.42 \$148,193.00 2040 \$158,933.22 \$151,579.05 \$151,517.82 2041 \$162,647.28 \$154,991.19 \$154,922.16

At the outset of this post, I said that my goal was to not to have to work.  From the above, I now know how much income I need in any given year, to maintain my current lifestyle, while factoring in inflation.  So, if my investments happen to generate at least \$114,667.71 in income in 2026, I know that I can then quit my job and not have to worry about anything.

In one of my upcoming posts, I’ll talk about forecasting my expected income, which is the flipside of this discussion.

Why do you invest?

A few people may stumble into financial security. But for most people, the only way to attain financial security is to save and invest over a long period of time. You just need to have your money work for you. That’s investing.

Simply put, you want to invest in order to create wealth. It’s relatively painless, and the rewards are plentiful. By investing in the stock market, you’ll have a lot more money for things like retirement, education, recreation — or you could pass on your riches to the next generation so that you become your family’s Most Cherished Ancestor. Whether you’re starting from scratch or have a few thousand dollars saved, Investing Basics will help get you going on the road to financial (and Foolish!) well-being.

Now that the markets are showing signs of life, the pundits and financial writers are pumping out investing articles of all kinds. Gold is prominently mentioned as are a wide variety of stocks, mutual funds, and exotic ETFs. More so than ever, when I read these articles I ask myself this question: Why should I invest in that? Or taken one step further, the question becomes: Why do I invest?

I actually struggled for a long time on how to open up this post, but taking a page from Finding Forrester, sometimes it is easier to let someone else write the intro for you.

It should come as no surprise that many folks have asked the age old question of, “why?”.  In fact, everything that I say in this entry, has likely been written in greater detail, depth, and clarity, by someone else.  However, it is a necessary step in my overall roadmap of investing.

So, the question as it stands, why do you invest?  And as an extension to that, how do you know that you did it well?

The three quotes cited above contain a wealth of information on the how and why of investing.  At the end of the day, If we ignore the mechanics of investing (e.g. compound interest, “buy low, sell high”, “long time horizons”, etc.), the reason that any of of invest is a deeply personal one.  However, in my view the reasons for investing can be broken down into one of three categories:

1. We invest for personal gain
2. We invest to achieve some target and/or goal
3. We invest for someone else

Fundamentally, these three reasons cover pretty much every scenario.  Saving for retirement?  That is #1 or #2.  Helping a relative?  That is #3.  Saving for school?  #2.

The reason that I have broken everything down into three categories, is that the why of investing is useless without some type of barometer as to how well you are investing . If you are saving for school, you know if you are successful if you have enough for your tuition.  If you are saving for retirement, then you have enough if you know that you can be financially secure after you stop working.  If you are saving for personal gain (e.g., “I just want to be rich”), you are successful if the personal decisions you make in your investing are better than those that would be made if you paid someone else to handle your money (e.g. a financial advisor).

There are really only two ways to monitor your performance: absolute, and relative.  In absolute measurements, you have some fixed, quantifiable goal against which you are measuring yourself.  If you are saving for your child’s education, and you know that the total cost will be \$50,000 with tuition, books, and residence fees, then you have an absolute target against which to work.  Contrasting this are relative measurements.  These measurements are typically against some benchmark, and fundamentally reflect the opportunity cost of investing relative to some other means.  For example, if your benchmark is one of the couch potato portfolios, the performance of your investment decisions shows how much better (worse) you have done by managing your own money, instead of following the couch potato formula.

With the above in mind, the question should not be “Why do I invest?”.  Rather, it should be, “Am I meeting my investment goal?”  Defining your investment goal will lay the foundation on which you base all of your future decisions.

-10d