Are Your Financial Advisor’s Fees Reasonable? A Unique Perspective – Retirees


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I started off this examination with a brief introduction to this question.  You can see that discussion by clicking on the following link:

As promised, I will start by using retirees as the individual investors.  The hypothetical example is meant to get you thinking about the reasonableness of investing fees and how they affect you reaching your financial goals.  Of course, I will discuss the same topic but using those individual investors who are saving for retirement.  But now, let’s dive into our discussion of this topic by focusing on those individual investors already in retirement.

Example for Retirees:

If you are retired and not independently wealthy, you are in the wealth distribution phase of your life.  There are some retirees that are permanently in the wealth preservation phase.  Wealth preservation simply means that an investor has enough money to live comfortably, but he/she does not need to deplete his/her investment portfolio.  Furthermore, this investor does not really try to increase the value of his or her investment portfolio.  A retiree in the wealth distribution phase of life is the most common example.  This investor is gradually depleting his/her investment portfolio to pay for living expenses on an annual basis.

Since this person is not working anymore, (thus has no income from work, and longevity keeps getting longer), he/she needs have an investment portfolio that is somewhat conservative in nature.  Therefore, it is not reasonable to expect to earn 8.0% per year.  A more common target return might be 5.5-6.0%.  If you are working with a financial professional who charges you 1.0%, you need to earn 6.5-7.0% on a gross basis in order to get to that target net return.  Now the long-term historical average of stocks is about 9.5%, so the higher your AUM fees are, the more weighting you will need to have in stocks and away from bonds and cash.  Well, we have already gone over that, and most individuals that present information will stop there.  I want to take this even further though.

Let’s say you are a current retiree with $1 million that you are living on an additional to Social Security income.  You have a target return of 5.5% to fund your desired retirement lifestyle, and your Financial Advisor charges you a 1.0% AUM fee.  Thus, you will need to earn a 6.5% return gross to reach your bogey.  Now I would like to put in the twist, and I want to do a thought experiment with you.  Your Financial Advisor will sit down with you and assess your risk tolerance and ensure that the investment recommendations made are not too aggressive for you.  If you cannot take too much volatility (fluctuation in asset prices up and down over the short term), your financial professional will reduce your exposure to equities.

Now let’s look at our example through the lens of economic principles.  If you just retired and are 65, you have one option right away.  You can simply invest all your retirement money in 10-year Treasury notes issued by the Department of the Treasury.  Treasury notes are free to buy.  All you need to do is to participate in one of the Treasury auctions and put an indirect bid in.  What is an indirect bid?  An indirect bid is simply saying that you would like to buy a set dollar amount of notes, and you are willing to accept whatever the market interest rate set by the auction is.  What is the yield on the 10-year Treasury Note right now?  The 10-year Treasury closed at 1.85% on January 13, 2020.  When you go to a financial professional, he/she is selecting investments in lieu of you simply purchasing the 10-year Treasury Note.  Keep in mind that US Treasuries are among the safest investments in the world.  They are backed by the full faith and credit of the US government.  Stocks, bonds, real estate, gold, and other investment options all have an added degree of risk.  With the additional risk, there is a possibility for higher returns though.  How does this relate to your 1.0% AUM fee?

Think about it this way:  why are you paying your Financial Advisor?  You are paying him/her to select investments that can earn you more than simply buying a US Treasury Bill, Note, or Bond.  As an investor, you do not want to just settle for that return in most cases.  With that being said though, you can just start out there and forget it.  You do not need to engage a Financial Advisor to simply buy a 10-year US Treasury note.  This means that you are paying the Financial Advisor to get you incremental returns.

In our example above for a retiree, your target investment return is 5.5%.  If you can earn 5.5% during the year, the incremental return is 3.65% (5.50%-1.85%).  Remember that you are paying the Financial Advisor 1.0% in an AUM fee.  Therefore, you are paying the Financial Advisor 1.0% of your assets in order to get you an extra 3.65% in investment returns.  Well, 1.0% is 27.4% of 3.65%.  Thus, you are essentially paying a fee of 27.4% in reality.  Now your financial professional would flip if the information was presented in this way.  He/she would say that it is flawed.  The mathematics cannot be argued with; however, I will admit that many folks in the financial services industry would disagree with this type of presentation.

 Remember that you started out with $1 million.  You could have gone to the bank and gotten cash and hid it in a safe within your residence.  AUM fees are always presented by using your investment portfolio as the denominator.  In our example, your investment fee is 1.0% ($10,000 / $1,000,000).  I urge you to think about this though.  Does that really matter?  Of course, the fee you pay to your Financial Advisor will be calculated in this manner.  But what are you paying for in terms of incremental returns?  If you want to calculate what you are paying for (the value that your Financial Advisor provides), the reference to the starting balance in your brokerage account is moot.  It is yours to begin with.  You have that money at any given time.  Therefore, it should be removed from the equation when trying to quantify the value your Financial Advisor provides in terms of investment returns on your portfolio.

Now remember that I said your target investment return was 5.5%.  The long-term historical average of stocks is approximately 9.5%.  If you choose to simply allocate only enough of your investment portfolio in stocks and the rest in cash to reach that 5.5% target, you will select an allocation of 53.0% stocks and 47.0% cash (5.5% = 53.0% * 9.5% + 47.0% * 1.0%).  Note that I am assuming that cash earns 1.0% and that you can select an ETF or index mutual fund to capture the long-term historical average for stocks.  Now your financial professional is working with you to select an investment portfolio that achieves the 5.5% target return, and their investment recommendations will be different than this hypothetical allocation.

The hypothetical allocation achieves your target return with a simple choice of two assets (an ETF or index mutual fund and a money market).  Keep in mind that you will normally have a portion of your portfolio allocated to fixed income.  The 10-Year US Treasury note is trading around 1.85% as of January 13, 2020.  If you allocate your portfolio to 60% stocks, 30% 10-Year Treasury Note, and 10% cash, your expected return would be 5.5% (5.5% = 49.0% * 9.5% + 41.0% * 1.85% + 10.0% * 1.0%).

Whatever your Financial Advisor is charging you in terms of fees, you need to make that percentage more in your total return on a gross basis such that your net return equals your target return.  In our example above, the assumed AUM fee was 1.0%.  That investment fee means that you must earn 6.5% on a gross basis because you need to pay your Financial Advisor 1.0% for his/her services.  After the fee is paid, the return on your portfolio needs to be 5.5% on a net basis.

So, how much weighting do stocks need to be in your portfolio to ensure that your overall returns are 5.5% after paying your AUM fee?  The answer is 62.5%.  Why?  The expected return of your portfolio is 6.5% (6.5% = 62.5% * 9.5% + 27.5% * 1.85% + 10.0% * 1.0%) before fees.  Given the average retiree’s risk tolerance at age 65 or older, many individual investors do not desire to have a portfolio with 60.0% or larger allocated to stocks.  The more salient observation is that the individual investor had to increase his/her stock allocation by 13.5% in order to pay the 1.0% AUM fee.  This increased allocation to stocks significantly increases the risk of our hypothetical portfolio.  And keep in mind that the historical, long-term average of stocks is just that.  It is an average and rarely is 9.5% in any given year.

But what if we could find a Financial Advisor that only charges 0.5% AUM fee?  How would that change our example above?  So, we now need to earn a gross investment return of 6.0% rather than 6.5%.  The new portfolio allocation is 55.0% * 9.5% + 35.0% * 1.85% + 10.0% * 1.0% = 6.0%.  Our main takeaways here are that the allocation to stocks only increases by 6.0% (55.0% – 49.0%), and this portfolio has a stock allocation less than 60.0%.

Now let’s look at some actual historical data.  The S&P 500 Index did not have a single down year since 2008 if we looked at the subsequent five years of stock returns.  The returns for 2009, 2010, 2011, and 2012 were 26.5%, 15.1%, 2.1%, and 16.0%, respectively.  The average return over that span was 14.9%.  As of December 31, 2019, the S&P 500 Index was up 31.5% for 2019 including the reinvestment of dividends.  Now I am by no means making a prediction for 2020.  However, I wanted to drive home the fact that, if your Financial Advisor sets up your financial plan with the assumption that your stock allocation will earn 9.5% on average, any actual return lower than that estimate will cause you to not reach your target return.  What is the effect?  You will not be able to maintain the lifestyle you had planned on, even more so if there are negative returns experienced in stocks over the coming years.

Essential/Important Lesson:

Let’s look at the next five years starting in 2015.  A five-year period covers 2015-2019.  If you start out with $1,000,000 invested in stocks and plan on earning 9.5% per year, you are expecting to have $1,574,239 at the end of five years.  Let’s say that the return of stocks is only 4.5% per year over the next five years.  You will only have $1,246,182 as of December 31, 2019.  The difference is $328,057 less than you were expecting.  The analysis gets worse at this point though.  How can it get any worse?

Well, if you were planning on 9.5% returns from stocks per year, the next five-year period 2019-2023 needs an excess return to catch up.  Thus, if your starting point on January 1, 2015 is $1,000,000, your financial plan is set up to have $2,478,228 as of December 31, 2023.  If you are starting behind your estimate in 2019, the only way you can make up the difference is to have stocks earn 14.7% over that five-year period which is 5.2% higher than the historical average.  As you can see underperformance can really hurt financial planning.  The extremely important point here is that a 1.0% AUM fee will cause you to be even further behind your goals.  Remember that the illustration above is gross returns.  You only care about net returns and what your terminal value is.  Terminal value is simply a fancy way to say how much money is actually in your brokerage account.

Are Your Financial Advisor’s Fees Reasonable? A Unique Perspective – Introduction


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This brief article introduces the topic for this article.  Since I will be looking at the issue of the reasonableness of investing fees from the viewpoint of individual investors saving for retirement or currently in retirement, I will devote separate articles to these groups.  Our journey will be an exploration of whether or not the fees you are paying to a financial professional are reasonable.  Furthermore, we will examine how the expenses affect your overall investment performance and reaching your financial goals.

Most financial professionals are charging clients based upon assets under management (AUM).  The most common fee is 1%.  For example, the fee for a $1 million portfolio would be $10,000 ($1,000,000 * 1%).  Now you have heard me talk about the importance of keeping fees as low as possible.  Essentially you are trying to maximize your investment returns each year.  If you have quite a few needs, a Financial Advisor usually can provide a number of different services and advice.  For example, you also may need assistance with legal and tax advice.  Additionally, you may have more complex financial planning needs.  Financial professionals will assist you with portfolio allocation always.

With that being said, I am going to look at AUM fees in a way that you may not be familiar with.  A significant number of induvial investors do not need all the services that financial professionals offer (e.g. tax planning, trusts, charitable giving, and more).  I can tell you already that the financial services industry is not happy with and/or does not agree with this presentation.  However, my only goal (the overarching goal of a good portion of my blog too) is to help you and provide you with an argument that may finally give you the impetus to manage your own investments or think seriously about working with a financial planner that charges fees on an hourly basis or a flat fee.

I also encourage you to read The Wall Street Journal newspaper for October 5, 2012.  On the bottom of the Business & Finance section, Jason Zweig discusses the many conflicts of interest that Financial Advisors have.  FINRA (a Self-Regulatory Organization comprised of all brokerage firms) issued a 22,000-word report about fees, conflicts, and compensation of Financial Advisors.  Oddly enough, the words “advice” and “investing” showed up less than 10 times.  The financial services industry is concerned about this matter, so you should take note and learn much more about what you are paying for.

Here is a link to the above article:

The next article will start off with individual investors that are currently in retirement.  Then another article will come out which discusses the same ramifications for individual investors that are currently saving for retirement.

Happy New Year, Beginning Thoughts, and Information for International Viewers


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I am looking forward to sharing more information regarding investing, finance, economics, and general knowledge about the financial services industry in 2020.  I am hopeful to increase the pace with which I publish new information.  Additionally, I am happy to announce that I reached viewers in 108 countries in all six continents.  Countries from Japan, France, Germany, and Russia to Ghana, Colombia, and even Nepal.

Since the number of my international viewers has grown to nearly 30% of overall viewers of this blog I wanted to allocate a short potion of this post to the international community.  Some of my comments are most applicable to the US financial markets or the developed markets across the globe.  If you are living in a country that is considered part of the developing markets, I would strongly recommend that you seek out information in your country to see how much of my commentary is applicable to your stock or bond market and situation in general.  It is extremely important to realize that tax structure, transparency of information, and illiquidity of stock and bond can alter the value of what I might say.  During the course of the coming year, I will attempt to add in some comments to clarify the applicability.  However, as the aforementioned statistic regarding the global diversity of viewers of this blog suggests, I would be remiss if I did not acknowledge that I will not hit on all the issues important to all international individual investors.

I encourage you to take a close look at your portfolio early on in 2020.  It is a perfect time in terms of naturally wanting to divide up investing into calendar increments.  As you listen to all the predictions for the New Year, I would encourage you to look at your personal portfolio and financial goals first.  The second step is to always look at that economist’s or analyst’s predictions at the beginning of 2019.  Now I am not implying that incorrect recommendations in the previous year will mean that 2020 investing advice will be incorrect as well.

To help you with a potential way to look at the outlook for positioning your portfolio of investments, I recently published a summary on the topic of rebalancing a portfolio.  You can find the link below:

Now, there will always be unknown items on the horizon that make investing risky.  You hear that we need to get more visibility before investing in one particular asset class or another.  It usually means that the analyst wants to be even more certain how the global economy will unfold prior to investing.  I will remove the anticipation for you.  There will only be a certain level of confidence at any time in the financial markets.

One can always come up with reasons to not invest in stocks, bonds, or other financial assets.  The corollary also is true.  It can be tempting to believe that it is now finally “safe” to invest even more aggressively in risky stocks, bonds, or other assets.  As difficult as it might be, you need to try to take the “emotion” of the investing process.  Try to think of your portfolio as a number rather than a dollar amount.  Yes, this is extremely difficult to do.  But I would argue that it is much easier to look at asset allocation and building a portfolio if you think of the math as applied to a number instead of the dollars you have.  Emotional reaction is what leads to “buying high and selling low” or blindly following the “hot money”; that is when rationality breaks down.

Here is an experiment for you to do if you are able.  There are two shows I would recommend watching once a week.  The first show is Squawk Box on CNBC on Monday which airs from 6:00am-9:00am EST.  The second show is the Closing Bell on CNBC on Friday afternoon which airs from 3:00pm-5:00pm EST.  You only need to watch the last hour though once the stock and bond markets are closed.  Note that these shows do air each day of the week.  Now depending on whether or not you have the ability to tape these shows first and skip through commercials, this exercise will take you roughly 12-16 hours throughout the month of January.  You will be amazed at how different the stock and bond markets are interpreted in this manner.

When you remove the daily bursts of information, I am willing to bet that you will notice two things:

Firstly, Friday’s show should demonstrate that many “experts” got the weekly direction of the market wrong.  It is nearly impossible to predict the direction of the stock market over such a short period.

Secondly, Monday’s show should illustrate what a discussion of all the issues that have relatively more importance are.  However, this is not always a true statement though.  Generally though, financial commentators and guests appearing on the show will have had the entire weekend to reflect on developments in the global financial markets and current events.  Since the stock, bond, and foreign exchange markets are closed on Saturday and Sunday, there is “forced” reflection for most institutional investors, asset managers, research analysts, economists, and traders.  The information provided is usually much more thoughtful and insightful.

I believe that the exercise will encourage you to spend less time attempting to know everything about the markets; rather, it may be more helpful to carefully allocate your time to learning about the financial markets.  After you devote your time to watching CNBC in this experiment, I recommend one other ongoing personal experiment.  Try picking three financial market guests that appear on CNBC during January and see how closely their predictions match reality.  You might want to check in once a month or so.  I think that this exercise will show you how futile it is to try and time and predict the direction/magnitude of the stock market and other financial markets too (e.g. bonds and real estate).

Best of luck to you in 2020!  As always, I would encourage anyone to send in comments or suggestions for future topics to my email address at

Rebalancing Your Investment Portfolio – Overview


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With the end of the year fast approaching, it is an excellent time to discuss the concept of rebalancing one’s investment portfolio.  The simplest definition of rebalancing is the periodic reallocation of an investment portfolio back to the original percentages desired.  The fluctuations of the financial markets over time will inevitably alter the amount of exposure in one’s investment portfolio to different types of assets.  The jargon in the financial services industry is your asset allocation

These changes may cause the portfolio to be suboptimal given an individual investor’s financial goals and tolerance for risk.  Knowing about rebalancing is so important because it is one of the most effective ways to eliminate, or at least reduce, the emotions surrounding investment decisions that affect even professional investors.  Additionally, numerous academic studies have concluded that 85% of the overall return of an investment portfolio comes from asset allocation.

I published a three-part series of articles to define and explain the various nuances of rebalancing an individual investor’s investment portfolio several years ago.  However, I thought that it would be a great idea to bring it back as an updated version because the end of the year is fast approaching.  The first article covers the definition of rebalancing in its entirety.  Furthermore, the article looks at an illustration of how rebalancing works in the real world.  It offers an introduction to this important investing tool.  The link to the complete article can be found here:

The second article discusses a unique way to get assistance with rebalancing an investment portfolio.  Many of the largest asset managers in the financial services industry, such as Vanguard, Fidelity, and T Rowe Price, offer life cycle or target date mutual funds.  These mutual funds have a predefined year that the individual investor intends to retire.  Moreover, the combination of assets in the mutual fund is structured to change over time and become less risky as the target date approaches.

Since these mutual funds report their holdings on a periodic basis, any individual investor is able to replicate the strategy for free.  Plus, another feature is that an individual investor can be more conservative or aggressive than his/her age warrants according to the mutual fund family’s calculations.  The individual investor is able to pick a target date closer than the endpoint (i.e. more conservative) or pick a target date later than the endpoint (i.e. more aggressive).  For a more comprehensive discussion of this facet of rebalancing an investment portfolio follow this link:

The third and final article discusses the most advanced feature of rebalancing utilized by a subset of individual investors.  The investing strategy is referred to as dynamic rebalancing in most investment circles.  Dynamic rebalancing follows the general tenets of rebalancing.  However, it allows the individual investor to exercise more flexibility during the rebalancing process of the investment portfolio.  Essentially the individual investor determines bands or ranges of acceptable exposures to asset classes or components within the investment portfolio.

For example, a lower bound and upper bound for the asset allocation percentage to stocks is set.  The individual investor is free to allocate monies to stocks no less than the lower bound and no more than the upper bound.  Note that the bands or ranges are normally fairly tight and applies to the subcomponents of the investment portfolio, such as small cap stocks, emerging market stocks, international bonds, and so forth.  To learn more about this fairly complex aspect of rebalancing follow this link:

The articles above capture the vast majority of information individual investors need to know about rebalancing an investment portfolio.  It is good to get a head start on learning about or reviewing this topic prior to the end of the year.  The reason is that most rebalancing plans utilize the end of the calendar year as the periodic adjustment timeframe.

Top Five Investing Articles for Individual Investors Read in 2019


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As the end of 2019 looms, I wanted to share a recap of the five most viewed articles I have written over the past year.  The list is in descending order of overall views.  Additionally, I have included the top viewed article of all time on my investing blog.  Individual investors have consistently been coming back to that one article.

1. Before You Take Any Investment, Advice Consider the Source – Version 2.0

Here is a link to the article:

This article discusses the fact that even financial professionals have cognitive biases, not just individual investors.  I include myself in the discussion, talk about Warren Buffett, and also give some context around financial market history to understand how and why financial professionals fall victim to these cognitive biases.

2.  How to Become a Successful Long-Term Investor – Understanding Stock Market Returns – 1 of 3

Here is a link to the article:

It is paramount to remember that you need to understand at least some of the history of stock market returns prior to investing one dollar in stocks.  Without that understanding, you unknowingly set yourself up for constant failure throughout your investing career.

3.  How to Become a Successful Long-Term Investor – Understanding Risk – 2 of 3

Here is a link to the article:

This second article in the series talks about how to assess your risk for stocks by incorporating what the past history of stock market returns has been.  If you know about the past, you can better prepare yourself for the future and develop a more accurate risk tolerance that will guide you to investing in the proper portfolios of stocks, bonds, cash, and other assets.

4.  Breakthrough Drugs, Anecdotes, and Statistics – Statistics and Time Series Data – 2 of 3

Here is a link to the article:

I go into detail, without getting too granular and focusing on math, about why statistics and time series data can be misused by even financial market professionals.  Additionally, you need to be aware of some of the presentations, articles, and comments that financial professionals use.  If they make these errors, you will be able to take their comments “with a grain of salt”.

5.  Breakthrough Drugs, Anecdotes, and Statistics – Introduction – 1 of 3

Here is a link to the article:

I kick off this important discussion about the misleading and/or misuse of statistics by the financial media sometimes with an example of the testing done on new drugs.  Once you understand why the FDA includes so many people in its drug trials, you can utilize that thought process when you are bombarded with information from the print and television financial media.  Oftentimes, the statistics cited are truly just anecdotal and offer you absolutely no guidance on how to invest.

                                       Top of All Time

Are Your Financial Advisor’s Fees Reasonable?  Here is a Unique Way to Look at What Clients Pay For

Here is a link to the article:

This article gets the most views and is quite possibly the most controversial.  Individual investors compliment me on its contents while Financial Advisors have lots of complaints.  Keep in mind that my overall goal with this investing blog is to provide individual investors with information that can be used.  Many times though, the information is something that some in the financial industry would rather not talk about.

The basic premise is to remember that, when it comes to investing fees, you need to start with the realization that you have the money going into your investment portfolio to begin with.  Your first option would be to simply keep it in a checking or savings account.  It is very common to be charged a financial advisory fee based upon the total amount in your brokerage account and the most common is 1%.  For example, if you have $250,000 in all, your annual fee would be $2,500 ($250,000 * 1%).

But at the end of the day, the value provided by your investment advisory is how much your brokerage account will grow in the absence of what you can already do yourself.  Essentially you divide your fee by the increase in your brokerage account that year.  Going back to the same example, if your account increases by $20,000 during the year, your actual annual fee based upon the value of the advice you receive is 12.5% ($2,500 divided by $20,000).  And yes, this way of looking at investing fees is unique and doesn’t always sit well with some financial professionals.

In summary and in reference to the entire list, I hope you enjoy this list of articles from the past year.  If you have any investing topics that would be beneficial to cover in 2020, please feel free to leave the suggestions in the comments.

Breakthrough Drugs, Statistics, and Anecdotes: Three Things Every Individual Investor Needs to Know – Yield Curve Inversion and Recession – Part 3 of 3


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Here is the last article related to our discussion of observations by the financial media with only a handful of observations, statistics, and time series data.  The goal here is to provide an actual example to see what some of the pitfalls are.  Prior to starting that discussion, I wanted to provide links to the first and second articles:

The first article laid the groundwork for the idea that there are many misuses of statistics and related items which appear most everyday in the print and television financial media.  Here is a link:

The second article focused more on time series data and using the normal distribution to make conclusions and predictions about the financial markets.  As promised, I will be posting a more detailed mathematical article as a supplement.  However, the point of this article is only to make you aware of what to look for in general.  You do not need to feel the need to get very granular.  The audience that really wants more information has contacted me offline and is very small.  Here is a link:

Now let’s begin our journey to sum up these two articles by using the specific example of a “yield curve inversion”.  First, what exactly is the yield curve?  Okay, we are going to keep this explanation simple.  The point of this article is not to become an expert on bond yields.  The yield curve is simply the interest rate (referred to as “coupon” in the financial jargon) of bonds at certain maturities.  For U.S. Treasury issues, you normally look at the interest rate on one-month, three-month, and six-month  U.S. Treasury Bills.  Then you add in one-year, two-year, three-year, five-year, seven-year, and ten-year U.S. Treasury Notes.  And finally, you have the thirty-year Treasury Bonds (otherwise referred to as the “long bond” in financial jargon).  Why bills, notes, and bond?  It is simply a naming convention for all U.S. Treasury debt less than twelve-months is a bill, between one-year and ten-years is a note, and anything greater than ten-years is a bond.  Once you know all those interest rates, you draw a line that connects all of those interest rates from one-month U.S. Treasury Bills all the way to thirty-year U.S. Treasury Bonds.

Why do people focus on this?  Well, first, you would expect that interest rates for one-month bills to be lower than thirty-year bonds.  Think of it like this:  if your friend borrowed $20 and was going to pay you back at the end of the week or in three years.  What interest rate would you charge him/her?  Now a totally altruistic person would say nothing.  But let’s say you are trying to teach your kids the value of money.  Most people would charge a greater amount of interest for three years compared to one week.  The U.S. Treasury debt market works very similarly.  People who loan the government money for one month normally demand a lower interest rate than those people who are going to have to wait thirty years to get their money back.  When the economy is growing normally, the yield curve is called steep.  It goes from lower interest rates and gradually moves higher.  But that is not the only shape of the yield curve possible.

The other two are flat and inverted.  A flat yield curve simply means that interest rates all along the various maturities are pretty much the same.  Now, as our article will shift to, an inverted yield curve means that closer maturities actually have a higher interest rate than the very long-term maturities.  Why does this happen?  Well, most economists and financial professionals will tell you that the economy is slowing down and a recession is coming.  Why?  The last 7-8 recessions were preceded by a yield curve inversion.  Let’s take a look at the yield curve over time by comparing two-year U.S. Treasury Notes with ten-year U.S. Treasury Notes.  Keep in mind that we are taking a look at the difference between the two.  A number that is positive means that interest rates are higher for ten-year bonds and a negative number means just the opposite.

Here is a daily comparison from June 1, 1976 through November 6, 2019:

Daily Spreads - All Data

Here is the same comparison but on a monthly basis:

Monthly Spreads - All Data

I used a graph of the month difference (“spread”) to smooth out some of the volatility.  Now if you remember your economic history, you will notice that there are negative “spreads” that occur prior to a downturn in the U.S. economy.  Let’s focus on the yield curve inversion prior to the Financial Crisis.  As you can see, the yield curve was inverted at various times over the course of 2006 to 2008.  It took approximately two years from the yield curve inversion before the Financial Crisis hit in full force in September 2008.  Because this pattern has occurred before, economists and financial professionals appearing on television or writing articles have pointed to the yield curve inversion just recently.

But you should take a closer look at the latest inversion of the yield curve.  It is only a small difference and only lasted for a short period of time.  I will blow it up to investigate and will show November 1, 2018 through October 31, 2019:

Daily Spreads - 2018 to 2019

I had to use a one-year timeframe to even be able to get the difference in interest rates to show up.  So, for a period during August 2019 and September 2019,  there were a plethora of financial markets’ articles and television commentators who talked about how soon a recession would take place in the U.S. economy.  In fact, there were days when over 25% of the day’s coverage of financial market news focused only on this yield curve inversion.  Now, will the U.S. economy go into recession in the next 12-24 months?  Well, that is still an open question.  The main point is that the financial news media focus on things that have similar patterns for only a brief period of time.  Even worse though, financial “experts” who know very little about the bond market and economics start making predictions.  And, as I have said many times in the past, the financial news media rarely, if ever, invites guests back or has another article written about how wrong they were.

Lastly, you will sometimes here people say that there is a 30% chance that the U.S. economy will enter a recession in the next 12-24 months.  Where does that percentage come from?  Oftentimes, it is a “best guess”.  Unless you hear that same financial professional talk about a probity econometric model that came up with that percentage of recession probability, you should take the comment with a “grain of salt”.  Trust me though, most financial professionals are not running probit models when they tell you their opinion on this matter (related to an inverted yield curve or due to another topics/event).  In the supplemental article that is forthcoming, I will actually discuss a panel probit model that the Bank of International Settlements (BIS) just ran to look at the phenomenon of yield curve inversion preceding a recession in an economy.  It is not that the percentages derived are “correct” per se.  The important point is that they are not “pulled out of a hat” by someone.

I hope that this series of articles has been helpful in covering this important topic.  The main takeaway is that, whenever you hear or read about a financial market prediction, you should always look to see how many examples (observations) are being used.  If it is less than 30, you should not take it very seriously at all.  Additionally, any time series data that is trending upward or downward cannot be used to talk about the financial markets.  Remember you need to first-difference the time series data or adjust it in some other manner.  Why?  Otherwise, there may be correlations between two or more time series that just are not really there because the trend dominates.  (Please refer to the second article for more information in this regard).  So, please be more aware and skeptical of what you hear or read.  It is not that the information/prediction is totally wrong.  The salient thing is that it should be based on sound statistics and mathematics.

Breakthrough Drugs, Statistics, and Anecdotes: Three Things Every Individual Investor Needs to Know – Statistics and Time Series Data – Part 2 of 3


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The first article of this three-part series covered the broad strokes of this issues to be aware of in terms of all the “data” and “relationships” that get thrown around by the financial media (print and television).  Most of the discussion uses data points that are not statistically significant to draw any sort of conclusion.  In fact, time series data is notoriously hard to model and predict the future.  Additionally, the specific time series data of stock market returns is even more difficult.

You can refer to the link below to examine the content of the first article:

The task at hand for the second article is to put some “meat on the bones” of the discussion.  I realize that anything to do with math and statistics is not easy for everyone (or of interest either).  Therefore, I will be writing a supplemental article that covers the mathematics and statistics in more detail.  The goal here is to be able to identify some of the more common errors that you will encounter.

The first item to talk about is any sort of data that has a substantial trend component.  In layman’s terms, there is a data series where the line graph goes up or down in more of a straight-line manner.  You can think of the Gross Domestic Product (GDP) of the United States here.  Every year the GDP figures will generally go up unless there is a recession.  But, even after the recession passes, the trend for GDP will resume upward.  So, where does the problem come in?

I am going to give a contrived example to illustrate why it is dangerous to compare two series that are trending.  The example will consist of two different equations which are trends.  Both have the same trend component and an error term (we will call that eta).  The variables will be exactly the opposite.  More specifically, the two equations we will use are the following:

Trend_1 = Time + 100 + 0.9 * x + eta

Trend_2 = Time +100 – 0.9 * x + eta

Now the x values and eta values were simply generated by selected variables at random between 0 and 1.  The eta values were also selected at random between 0 and 1.  You can think of eta as representing the general “noise” that occurs on a daily basis when observing stock prices in the financial markets.  So, let’s graph the first 100 observations for these two equations:


You will notice that the trend component dominates the line graphs.  However, we know by construction that the two equations which produce trend_1 and trend_2 are fundamentally different.  Now the correlation coefficient between those two equations is 0.9984.  A correlation coefficient of 1 means that the two lines move in lockstep.  Why is this important?  Why is it very dangerous?

Well, financial pundits will talk about these types of graphs all the time.  It looks like there is some relationship, but we know there is very little relationship between the two trends.  In fact, we can look at these equations by subtracting the current value from the previous value to see what changes.   Formally, this topic is called first differencing.  It will allow us to see more clearly what we already know.  Here is the graph:


Now we have a totally different picture.  We can see that at many times the two trend equations are moving in exactly the opposite direction.  In fact, the correlation coefficient for the first-differenced equations is 0.2675.  There is only a slight positive relationship between the two trends.

In the example above, we can see that looking at the two trends is very deceiving.  Remember that I added the eta term to represent “noise” that is always present in financial market data.  So, anytime someone talks to you about the comparison of two trends, you should be very skeptical.  You always want to see first-differenced data or at least a comparison of changes in some manner.  Otherwise, you will mistakenly assume that there is a strong positive or negative relationship between two time series.

The second example that I am going to use is stock market returns for the S&P 500 Index from 1966 through 2018.  Why start at 1966?  Well, the S&P 500 Index started with its current number of component stocks back in 1957, and I would like to show annual stock returns and also ten-year annualized returns.  This particular topic can get messy quite quickly, so I am not going to cover it in a lot of depth with statistical and mathematical jargon.  For those of you who are interested, I had mentioned that it will be contained in a forthcoming supplemental article.

A great many individuals in the financial markets talk about stock market returns in the same breath as the normal distribution.  What is the normal distribution?  It is the old bell curve that you are familiar with.  The normal distribution is symmetrical and tails off at the end as more and more data points are gathered.  Well, stock market returns are anything but strongly normal.

Let’s first take a look at one-year stock market returns for the S&P 500 Index.

One Year Returns - Histogram - Non Normal

A useful test to see if a particular distribution is normal is the Jarque-Bera test.  Now it is not necessary to know exactly what is being calculated.  However, you should refer to the bottom of the box that reads “Probability”.  The value of 0.179 is called a p-value.  A p-value less than or equal to 0.10 means that we can reject the hypothesis that the one-year distribution of stock returns is normal.  At a value of 0.179, we would not reject the hypothesis of normality for this distribution.  However, the p-value in our case is not large enough to be totally sure and confident. But what about looking at annualized stock market returns over ten-year periods?

We can look at a similar graph to check to see if stock market returns over longer timeframes are indeed akin to the normal distribution (i.e. the bell curve).  Here is the graph:

Ten Year Returns - Histogram - Non Normal

Looking at the same “Probability” value, we have 0.489.  Therefore, we cannot reject the hypothesis that these stock market returns follow a normal distribution. Looking at ten-year annualized stock market data tells us that we can use the normal distribution as an assumption for calculating statistics.

Now why does this matter?  Well, you will here over and over again statistics that apply only to the normal distribution in relationship to actual, observed stock market returns.  We have just seen that stock market returns over the short-term stock returns weakly follow the normal distribution. On the other hand, long-term stock returns are definitely normal. Now I will not get into the technicalities, but time series data is indeed asymptotically normal.  What?  Say again?

This is just a fancy way of saying that, as the number of data points (sample size) approaches infinitely, the time series will look like the normal distribution.  Pretty much all financial market and economic data have very few data points.  In fact, you usually need several hundred data points prior to making any assumptions and using the statistics related to the normal distribution (think standard deviation or correlation coefficients).

Thus, most of the banter in the financial media is just subjective notions of what is going on in the stock market and the economy. More often than not, an assertion by someone in the financial print or television media is more of an educated guess than based on a solid mathematical foundation. That fact explains why financial pundits hedge their statements. Like I say half-jokingly, “I see the stock market going up in the next several months, but of course it might not resume its uptrend or could even take a leg downward”.

Well yes, I guarantee you that every day stocks will go up, down, or remain unchanged. This type of daily commentary in the financial press about the short-term performance of stocks (or other financial assets) is just not helpful and can be downright distracting you from investing for your long-term financial goals.

I apologize for getting too detailed in certain parts of this article.  What are the key takeaways?  First, you should be extremely leery of drawing any conclusions from the comparison of two or more data series that are trending upward or downward.  Second, you need to have several hundred observations prior to invoking any reference to the normal distribution.  So, what is left after that?  As you might imagine, there are not too many comparisons or studies that pass the muster to give you insights on investing or actionable information to make changes to your investment portfolio.

Don’t focus on the mathematics or statistics.  All you need to remember are the two takeaways above.  And, first and foremost, you should always be skeptical whenever you are presented with comparisons and statistics related to the financial market or the economy as a whole.

Breakthrough Drugs, Statistics, and Anecdotes: Three Things Every Individual Investor Needs to Know – Part 1 of 3


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Although the title might appear to be random at first glance, I promise that there is an underlying theme.  This article is the first in a three-part series that will discuss how individual investors are bombarded with information about what happens in the financial market.  Most of the time you might hear that, 5 out of the last 7 times “x” happened, the S&P 500 index went up by 10% or more.  I will argue that most of these types of comments might be useful trivia for the television show, Jeopardy; however, they should not impact your long-term investment plan.

So, why did I use breakthrough drugs?  Prior to any drug coming to the marketplace, the FDA does a very thorough review of the test results to ensure that the drug is safe and also its efficacy is not overstated.  What if I told you that a pharmaceutical firm came up with a possible cure for lung cancer, and there were successful trials of 10 individuals.  Does that sound like a group too small to draw any conclusions?  Would you take a drug that the testing was only done on a handful of people?  Now the FDA would never allow such a thing, and there are tons of protocols and blind or double-blind randomized testing of many individuals.  It just sounds weird if only 10 people were tested, and there was also no control group (i.e. a separate group given a placebo).

While the drug example seems a bit outrageous and contrived, I bet you can think of similar examples in the daily financial press (e.g. financial television or print media).  Whenever you hear a small number of events happening that “tend to” lead to certain financial market outcomes, you should be extremely wary.  For instance, I just heard today that, after the Singles Day huge ecommerce sale by Alibaba, the stock (Ticker Symbol:  BABA) is up 80% of the time over the course of the next two weeks.  Well, when did Alibaba start Singles Day?  The first Singles Day sale was in 2009.  Therefore, we have 10 data points to work with (2009 to 2018).  Given the information I referred to above, the comment made today simply says that the stock has been up after two weeks 8 out of the last 10 years.  Now I will try to hold in my red flags and bit of ludicrous thoughts, this type of information is not informative at all.  There are just too few observations to draw any sort of valid conclusion.

Here is the plan of attack for the next two articles.  The second part of this discussion will focus on statistics.  Yes, I know this topic is not too much fun and can get complicated very quickly.  However, individual investors need to know a bit about statistics to recognize when a quantitative quote is totally useless.  We will not get too granular though, I promise.  Essentially most financial market data is time series data.  Different rules apply in that case, and these rules are broken all the time by even the most sophisticated professional investors and commentators.  The third part of this discussion will be an in-depth examination of an actual event that grounds my argument in recent events.  I will examine what is called the inversion of the yield curve and how it normally portends a recession for the U.S. economy.  Don’t worry; I am going to explain those terms when the third part of this series rolls around.

Please join me in a critical review of all the financial market and economic data you get bombarded with.  So much of it is just “noise” or simply interesting trivia at best.  Note that the interesting trivia cannot guide or inform your particular asset allocation of investments.  As always, if you have questions along the way, please feel free to comment on this or any other article.

Individual Investors Should Treat Obtaining Financial Advice Like Buying a New Car


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I had a long conversation with a friend and business associate about how I think individual investors approach obtaining financial advice.  We went back and forth for almost 30 minutes.  However, I found myself stumbling upon the analogy of purchasing a new vehicle.  This analogy encapsulates how individual investors might want to think about building their investment portfolios, setting financial goals and how to obtain them, establishing their risk tolerance, and addressing any special situations that might pertain to their specific situation (e.g. caring for an elderly parent in their house).  I should state at the outset that, if you have more than $1 million in investable assets (i.e. an accredited investor), the size of your portfolio demands special attention.  If you have not amassed $1 million, please read on to the rest of this article.

First, I would like to lay out the typical new vehicle purchase scenario and then turn to its applicability in the case of financial advice.  Most people start off the process by doing a good deal of research on the available options.  After considering his/her situation, the individual will go to the vehicle dealership.  For the purposes of this particular example, let’s suppose that the vehicle dealership offers a number of different car manufacturers as options and then the various models associated with them.  Luckily today, there is a lot less haggling (well at least upfront in the process) and the vehicles’ prices are normally right around the MSRP.  However, you as a consumer need to select the car make and also the specific model.

Usually a salesperson will assist you with the process.  Even though you can do a lot of homework prior to picking out a new vehicle, it still does not fully capture actually looking at the vehicle.  Of course, you also need to sit in it and take a test drive.  The salesperson is able to translate what your needs are to try to select the best option.  For example, do you need to transport the kids to basketball practice?  What if you take turns carpooling and pick up an extra 3-6 kids?  How big should your SUV be?  What if you drive a lot of highway miles and a lease option may not work for you?  Do you like to have a decent amount of horsepower to be able to merge onto highway traffic?  What about the manufacturer’s warranty?  Does the dealership service the vehicles onsite?  What about financing options (i.e. buy or lease)?  The list of questions could go on and on.

Given the entire list of questions you might ask, the salesperson is an integral part of the vehicle buying, or leasing, process.  After the salesperson has finally answered all of your questions, let’s say you decide on a price, the financing options, and the color/options/model.  If you make the purchase, the salesperson will earn a commission.  Once you leave the dealership’s parking lot, you are then responsible for the maintenance of the vehicle.  Fingers crossed, you should only need to take car of oil changes and normal maintenance (e.g. changing the air filter, flushing the transmission fluid, etc.).  What would you do if the salesperson came over to your house and wanted to check if you were still pleased with the vehicle you selected in the second year?  Does it fit your needs and perform as expected?  Wow, that experience would be one of pretty good customer services.  But now, the salesperson’s next utterance is that you own him/her $500.  What?  Well, he/she responds that he/she helped you out and things are going according to plan.  My guess is that you would be dumbfounded and refuse to pay another commission to the salesperson in year two of ownership.

What in the world does this have to do with financial advice?  I would argue that the analogy fits quite well with the normal way financial advice is given to individual investors.  When you first sit down with a Financial Planner, Financial Advisor, or Registered Investment Advisor, he or she really walks through your entire life situation.  Additionally, that person will assess your tolerance for risk which is not always as easy as it sounds.  Usually most financial professionals will include questions that relate to your behavior under certain instances of financial market conditions.  So, you cannot simply ask only objective yes/no questions.  Other big thing that may come up are any insurance, tax planning, or estate planning needs that you have.  Another significant area is trying to find out if you might have any special circumstances.  The caring of an elderly parent was provided above.  But there are myriad other situations that might require special planning considerations unique to your family.

The vast majority of financial professionals no longer charge commissions.  Rather, they will charge a fee based upon the total asset in your portfolio of stocks, bonds, other assets, and cash.  The financial services industry calls this an AUM (assets under management) fee in the jargon, and a very typical fee that one will see is 1%.  What does that mean?  Well, to use round numbers, let’s say you have $1 million dollars in your account of financial assets.  You would then pay a fee of $10,000 ($1 million * 1%).  To be technical though, the fee is normally prorated over four quarters throughout the year and not in one lump sum.  Given all the assistance that I listed in the previous paragraph, there is no doubt that the financial professional earns his or his AUM fee.  But what happens when year two of your financial relationship begins?

For illustrative purposes, I am going to assume that your life situation does not change at all.  In the first year of your relationship with the financial professional, he or she is likely to have prepared an asset allocation for at least the next five years.  One would expect a long-term investing plan.  Of course, he or she may recommend that based, upon the price movement in the financial markets, you should reallocate your investments to either the same target allocation in year one or slightly different percentages.  He or she may even recommend that you sell a particular investment and replace it with what he or she deems to be a better performing investment vehicle for the future.  Well, to keep using round numbers, if your investment portfolio stays constant, you would pay another $10,000 (again $1 million * 1%).

The year two situation is akin to car maintenance in year two of your ownership of that vehicle from my car vehicle purchase analogy.  Now, if you blew a head gasket in your car’s engine, you would want to take the vehicle back to the dealership or go to a trusted mechanic.  The latter represents a major change in your life situation, financial goals, income tax ramifications, and other major events.  Otherwise, we have a situation where you are paying the car salesperson another commission in year two.  Now my analogy may not be entirely “apples to apples” (as my business associate said during our discussion).  However, it is close enough to get to the point that I am trying to make in terms of financial advice.  You need to be very cautious with how much money you pay in expenses for financial advice.  Why?  It really eats into the investment performance returns you will realize.  I am all for paying for financial advice when there is a complicated situation, but, if nothing of import changes, it can be hard to justify.

So, what can you do if my analogy resonates with you?  Well, there are two options that I will provide.  However, there are other avenues to proceed down.  I will discuss each in turn.

First, you can select a financial professional that charges a fee-only amount or one that charges by the hour.  The fee-only financial professional will charge you a set amount per year for financial advice, and, in almost all cases, it is significantly lower than the $10,000 in our example.  The hourly financial professional is just as it sounds.  In the second year, you might require 10 hours of financial advice throughout the year, some of which might include just coaching you through the inevitable volatility in financial markets.  Depending on the area that you reside in, you can expect to pay anywhere between $250 to $500 per hour.  Using the 10-hour amount, you would be paying anywhere from $2,500 ($250 * 10 hours) and $5,000 ($500 * 10 hours).  Using either type of financial professional with a different fee structure will lower your overall investment fees.  Note that the quality of financial advice usually does not decrease in most cases.  And yes, there are certain cases where the quality will increase markedly.

Second, you can use an external investment account at the beginning of your relationship with a financial professional that charges a percentage of assets under management (AUM).  What does this mean?  The vast majority of asset managers are large and sophisticated enough to handle this arrangement at the outset.  For example, you would establish an investment account where your financial professional is located.  Next, you would establish an investment account with another brokerage firm and allow your financial professional to have access to the investment portfolio you maintain.  Note that the access is only for purposes of preparing reports for you and not to execute actual trades of stocks, bonds, mutual funds, or any other financial asset.  For instance, you might keep 50% with the financial professional’s firm and another 50% in the external account.  You would just maintain the portfolio allocation that your financial professional would like you to have in the external account.  In order to ensure that you do not deviate from his or her investment recommendations, your monthly or quarterly investment performance reports would lump together the assets at the financial professional’s firm and your external account.

In regard to the second option, just because asset managers can easily do this reporting for you, does not mean that they will not push back.  Some asset managers and financial professionals get even confrontational.  It is understandable since the more assets you maintain at their firm the larger the investment advice fee.  But this response can be very informative for you.  If your financial professional does not handle your request of this potential option diplomatically, this may be a cue to seek financial advice elsewhere.

So, have I successfully convinced you that buying investment advice is just like buying or leasing a new vehicle?  My guess would be that you think the analogy is not a perfect one.  I will readily admit that it is not and really is not meant to be.  Rather, I wanted to get you thinking about the financial advice you receive and investment fees from another viewpoint.  Investment fees have an outsized effect on the returns that you will experience over time.

Their impact is even greater if you take into account the “opportunity cost” of investment fees.  However, that is another topic entirely that I will not delve into.  If you would like more information on the idea of “opportunity cost” and investment fees, you can refer to a previous article that I wrote.  Here is the link:

Now that Commissions on Stock Trades Are Zero, Should You Start Trading Stocks?


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Quite recently, Charles Schwab (an e-broker) announced that they would no longer be charging commissions on stock trades.  Shortly thereafter, TD Ameritrade, E*TRADE, Interactive Brokers, and Fidelity Investments all followed suit.  A financial technology (fintech) firm, Robinhood already offered commission-free trading.  So essentially, anywhere you open up a brokerage account to trade stocks, you will not have to pay any commissions.  The question is…….should you start trading stocks?

The aforementioned question is difficult to answer in relation to all the types of people that are reading this article.  However, whether or not you decide to trade stocks, I simply want to ensure that you are using the proper benchmark to gauge your success in terms of the performance returns you achieve.  Now I am assuming that, since you are trading stocks, the assets are held in a taxable brokerage account.  Furthermore, an active trader is likely to have a holding period for those stocks that is less than 365 days.  Therefore, the gains are fully taxable as ordinary income.  With that groundwork laid, let’s move on to a further analysis.

Trading stocks and “beating the stock market” is an extraordinarily difficult task to do.  Most of the professional asset managers fail to beat their respective benchmarks for performance returns.  Additionally, trading stocks in the short term requires two things:  gauging market sentiment correctly and the valuation of the stock based upon its fundamentals.  You have to be right on both accounts.  There are many times when a company has a ton of good announcements that should cause the stock price to increase, but other factors hinder the upward movement in the stock price.  Examples include:  negative sentiment about the stock market in general, negative sentiment about the industry the company is in, geopolitical uncertainty, poor economic data, central bank (Federal Reserve) policy, and many others.  The bottom line is that you can be exactly correct on positive news for the stock you are buying, but, if there are negative overhangs in the stock market for any reason, the stock price may not go up.

Another word of caution is just to identify what it means to trade stocks in the short term.  Trading stocks in the short term is speculation, plain and simple.  Short-term trading is not investing at all.  There are myriad reasons why, but I will not address that in this article.  Just know that you are a trader who is speculating on stocks and market sentiment related to the stocks you choose to trade.  Any holding period of a stock less than one year does not meet the bar of what investing means.  As long as you know that going in, that is fine and I will not dissuade you in any way from trading.

The important thing to remember is that you need to gauge your performance in relation to the overall stock market based upon after-tax returns and not gross returns.  Why?  At the end of the day, you only care about the terminal value of the asset in your brokerage account.  What do I mean by terminal value?  Terminal value just means the amount of money you have after paying capital gains taxes as ordinary income.  For example, if you have a 10% return in your stocks and the S&P 500 Index is only up 8%, you need to look at your taxes too.  Just for illustrative purposes, let’s assume that your marginal rate for federal and state taxes is 25%.  If we go back to the 10% amount, you will have a 7.5% (10% – 10% * 25%) after-tax gain from trading.  Yes, you beat the stock market return on a gross basis, but you end up with 0.5% less after all is said and done.

I am going to use the historical returns of the S&P 500 Index from 1957 to 2018 as the benchmark that you should be referencing when examining your success (or failure) as a result of trading.  As I have mentioned in many prior articles, I use 1957 as the starting year because the S&P 500 Index was created in that year.  Prior to 1957, the S&P Index had less constituents so going back in history further than that year does not yield an apples-to-apples comparison.  The long-term historical return of the S&P 500 Index over that period was approximately 9.8%.  Therefore, I will use that historical return to reference the gross return versus after-tax return issues.

Here is a table to look at the performance return you need to equal just to be even with the S&P 500 Index after taxes:

Gross Returns Versus Tax Equivalent Returns

As you can see, the gross return equivalents in relation to the historical return of the S&P 500 Index range from 12.3% to 16.3% for the various marginal tax rates shown.  For instance, if you are in the 30% marginal tax bracket for federal and state income tax purposes, you will need to earn 14.0% returns just to break even.  Most people add or remove monies to their brokerage accounts over the course of any given year, so you need to adjust for those cash flows.  The computations are a little trickier and beyond the scope of this discussion.

Another important thing to take into account is the types of stocks you purchase.  The stocks included in the S&P 500 Index are very large companies by market capitalization (large caps).  Market capitalization is simply the number of shares outstanding times the stock price.  If you invest in very small stocks that you deem to be good trading opportunities, you should not be using the S&P 500 Index table above to do your calculations for after-tax returns.  For example, if you tend to invest in smaller companies, you would want to use the Russell 2000 Index or the S&P 600 Index.  For any companies below $1 billion in market capitalization, you should seek out what are called microcap indexes.  The best way to build your personal table is to use a “blended benchmark” for performance returns.  A “blended benchmark” is what large institutions and high net worth individuals use, and it is the gold standard because you are truly comparing apples-to-apples.

If you want to learn more about how to create your personal “blended benchmark”, I addressed that topic five years or so ago and here is the link to that article:

In summary, if you decide to trade individual stocks because commissions are zero now or you have always done so in the past, you need to compare your after-tax return to what you would have earned if you had simply bought the S&P 500 Index via an index mutual fund or an Exchange Traded Fund (ETF).  Why?  Those performance returns would be available to you if you simply invested in one.  Note that the fees on index mutual funds and ETFs are extremely low (0.05% or less and in some cases like Fidelity Investments are free).  You always want to select your next best alternative to measure whether or not you are earning more than the stock market on an after-tax basis.  Remember that all you really care about at the end of the day is how much money you have leftover in your brokerage account minus what you pay in federal and state income taxes.