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Investing in the Game of Life

There’s something about Mindfully Investing that’s been bothering me for a long time.  I’ve often written about how a portfolio of 100% stocks is better than a portfolio with a mix of stocks and bonds, assuming that you’re mindful enough to handle the sometimes wild ups and downs involved with an all-stock portfolio.

Stocks make the most sense for long-term investors because historical data indicate you have an 85% chance of making money after 10 years of stock investing.  Selling stocks before that “time horizon” increases your chances of a permanent loss of your original investment.

That all sounds good, but many investment regulators, professionals, and bloggers point out that our investing time horizons may be shorter than we assume.  For example, most informed sources say you should have an emergency fund covering 3 to 6 months of living expenses.  But what if you lose your job and can’t quickly find a new one?  Once your emergency fund is drained, it won’t be very long before you start measuring your stock portfolio in terms of how many mortgage payments it could cover.

The Game of Life

The question of investing time horizons reminds me of the Game of Life.  I used to play this board game with my daughter when she was younger.

For those who aren’t familiar with the game, players take turns going down a tortuous path with the number of spaces moved determined randomly by a small Roulette wheel; sometimes you land on certain spaces and sometimes you pass them over.  Each space represents different life events like going to college, getting a job, getting paid, having children, buying a house, and even investing!  The most relevant spaces for today’s post are the ones with big financial setbacks, such as getting sued or losing a job.  The winner is the player who has the most money at the end of the path where players “retire”.  I guess the game creators decided it was a bit too morbid for the kiddies to drop dead at the end of the game.

Whether we’re talking about the Game of Life or real life, how do we mindfully invest for the long term when random financial setbacks can force us to divest at almost any time?  The conventional answer is to assume our time horizons are shorter than we might expect and allocate more of our portfolios to safer (less volatile) investments, the prime example being government bonds.

Bonds typically suffer fewer and less precipitous declines, than stocks.  For example, according to 92 years of Shiller and Damodaran annual return data, 10-year Treasury bonds lost value much less frequently than stocks, and the biggest single-year declines were:

  • -11% for bonds.
  • -44% for stocks

This implies that if you need the money back in an unexpectedly short timeframe, you’re much less likely to have lost money with bonds than with stocks.

It’s this Game of Life problem that has been bothering me about the mindful all-stock investing approach for several years now.  And today’s post is going to finally lay my concern to rest, one way or the other.

Risk Assessment

The problem of unexpected financial setbacks can be addressed with a tool known as “risk assessment”, which is a science that attempts to quantify (always with some uncertainty) the magnitude and likelihood of almost any negative outcome.  Fortunately, I’ve conducted quite a few risk assessments over my 30 years as an aquatic toxicologist, and I applied these methods to the Investing Game of Life.  A complete description of all my methods would be too detailed for a blog post.  So, if you’re interested in more information than I provide here, you can inquire via my contact page.

The primary question I wanted to answer was:

  • Does a mixed 50% stock/50% bond portfolio provide a better outcome in the face of life’s unexpected financial setbacks as compared to a mindful portfolio of 100% stocks¹, assuming the investor has a goal to retire at age 65?

Typical Investor – To answer this question, I tried to imagine a typical investor who is reasonably savvy with her finances.  So, I won’t be addressing issues like low saving rates, flagrant spending, huge credit card debts, etc.  Specifically, I assumed that our typical investor:

  1. Went to four years of undergraduate college
  2. Graduated with the average U.S. student loan debt ($30,000), which she paid back before starting to invest
  3. Got a job at age 23 with an average U.S. salary ($50,000)
  4. Saved 10% of her gross salary each year for investing, which may seem ambitious but is consistent with standard recommendations
  5. Received annual salary increases at the average historical rate of inflation of 3% per year
  6. Bought an average-priced housed in the U.S. at age 35 (which inflation-adjusted to 13 years from now gives a price of $322,000)
  7. Put an average downpayment of 12% on this first home
  8. Was able to pay the 30-year mortgage without reducing her 10% saving rate.

Bad Events in the Game of Life – Now comes the fun part.  I gathered statistics on the probabilities and the dollar magnitudes of some common financial setbacks that are pretty unexpected.  I included the potential occurrence of the following “bad events”:

  1. An under-insured home disaster (like a flood or fire)
  2. Long-term medical disability costs and lost wages
  3. Obtaining a 2-year post-graduate degree
  4. Long-term unemployment (like being laid off in a global recession)
  5. A legal, tax, and/or liability situation involving legal fees and a big check to settle the matter
  6. Marrying into a large debt
  7. One or more divorces (50% of all U.S. marriages end in divorce, but no one plans for it)
  8. A small business or similar commercial bankruptcy (not personal bankruptcy given our investor is supposed to be savvy)
  9. Paying for 4-year college educations for 1 or 2 children
  10. Criminal fines or imprisonment including lost wages.

The dollar amounts associated with each bad event were inflation-adjusted to the future year when they randomly occurred.  Also, you might argue that some of these events seem more planned than unexpected.  However, I know quite a few people who never expected their careers to push them into more schooling or saved enough to fully cover the sky-rocketing costs of their kids’ higher education.

Putting It All Together – The final step in the process was to run randomized trials, where some (but rarely all) of these bad events could happen throughout a lifetime based on relatively realistic levels of probability.  The trial results were applied to the growth of both the 100% stock portfolio as well as the 50/50 portfolio.  I ran one hundred² such trials with the computer picking random pairs of stock and bond annual returns from the Shiller and Damodaran datasets.  That is, I used actual historical data to generate random and unique “future” sequences of stock and bond returns for each trial.

And The Winner Is…

This exercise produced mountains of data, but I’ll try to stay focused on our main question about which of the two portfolios produced a better outcome for retirement at age 65.  I defined “better outcome” as a larger final account value.  Even if the 50/50 portfolio had fewer ups and downs along the way, the final value seems most relevant to the goal of a comfortable retirement.

This graph shows the final value at age 65 for the all-stock portfolio minus the 50/50 portfolio with the 100 trials sorted in descending order.  So, positive columns mean the all-stock portfolio “won” the trial, and negative columns mean the 50/50 portfolio won.

I cut off the extremely high values for the first eight trials on the left side of the graph to show the rest of the results more clearly.  Moving our attention to the right side of the graph, we can see the 50/50 portfolio produced a better final value in only 11 trials, as indicated by the negative values.  It turns out that the all-stock portfolio provided a better outcome 89% of the time!

But some of the 100 trials had few if any bad events randomly occurring.  So, let’s take a closer look at the 25 trials with the highest magnitude of bad events (the worst quartile).  The average unexpected expenses for these 25 worst trials was over $660,000!  The total dollar amounts of the bad events for each trial are shown by the thin black line on this graph.

In every case, the all-stock portfolio final value (blue line) was similar or better than the 50/50 portfolio final value (orange line).  So, even during a very hard life, which is what we all worry about, an all-stock portfolio performed better.

It’s also noteworthy that $1 million in today’s dollars equates to more than $3 million in inflation-adjusted dollars at the assumed retirement date 43 years from now.  And both portfolios frequently failed to reach a final value north of $3 million in the face of substantial financial setbacks.  The all-stock portfolio produced final values greater than $3 million in only 21 of the 100 trials.  So, we can say the all-stock portfolio “wins the contest”, but in most cases, it was a feeble victory.

This may suggest that the probabilities I assigned to bad events happening might be unrealistically pessimistic in aggregate.  On the other hand, I realistically assumed that divorce, which is pretty common in the U.S., usually halves the existing account value of each person in the marriage.  Splitting assets can result in huge dollar losses, particularly if the divorce occurs later in life.

The results may also suggest that it’s important to maximize your income and savings rate as much as possible throughout life to increase your chances of retiring comfortably.  Either way, the all-stock portfolio provides a better chance of a larger retirement nest egg if you do happen to suffer an unexpectedly hard life.

Conclusions

So, what’s going on here?  The standard advice is to use bonds to protect against permanent losses.  But if we follow that advice throughout our lives this risk assessment shows it will mostly exacerbate our problems.

The apparent disconnect here is that most of the time when people talk about the risk of a “permanent loss”, they’re thinking about a one-time investment.  The most common example is an investor who sporadically scrapes together enough cash to buy 100 shares of fund X and then reverts to not saving and investing for a long period.  (A less common example is an investor who gets a windfall like an inheritance or winning the lottery.)  I’m not casting aspersions here.  Sometimes sporadic investing is all people can manage, and that understandably puts them in the mindset of tracking the gains/losses of each one-time investment.

But this whole exercise shows that it’s much more effective to save regularly and invest regularly.  The only exception would be when you’re in debt due to unexpected financial setbacks, in which case it’s often best to pay off the debts before starting to invest again.  This graph of account values over time for one trial provides a great example of what I mean.

Again, I cut off the vertical axis to show the results better, but the all-stock portfolio ended up at almost $4.5 million.  Despite three distinct financial setbacks totaling $670,000 of unexpected expenses, the all-stock portfolio manages to recover each time, while the 50/50 portfolio keeps getting knocked back down into debt.

If you tracked every annual investment, you’d undoubtedly be able to identify some instances of a permanent loss in both portfolios.  But the key point is that those permanent losses mean less with an all-stock portfolio and a consistent regular approach to saving and investing.

This is not to say that every trial looks this good for the all-stock portfolio or this bad for the 50/50 portfolio.  There were some pretty stellar returns for the stocks in this chart, but they all reflect actual annual returns from past years.  So, this sort of trajectory is certainly well within the realm of possibility.

My concern about Mindfully Investing has been laid to rest.  Clearly, a steady stream of savings that are steadily pumped into a mindful all-stock portfolio (or paying down unavoidable debts when necessary) is the best defense against the unexpected financial setbacks that are an integral part of the Game of Life.


1 – Specifically, a mindful portfolio holds a moderately diversified set of low-cost stock index funds and no bonds (at least while bond yields hover around 5000-year historic lows).  The reason for this stock configuration is described more here and some example portfolios are provided here.  Also, I chose the 50/50 portfolio to represent a fairly aggressive application of the already conservative 60% stock/40% bond portfolio often recommended by financial advisers.  Stocks are represented in both portfolios by the S&P 500 returns history from Shiller, and bonds are represented by the 10-year U.S. Treasury bond returns history from Damodaran.

2 – It’s not unusual for thousands of trials to be conducted for this type of “Monte Carlo” simulation.  But in my experience, with these levels of event probabilities, I never learned much more from 1000, or even 10,000 trials, than was pretty apparent after just 100 trials.

2 comments

  1. Rao Mikkilineni says:

    I think you are right.But what happens once you are retired say at 68 and have another 20 years to live and no ability to add money for investing but more likely to have an adverse event. can one save for five years of expenses in cash equivalents and put rest all in stocks?The difference is you are not adding new money in market ups and downs.In reality this person needs stocks like returns.Will bonds help like in a Bucket like approach,

    • Karl Steiner says:

      Great comment! The math certainly does change once you enter retirement, and you no longer have new savings to invest every month. I probably should have mentioned that in my post. I discuss how the math of losses changes in retirement in this article. And it’s funny you should mention it, but I’ve found that five years of “short-term” investments (cash or bonds) is a pretty reasonable way to approach this as part of a larger bucket approach. However, I have also pointed out that currently, bonds are a poor choice for the “short-term” and even “mid-term” buckets because bond yields are so low. I’ve written most recently about the problems with investing in bonds right now in this article.

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