How To Not Blow 20k

…Over a decade and a half.  I know: bad trick, using the headline that way.

But seriously, lots of people talk about how using low cost investing options is a good idea.  Put your money in index funds rather than actively managed mutual funds or with an adviser.

Why?

One word: fees.

Unfortunately, the investing world does not operate on the, “You get what you pay for principle.”

And, over the long haul, those little fees add up to be a drag on your returns.  How big of a difference?  Let me tell you a story…

 

When I was 18, my Dad gave me a gift that I will never forget.  He started me (now us) on the path to financial independence.

When I was 18, I had my first W-2 job working as a sales associate in the electrical section of the regional hardware store.  (I worked for years before that, but I was always a small amount and paid in cash, so it was never eligible for taxation let alone retirement savings.)  At the then-minimum wage rate of $5.15/hr, I didn’t make much.  But, the little I made was reported to the government as earned income.  “Fortunately,” my earned income was so small, I was ineligible to pay taxes.

I was using the money I earned to pay for some of  my college expenses.  So, my Dad said he would match up to my earned income and put the money into something called a Roth IRA.  Of course, this became table stakes to hold a discussion on the general topic of saving for retirement.  We talked about the differences between a Roth and a traditional IRA.  We talked about contribution limits and the difference in withdrawal rules.  Once, we made it through the lecture, we got into the fun stuff: what to do with the money.  Pretty quickly, we ruled out a down payment on a car or storing it in my sock drawer.  Instead, he suggested investing in a mutual fund, The Growth Fund of America (ticker: AGTHX).  AGTHX is, you guessed it, an actively managed fund.  Its annual expense ratio (one of several potential charges people pay to invest their money) is 0.6%.

So, why is that a problem?

If a typical index fund charges ~0.1% in fees, the observation is that actively managed mutual funds at ~.6% or a human adviser at ~1-2% don’t make you enough extra money in the long run to justify their cost.

Compare AGTHX to Vanguard’s S&P500 index fund (Admiral shares because we’re over $10,000).  The Admiral shares have an expense ratio of 0.04%.  While the Investor shares (minimum of $3000) have an expense ratio of 0.14%.  Last, I checked, 0.6% is more.

But, wait!  You say, “don’t the hotshot fund managers get a better return for their customers?”  How else can they justify charging more?

Maybe…

 

Let’s look at the numbers.

I used Morningstar’s portfolio analyzer to get a bit more information.  Note that it only looks at changes in share prices (no capital gains/dividend reinvestment included).  I simulated buying $100,000 of each fund on Jan 5 of 2001.  How have the two funds done over the past ~15 years?

Source: www.morningstar.com

If you look at a Google Finance image of the two mutual funds’ values over time, it looks kind of like this:

AGTHX vs INX

So, what gives?  For much of their history, AGTHX outperformed VTSAX (the blue line is higher than red line). But, something called “reversion to the mean” seems to have kicked in.  That’s fancy talk for an idea that most investments eventually delivery average performance.  They may out/under perform for years or a decade and a half, but eventually, they produce average results.  This is one of the core reasons for selecting low-cost index funds as your primary investment vehicles.  Over the long haul, if most funds perform similarly, then the lowest cost fund wins. You can read a lot more about this from John Bogle, inventor of the index fund, founder of Vanguard, and personal hero.   While AGTHX may have outperformed VTSAX for many years, in the long run, the two funds have had roughly equivalent performance for over 15 years, yet AGTHX consistently charges fees that are almost 10x higher.

By the way, those fees are pretty insidious.  If you look at your statements, you will not see actual dollar values coming out of your account.  Instead, the fund management team takes them off the top before they show up in any individual statements (I spent a few hours looking through some pretty arcane sections of both American Funds and Vanguards websites before I convinced myself of this).

So, now the conundrum.  I admit, it’s an emotional one.  Math says, roll everything from AGTHX into a lower cost fund (e.g., VTSAX).  Our goal is not to tap these funds for at least a few decades.  So, shedding the fees should be the right decision.  But emotion says maybe those über-smart folks at American will outperform the index once again.  And, what about diversification?  If hackers get into Vanguard, they may not simultaneously get into American.  And besides, my Dad is the one who got this ball rolling, even if I’ve done the vast majority of the contributions.  I feel some (totally irrational) guilt at moving away from this fund.

 

So, what to do?  I’d love some other perspectives…drop me a line in the comments.

 

Don’t Confuse Brains With A Bull Market

Photo Credit: Bouncey2k (https://commons.wikimedia.org/wiki/User:Bouncey2k)

According to the Shiller 10 Year PE, the S&P index is expensive, valued at 30.23 as of this writing (Thursday 8/03/2017).   Two US Federal Reserve Presidents have also gone on record stating that the US market is getting, “frothy.”

What does that mean?

If you read Nate Silver’s awesome book, The Signal And The Noise, he illustrates the relationship between the Shiller 10 year PE and average stock market returns.  Here’s a great summary of the chapter.  The basic premise is that while the Shiller 10 year PE is a pretty lousy predictor of short term returns, it is a very strong predictor of long term returns.  The higher the Shiller 10 year PE, the lower the expected return.  The lower the Shiller 10 year PE, the higher the expected return.  The long-term average Shiller 10 year PE  is about 16.  The take away: the market feels expensive.

I can tell you from our personal experience, it has been an outstanding ~decade.  I started tracking our net worth in early 2009, and it’s safe to say that we’ve done well.  Obviously, saving as much as we can helps.  Our net worth has doubled since mid 2015.  That’s right, in 2 years!  In those two years, a couple of pretty big things have happened for us:

  1. The S&P went from 2028 on Jan 1, 2015 to 2472 on July 21, 2017.  An aggregate gain of about 21%.  (2472-2028)/2028 = 444/2028 = 21%.
  2. We substantially increased our retirement savings rate via our 401(k)s, Roth IRAs, etc.
  3. We bought a rental property that has appreciated (in funny money dollars) and generates real positive cash flow
  4. We had a kid (probably not a net worth boost, definitely not a cash flow boost…but totally worth it nonetheless!)

Here’s the plot of our net worth over time:

Being a nerd, I keep a trend line fitted atop our net worth vs time chart.  Among other things, I can use the line equation to estimate when we’ll achieve financial milestones.  Here’s the problem though: the linear trendline doesn’t fit so well anymore.  Our R^2 (a measure of how much variation is explained by the trendline) is at 0.96 for the linear fit.  A better measure when comparing non-linear models is actually s (standard error).  For the linear model, ours is $34,690.

Here’s the same chart with an exponential trend line.

Look at the standard error… it’s less than a third of the original model.  To me that says that the exponential curve better fits our actual data.  And, that fits what folks say about saving and investing.  It takes a long time to feel the effects of building a portfolio.  But, time is one of the greatest tools we have.  And, once you get going on that exponential curve, it’s hard to get off!

Now, to connect everything.  Like most “normal” investors, we benefited from steady savings through the past decade riding the wave of rising values.  Our portfolio gains have almost nothing to do with intelligence and everything to do with time, consistent savings, and maintaining low costs.  It’s not very sexy, but it works!  We have no illusions that we are different from any other investor.

So, maybe it’s time to take some age old advice.  Maybe it’s time to rebalance our allocations, locking in some of the stock gains while shifting our hard working dollars into bonds or even cash to preserve our capital for when the inevitable downturn does come.  The trade off is the opportunity cost of keeping those dollars in the market so they could reach even higher valuations.  I think it makes sense for each person to consider their own risk tolerance, time horizon before needing to tap their investments, and asset allocation to make the best decision for themselves.  But with market valuations approaching, “frothiness” I also think the time is right to do that consideration soon.

Are you taking any action to re balance your portfolio?  Are you letting things ride?

Self Directed Retirement

I’ve read more than a few passing mentions of so-called self directed retirement accounts.  I never really understood what that meant.  But the message was usually delivered with lots of exclamation points:

  • As a self employed business owner, you can reduce your taxable income, save for retirement, and increase your capital for investment!
  • As a full time employee with a side hustle, you can direct your retirement savings into your side business!

See!?  Why are you still reading these words?  Who wouldn’t want to have a self directed retirement account?  Why haven’t you called a broker yet?

 

Not so fast. Let’s dig into this a bit further.

Disclaimer.  Keep in mind: I’ve never formally studied retirement planning or financial advising.  Any decisions you make are your own. 

Let’s start with my motivation: with a potential opportunity to acquire our second (and maybe third!) on the horizon and a need for more cash, I figured it was time to figure out how we could afford our next opportunity.  And, a self-directed IRA represents a way to get cash without selling a kidney.  Here’s what I found:

 

 

What is a self directed IRA? 

It is a tax-advantaged (tax deferred) account offered by the US Government (IRS).  The account requires a custodian and allows for investment into alternatives (e.g., real estate, notes, or private companies). The account is funded with pre (traditional-IRA) or post (Roth-IRA) tax dollars.  The account then grows or shrinks as your investment choices grow or shrink and is subject to similar tax rules with a few extras.  For example, a self-directed IRA is prohibited from a bunch of transactions with “disqualified persons,” namely anyone closely related to you or businesses where “disqualified persons” have more than a 50% stake.

Honestly, It’s a bit tough to find details on the IRS’s website in one place (odd, right?).  I found that the fine folks at Cornell Law publish the internal revenue code  from which all the retirement accounts are authorized.  And, there’s an innumerable set of documents that the IRS publishes on all manner of arcane tax rules.  I also found IRC 4975(c)(1) and IRS Publication 590 to be the most referenced ones.

I did find a bunch of company websites that are selling their services as custodians.  Note: I’m not affiliated with any of these companies, nor am I receiving any compensation for mentioning them.  Some of these have pretty thorough documentation of the ins/outs of a self-directed account.

OK.  Enough overview.  I want to buy real-estate with my retirement dollars already.

 

 

Why is a self-directed IRA useful?

You can invest your retirement dollars into a wider variety of investment types.

Typical retirement accounts (401(k), 403(b), IRA, Roth IRA) are set up through an investment company like Vanguard, Fidelity, etc.  In a typical account, you can choose to put your money into stocks, bonds, mutual funds or other publicly trade-able assets.

I don’t want to do that. I want to buy a building or a note or shares of Tesla before they went public, and I want to do it with my retirement dollars.  This site lists a bunch of different types of assets (some of which you can invest in through traditional IRAs):

    • Real Estate
    • Private Company Stock
    • Tax Liens & Deeds
    • Oil, Gas & Mineral Rights
    • Crowdfunded Ventures
    • Trust Deeds & Mortgages
    • Private Loans to Businesses or Individuals
    • Venture Capital
    • Precious Metals
    • Traditional Stocks, Bonds & Funds
    • Anything the IRS rules allow for

Here’s one of the exciting benefits of using retirement dollars this way: your self directed IRA can get a non-recourse loan to finance the purchase of a property.  What!?  Well, yes.  You have to find a lender comfortable with this, and at typical loan to value ratio is closer to 50% but, it sure looks like you can leverage your retirement dollars.

One of the biggest reasons to look into a self directed IRA is if you are self-employed.  Lets say I decide to “retire” early from my day job to manage my real estate portfolio.  The self-directed approach allows me to continue putting aside retirement dollars, and I could elect to simultaneously supercharge my real-estate holdings.

There’s a few different flavors of self directed accounts: a solo 401(k), a self directed LLC (typically with “checkbook control”), or a business funding IRA.  I’ll leave the detailed overview to you to click through the links.  Suffice to say that each has minor differences in rules and benefits.

How to get started?

Think of setting up a self-directed IRA as starting a business.  That looks closer to the level of complexity to expect.
First, you need a custodian company that does this sort of thing.  Vanguard, Fidelity, Charles Schwab aren’t the go-to places for this kind of investment.  Some of the linked companies in this post are a good place to start your research.  Here they are:

How to fund a self-directed account?

Once you have your account set up, there are two basic ways to add funds into the account

  1. You can convert an existing retirement account into a self directed one.  This will of course require the support of your custodian company. And, all the IRS rules about taking possession of the funds apply.
  2.  Once the account is set up, you can start contributing much as you would a regular IRA.  The specifics will vary depending on which account custodian you’ve chosen.

How do you get your money out?

The short answer is just like any other retirement account: you cannot.   The longer answer is that you cannot until you reach the minimum age to begin distributions without paying a penalty (all the usual IRS rules apply regarding early withdrawals).

So you’ve invested in a nice little rental property.  You’re earning a great return on your investment.  What do you do with the proceeds?  You can either re-invest in the existing property (e.g., pay down any non-recourse loan balance) or save the cash to buy your next property!  Either way, don’t just take a distribution without ensuring you understand the rules or you may end up paying a penalty and income taxes.

Some other pitfalls of a self-directed account:

  • Cannot use money to interact with “disqualified parties.”  For reference, here’s the list of folks who cannot interact with the funds in the plan:
    • The IRA owner (don’t think you’ll buy a beach rental for your family this way!)
    • The IRA owner’s spouse
    • Ancestors (Mom, Dad, Grandparents)
    • Lineal Descendents (daughters, sons, grandchildren)
    • Spouses of Lineal Descendents (son or daughter-in-law)
    • Investment advisors
    • Fiduciaries – those providing services to the plan
    • Any business entity i.e., LLC, Corp, Trust or Partnership in which any of the disqualified persons mentioned above has a 50% or greater interest.
  • You likely won’t get any advice from the custodian on the tax implications, investment soundness, or legality of any moves you make.  Make sure you know what you’re doing or that you’ve hired a team who can give you good advice!
  • Variable costs.  I’ve not seen many published values, but Clint Coons suggests setup fees run $1500-$2000 and $300-$700 annually.  Depending on your asset base, a self-direct IRA will likely cost more than typical IRAs that limit your investment options to stocks and bonds.

 

What am I planning to do?

For now I’m focusing on more traditional approaches:

  1. I don’t have enough cash in my non-401(k) retirement accounts to justify the transaction costs of a self-directed IRA…and I’m not quite ready to quit my day job!
  2. I still believe in diversification, and real estate makes up a slightly out sized portion of our total net worth.

Presidential “Pop”

Wow.

An upset worthy of hyperbole: Donald Trump will be our next president.

Almost immediately, the markets started reacting.  US Futures dropped like a rock.  Foreign markets dropped for real and then rebounded.  Now, almost a week later, lots of folks are starting to interpret what a Trump presidency means.  I wondered what typically happens shortly after an election.  Let’s just stick with the S&P 500 and look at how it closed on November 1 (before an election) vs. December 1 (after an election).  Maybe we can see how panicked or calm we should be…

Here’s a table showing the 1 month closing values and the % changes since 1900.  If you’re wondering why that particular window, it covers a pretty significant span of US history and a range of tumultuous to halcyon periods.  By the way, the S&P Data is from here.   Special thanks to Robert Shiller for making it freely available.  And, the Electoral College data is from here.

One month S & P 500 changes since 1900.

One month S & P 500 changes since 1900.

 

For all years since 1900 without a presidential election, the average one month change was a positive increase of 0.5% (standard deviation of 0035).  For all election years in the same period, the one month change was a 0.3% increase (standard deviation of 0033).  Here’s a histogram to help visualize things.  See the overlap?  The stats seem to suggest that for this time window, there’s no net benefit to either jumping into or out of the stock market in response to election results.

preselectionyrs-vs-non

 

But, wait a minute.  Aren’t Republican presidential candidates better for business and the stock market?  In the days since The Donald was elected, the US stock market hit record highs.   See!  Well, let’s look at the data.  For all election years in our data set, we can split the one month returns by the winning party.  When Republicans win the White House or Democrats win the White House, there is no difference compared to non election years.

So, forget about non election years: let’s pit Democrats against Republicans directly.  Since 1900, there have been 15 Republican presidential terms and 14 Democratic ones.  Here’s the histogram of the one month change in the S & P 500.  Visually, it looks like there might be something there: a couple more high returning years in red vs. blue.  Again, the stats don’t show any meaningful difference between the two parties.

reps-vs-dems

 

So, what’s the take-away?  Warren Buffet’s sentiment: “For 240 years it’s been a terrible mistake to bet against America, and now is no time to start.”  Despite all the rhetoric, punditry, and discord, America is a great nation to belong to. 

sandp-over-time

Regardless of your political affiliations, invest.  Invest for the long haul.  Plant that seedling as soon as you can.  It will grow into your own money tree.

I Have a Dollar. What Should I Do With It?

George Zoomed

It depends.

Of course.  Smart A$$.

No, really. It depends on a ton of different individual factors that are unique to your specific situation.  Funny enough, I’ve been taking about this very question with a bunch of folks. One friend has retirement savings that need a new purpose. Another is debating between adding debt to purchase a rental property vs. pay down their home mortgage.  And, we’re asking a similar question about how we could move closer to our work locations and acquire a second rental property.  My point is simple: everyone faces these kind of trade off decisions routinely.  I don’t think I could or should answer the question for anyone else, but I think there is a framework that folks can apply to their own situation.

At the heart of this topic is the concept of opportunity cost.  (Hold on to something solid; this gets heavy quickly.)  Opportunity cost is what you give up when you commit.  Just got married?  Congratulations; you just gave up your chance to date Claudia Schiffer (Or Justin Timberlake).

Bought a CD?  For the money you invest in CDs, you’re giving up on the chance to buy Amazon stock with those dollars.

Bought Amazon Stock?  Those dollars won’t be buying into the Uber IPO.

Bought Uber?  Those dollars won’t be buying a rental property for you.

To get more technical:

…opportunity costs are used to measure the differences in returns between a chosen investment and one that is forgone. For example, consider a person who invests in a stock that returns a paltry 2% over the year. By placing his money in the stock, the investor gives up the opportunity to invest in another investment, such as a risk-free government bond yielding 6%. In this situation, the opportunity cost is 4%, or 6% – 2%.

Read more: Opportunity Cost Definition | Investopedia http://www.investopedia.com/terms/o/opportunitycost.asp#ixzz4HBW1h1hG

Follow us: Investopedia on Facebook

Sounds easy doesn’t it?  Let’s take a more personally  relevant example to understand some of the nuances of this kind of decision.  Say that I have an extra  $1000 sitting around.  As cash, it might as well be under Aunt Bertha’s mattress.  What should I do with it?  I see a couple of options.

  1. Pay down bad debt: one of our car loans
  2. Pay off our other car loan and start a “debt snowball
  3. Save/invest it for our next rental property

Option 1

This one is pretty straightforward.  Say our loan balance is about $5000.  The interest rate is 2.25%.  We’re a few months into this one due to the untimely demise of my beloved Scion xB.  Of course, our first car loan doesn’t change at all.  So, by paying down Loan #2,  we payoff the loan 14 months earlier, and avoid about $80 in interest over the life of the two loans. Our total interest paid for Option 1 would be $743.02.

Option 2

After almost 4 years, we have about $1000 left on our first car loan.  Let’s say our payments are $100/mo.  So, by paying the loan off now, we save a whopping $11 in remaining interest and free up $100/ mo to apply to the other car loan.  This is the start of the “debt snowball” popularized by folks like Dave Ramsey.  In short, it’s an emotionally satisfying way to pay down your debt.  Although, it’s not financially optimal(this is an awesome tool; check it out for your specific situation).  After paying off the first and applying the payments towards the second, we  find the total interest paid for Option 2 is $689.60.  Sounds a bit better.

Option 3 

This is the most complex of the three. We carry the existing two loans without avoiding any interest.  The rates are pretty low, so maybe it’s OK.  Now, a low cost bond fund has historically returned 3% (Vanguard’s has been a bit better with all the craziness going on over the past few years).  We’re looking to invest the money for three years.  If we assume past performance is indicative of future (possibly a BAD assumption), we’re looking at a potentially life changing $91.32 in distributions.  Our net interest paid for Option 3 would be $651.70.

So, how do these three options compare?  Someone play the “wah, wah” trumpets.  OK, I’m hoping that while our numbers aren’t terribly exciting, this concept is.

Opportunity Cost

Trade-off between paying down one loan, debt snowballing another, and investing funds instead.

It looks like Option 3 provides us with the best overall benefit.  What if we were willing to wait a few more years? What if we consolidated our car loans into a lower cost HELOC?  What if …?  And, that’s why I said, “it depends” way up front.  Your specific situation will vary.  Maybe you have higher rates or larger balances.  Maybe  you’re questioning weather or not you can afford to make extra payments each month.

The point is, you can use math to help make the best decisions possible with your limited dollars.  Those dollars can be the seeds of your future.

Let’s Go to the Casino!

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

https://i2.wp.com/upload.wikimedia.org/wikipedia/commons/5/53/Gambling_chips.jpg?resize=652%2C435&ssl=1

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:

https://i0.wp.com/upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/800px-Standard_deviation_diagram.svg.png?resize=652%2C326&ssl=1

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:

=$B$1*(1+NORM.INV(RAND(),$B$2,$B$3))

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:

=B6*(1+NORM.INV(RAND(),$B$2,$B$3))

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.