Let’s Go to the Casino!

We’re going to take a trip through the Monte Carlo.


Photo Credit: Jamie Adams

What is Monte Carlo?

Nope, not the one in Monaco with the beautiful beaches, fast cars, and the roulette tables.

Not the one in Las Vegas either.

I’m taking about a statistical technique for simulating a process or phenomenon.  Remember that infernal “Bell curve” from school?  It looks kind of like this:


Photo Credit: Jeremy Kemp

All the Bell or Gaussian distribution does is tell you how likely an event is to occur (think of the vertical axis as probability). When you have a known, stable distribution, you can use that distribution to quickly simulate a whole bunch of events.

For example, it takes me an average of 30 mins to get to work.  Some days, it’s shorter. Some days it’s longer.  Once, a car, 3 cars up from me got T-boned while going almost 60 miles per hour.  It took me almost 55 minutes to get to work that day (and no one was seriously injured).  Do here’s what my commute looks like as a distribution:

My commute duration averages 30 minutes. There’s variation. It’s rare for me to make it in 15 minutes or take more than an hour.

Once we know the distribution of historical values, we can use this information to make some educated guesses about what the future will be like.  Remember, when I looked at the long run returns for CDs, Bonds, and Stocks?  All I did was compare actual annual returns against a medium term average: 7%.

Let’s see what a simple Monte Carlo simulation can tell us about the range of future possibilities for our investment.  As always, this is just a thought experiment.  Any investment decisions you make are your own.

Here’s the histogram showing the past annual S&P returns since 1928:

Folks often tout an average S&P500 return of 7%.  Without understanding variation around the average, it’s easy to be mislead.

Here’s the scenario.  At 20 years of age, your Great Aunt Bessie passed away. She hated stocks, bonds, and even CDs.  “Too much risk for me!” She used to chortle from her rocker. “I keep my money cash and close at hand in case I need it.”  So she left you $1000 of cash out of her under-mattress stash. Let’s assume a 40 year investing horizon.  Let’s also assume that inflation and investing costs are zero!  Is Bessie right?  How much money might you have left if you invest it in the S & P 500?

I’m going to use Excel to do the Monte Carlo simulation.  I’m too cheap to spend money on a fancy software package.  And, this way you can do this on your own without needing fancy software.  Using the long run average return might be misleading, so we’ll stick with more conventional short run data 2006-2015.  The average return for the S &P 500 in this period was 9%.  The amount of variation around that average is described using the standard deviation.  In this case it is 0.187.

Don’t freak out if you’ve never loved statistics (most normal humans don’t).  All we’re doing is describing/summarizing the shape of the distribution. In Excel, we’re going to create a column called year.  Start at year 1 and count up to 40. In the next column, were going to enter a formula to calculate the new balance (warning for the faint of heart: there will be an equals sign coming up shortly). Here’s what the setup looks like thus far:

Excel monte carlo setup1

In cell B6, The formula is:


Plug this into Excel so it looks like this (if you’re really scared of doing this yourself in Excel, you can get to a Google docs version here):

In cell B7 copy the previous formula and make one change.  Switch $B$1 to B6.  It should look like this:


Now drag the formula down to year 40.  You just ran a single simulation of 40 years worth of S&P 500 returns.  That’s about all there is to it.  Keep in mind that your actual values will be different from mine, and they will recalculate every time you make a change to the sheet.  It should look something like this:

Excel monte carlo setup2

Now, are you ready to get really nuts!? Copy/drag the second column out 500 times.  You’ve created a (crude) 500 run simulation of the stock market.  Feel that mathematical prowess coursing through your veins?  This is one of the most useful tools you can get for doing some pretty powerful simulations…and it’s almost free!

Let’s look at the results. Copy the last row (year 40) for all runs and then paste values/transpose the data to a new worksheet.

Excel monte carlo setup 3

Once you have a column of final values, you can re-run the data analysis tool to create a histogram of your results.  Again, your specific results will vary, but from what I saw:

Excel monte carlo results

  • In 3 out of 500 runs, you did lose money.  That is roughly a 0.6 % chance.
  • In 151 out of 500 runs, you ended with between $100 and $1000. That is ~30% chance.
  • In 123 out of 500 runs, you ended with between $1001 and $2000.  That is ~25% chance.
  • In 223 out of 500 runs, you ended with between $2001 and %50,000.  That is a ~45% chance.

Tell Aunt Bessie, “Thank you for the gift of money, but you’ll use math to help make decisions about what to do with it.”  Your odds are better in the market than her 100% certainty of gaining nothing.  We’ll keep using tools like Monte Carlo to help make better decisions about a bunch of upcoming facets of our financial lives.  In the meantime, play around with this approach.  It’s a powerful tool for making better decisions.

Return On Invested Capital 

There’s an investment class I’ve deliberately not spent much time discussing yet: real estate.  In light of Brexit and some increased volatility in the stock markets, I think the time is right to start talking real estate.

I don’t mean your home.  I don’t mean that piece of swampland Aunt Bessie left you in Central Florida either.  I mean rental properties.

Ask some people you know if they’ve ever looked into the rental property business.  You might be surprised at how many folks have already taken the plunge.  I know the more folks I’ve asked, the more surprised I’ve been at how many people and who owns one or rental properties.  I think there are a couple of reasons for this:

  1. Almost passive income
  2. Sustainable side hustle
  3. Return on Invested Capital

Almost Passive Income 

Most folks work for their paychecks.  We trade our priceless time for an hourly wage.  Passive income lets us change the game by avoiding this traditional approach to creating income.  I first started reading about passive income as a concept in Rich Dad, Poor Dad (Affiliate link).  To this day, it remains one of my all-time favorite personal finance books.  Passive income has the ability to help each of us achieve our financial freedom earlier.  Passive income lets us get to that “Freedom Uttained” point faster.

Think about it like this: let’s say I have an annual salary of $100k.  And, I spend about 2000 hours a year to get that salary.  That works out to $50/hr.  Not too bad, right!?

I Love Cubicles..

I should even tolerate grey cubicle hell for a while at $50/hr.  But, I can’t.  I want more.  And, I suspect most other people do too.  I’ll dive into the details of my experiences with rental property in future posts.  But, for now, let’s say I net about $500 a month from a rental property (net = rent – all expenses/reserve contributions).  And, I spend an additional 5 hours a month managing my rental property.  That sounds pretty doable.  Apparently, Americans spent more than 5 hours a day watching TV in 2015 according to the Bureau of Labor Statistics.  You know where I’m going with this: the simple math says, I just made $100/hr.  Each month (on average).  Until I sell the property.

Turn off the TV and go make your own life better!!!

And that is the beauty of the rental property business.  You still have to trade some time for cash.  But what you get in return is a seedling.  Your first money tree sprout that may eventually blossom into the life you want to live.

Sustainable Side Hustle

Let’s say my wife and I spent almost 500 hours researching, screening, visiting, negotiating, reviewing contracts, rehabbing, and finally renting out our first rental property.  (It was our first, and I’m pretty risk averse!)  Now we spend about 5 hrs a month managing it.  Some months it’s more.  Some months it’s less.  But, we manage it outside of our day jobs.  And, the checks keep coming in.  To be sure, we don’t plan for 100% occupancy.  In fact, we’re coming up on our next lease renewal, and we will likely have some down-time while we make a couple of improvements and complete some maintenance items.  But overall, we’ve found a way to take some of our surplus cash flow and turn it into gold.  Now, someone else pays our mortgage on the rental property.  Their rent covers the routine maintenance costs and fills out a savings account for bigger items.  All we have to do is wait…

Return on Invested Capital

And that brings us to the actual topic I wanted to dive into.  You see, we didn’t pay cash for the full value of our rental property.  We have a mortgage.  So, let’s do a little math with simplified numbers:

We’ll buy a $100,000 property at market value.  In the first situation, we’ll put down 25% because this is an investment property, and the bank wants a little more skin in the game (or they charge a higher interest rate).  The bank offers us a 4.5% rate resulting in ~$500 per month in principal and interest payments.

In the second situation, we’ll buy the same property with a suitcase full of cash.

Is this the best way to buy a rental property?

Our rent is the same for the property: $1500/mo.  Our costs for taxes, maintenance allocations, utilities, etc. are the same regardless of how we bought the property. Again, keeping things simple, we’ll estimate that at $500/mo. Also, for the sake of simplicity, I’m ignoring closing costs,any renovations, and a few other items that are roughly comparable regardless of how the property was financed.

Is it better to buy with leverage or all cash?

Is it better to buy with leverage or all cash?With

With our loan, we put down $25,000.  Each year, we would bring in a theoretical $6000 of profit for this property.  That’s a whopping (hypothetical) 24% return on the investment we made.  Compare that to buying the property with $100,000 in cash.  We bring in $12,000 profit.  Even though the total dollar amount is higher, we’re only making 12% on our $100,000 investment. Not too shabby, but now we’re out of cash.

In theory, we could use the $75,000 we didn’t spend in the first scenario to buy three more properties!  Using leverage, our new situation looks like this:

Full Leverage ROIC

Living dangerously? Or, spreading the risk?


Now, we’re making that same 24% on our money.  And, we’re clearing $2000 a month.  Freedom Uttained point, here we come!  Of course, we had to take out $300,000 in loans to get there.  There’s now a higher chance that we cannot pay all 4 of our mortgages if all our properties are vacant.  But, what are the chances that all four properties are vacant at the same time?  Probably smaller than the chance that the single one is vacant in the case of our all cash purchase!  We just spread out our risk, boosted our returns, and launched ourselves on the path to real estate mogul.

In my mind, this illustrates why real estate is such a neat asset class.  You can buy a full property with 20-25% down.  Doing that with stocks seems way riskier.  If you hold the property long enough, your tenants completely pay off your mortgage for you.  Now, your net returns go through the roof.  Leverage lets us either get into the game a lot earlier or use the cash we didn’t deploy by borrowing to further increase our holdings.  Either way, what we do with our limited resources matters.  And Return on Invested Capital is one way of looking at investments to help us decide where to allocate our limited resources and reach financial freedom that much sooner.

Wealth to Lifetime Earnings Ratio: Part 2

This is Part 2 in a short series exploring the concept of lifetime earnings vs. net worth.  It’s pretty heady stuff so I’m breaking it up into a couple of linked posts.  You can find Part 1 here.

Today, we’re going to look at the lifetime earnings part of the wealth to lifetime earnings ratio:

1. How to calculate it
2. What you can learn from it
3. How yours compares to others

Step 1: calculate your lifetime earnings
As of 2016, if your income is from the U.S. and you make less than $118,500, your task is easy. Go to the social security website and logon (create your profile if needed). Once you’re in, find the “Your Earnings Record.”. Download your earned income history so we can do some math (yes, math… unless you’d prefer to go back to watching cat videos).

If you’ve ever earned more than $118,500, you could take the extra step of finding out your actual earnings for those years. (Americans are only taxed on the first $118,500 of earned income). Every earned dollar above $118,500 is exempt from social security taxes. If you want to find your real wages for years when you made more earned income than $118,500, tax returns, old pay stubs, or the spreadsheet you started this exercise on when you first read Your Money Or Your Life (affiliate link) in the 90’s are your best bets to find this information.

Step 2: what can you do with it?

The first thing to do once you have your earned income history is plot it over time. Here’s the median US household income plotted over time.  Depending on your personal situation, your actual income may be close to the median or far from it.  But, it’s a consistent yard stick that you can measure yourself against other Americans.

US Median Income

Median US household income in 2014 dollars, from Census.gov

Has your earned income grown over your career? What kind of disruptions can you see (e.g., Dotcom era, Great Recession)?

If you take each year’s % change, you can see your annual earned income growth/decline.  Here’s a view for % change from year to year for the US Median Household.  Not terribly exciting is it?

US Median Income Percent Change

Year/Year % Change in median US incomes.  Source: Census.gov

The long-run average annual % change: 1.0.  Not a 1% increase.  Flat.  It took me longer than I care to admit to extract the data from the census website.  I kept thinking there had to be a better way than just re-typing.  (There probably is, but I gave up).  So, I made a Google spreadsheet that has the raw data, the percentages, and space for you to put your values in and see how you’re comparing to the US median over time.

Please, please download the sheet to your local system first!

Here’s a snapshot of what the spreadsheet would look like for someone starting with $60,000 of earned income in 2000 and making a 3% raise year over year for 10 years.  Let’s hear it for compounding growth!



So, how does your income compare to the US median?  Did your earned income keep up with the median year/year rate changes?  What insight did you get from plotting your data this way?


Returns Matter


We’re all in a race against the clock.  How we handle the ups and downs sets us up for long-term success … or an ulcer.


Sometimes, the path to financial freedom can be a little scary.  Photo Credit: Alex Brogan

Regardless of whether or not you work for someone else for your living, how we deploy our available resources over our lifetimes matters greatly. Most folks are familiar with the idea of compounding interest: where over enough time, your money makes a tremendous amount of money without you having to do much additional work. Once you have enough money to last your remaining lifetime, you’re financially free. So how do you get there? Making payday loans? Putting all your savings into a big pile of cold hard cash under your mattress or more comfortably into your closet?

Let’s explore the relationship between risk and reward.

Starting with the classic compounding interest chart from high school, we see a hypothetical pathway to awesomeness. 7% average returns from the time you start putting money into the Wall Street piggy bank. Put your hard earned cash into a bunch of 3-4 letter acronyms representing businesses. Add a bunch of time, and the road to Millionaire status couldn’t look simpler, right?

100 over 87 ave yrs

What this view fails to consider is volatility. Here’s what actual annual returns look like for the US market. Not such a smooth pathway is it?

100 over 87 real years

OK, I admit that I played with the scales to make this look more equivalent.  Here’s the first two plots overlaid on top of each other.  Now you start to see why the stock market has been long-considered one of the best investment vehicles around.  Cool, huh!?  The point remains: you had to have some serious gumption to not sell as things were crashing in the late 90’s/early 00’s and 06-09.

100 over 87 yrs real vs. ave

Don’t feel like putting your investment dollars on a roller coaster?  What if you want guaranteed returns? Just about the safest investment around is a CD. The FDIC guarantees all investments for up to $250k. In exchange for that nice safe blanket, you get low returns. Currently 0.5%-1.5% depending on the term. Long-term, CD rates look like this:

CD Rates

Long-term CD rates. Source: Bankrate.com

Where CDs may have once provided a decent return %, it’s now tough to lock up your funds for 12 months to 5 years in order to attain rates greater than an online savings account. Probably not the fastest way to financial freedom, right?

CD balance growth over time


What if you are willing to take on a bit more risk than a CD?  For example, it’s quite likely that the US will continue to meet it’s debt obligations.  US Treasury bonds are historically one of the safest investments out there, especially relative to other countries with less stable economies or companies.  Understanding how to assess bond risk and pick out what debt to invest in is beyond the scope of this post, so lets just stick with medium term US debt (10-year US Treasury Bonds). To simplify things, we’re also going to assume that we’re investing our $100 into a fund that costs nothing and lets us take advantage of annual rate changes while re-investing the interest.

TBonds over 87 real yrs



Get to the point already, right!?

Let’s put it all together and see which investment strategy gets us closer in a hypothetical race.  Let’s assume that most folks work about 40 years in their traditional 9 to 5’s.  We’ll start with an initial investment of $1000.  That’s right, $1000…and that’s it.  If you invested $1000 at age 22, what is the theoretical balance for each when you’re 62?  So, we’ll take the most recent couple of years for each of our asset classes (CDs, Bonds, and Stocks) and hold those interest rates constant for 40 years (I know, it’s a contrived example, but it’ll illustrate the point).

40 year race

And the winner is…


As expected, higher returns result in a higher ending balance at the end of one’s career.  And, that’s the take-away: over a long enough time frame, maybe the short-term risk associated with asset volatility can be discounted.  Maybe we spend too much time worrying about 0.25 point returns for a 60 month CD at one bank vs. a high-yield savings account.  Instead, perhaps we should acknowledge that we are our own worst enemy.  Our emotions when news headlines blare negative returns, tempt us into making bad decisions.  We want to, “stop the bleeding.” We sell everything.  In so doing, we typically take a big loss and miss out on the next market rebound.  John Bogle might say just invest in the whole market regularly.  Hold your investments for the long term.  Keep your costs low.

I would distill that into an expression from Las Vegas and simply say, “let it ride!”