The Big, Useful Lie

You probably recognize the picture below.  It’s the standard bell curve, used (and mis-used) by everyone from high school math teachers to insurance company actuaries, government officials, and news reporters.


You don’t need to know the math behind the bell curve in order to understand and apply its basic concepts: for all kinds of measurements, there are more average results than any others; and the farther away from the average, the fewer results.  So, the average person is of average height, but there are quite a few people who are either a few inches below or a few inches above that.  Very short and very tall people are more rare.  Again, the average car gets average gas mileage, but there are quite a few cars with close to typical fuel usage.  Serious gas guzzlers and extremely efficient cars are more rare.  And so on.

One of the most important things to understand about the standard, idealized bell curve is that it is a big, fat lie!  There are very few things in life that “fit” this perfect shape exactly.  But if it’s a lie, it’s a useful lie.  Even though few real life systems fit it exactly, many systems follow it approximately.  Including many types of financial investments, which is why I am talking about it.

Another critical concept is that the application of the bell curve depends on the “population” you are measuring.  Consider height, for example.  When we say someone is of average height, we have to ask: the “average” of what kind of people.  Everyone in the world?  North Americans of European descent?  Men?  Women?  Fifth graders?  Each of these groups has its own average and its own curve.  You can’t compare two results until you know what statistics were collected in the first place.

The width of the curve tells you how much variability there is between the largest and smallest numbers plotted on the curve.  Again, you don’t need the math to understand the concept:  the broader the set of observations plotted, the fatter the curve.  For example, the height of 30-year-old European males would vary less than the height of everybody on the planet.

Statisticians measure the width of the bell curve with a calculation called the “standard deviation,” which we will abbreviate SD.  We already discussed the fact that most numbers don’t exactly fit the bell curve, but if they did, the following would be true:  about two-thirds of the numbers would be within one SD of the average, 95% would be within two SDs of the average, and 99.7% would be within three SDs.  So we can compare the SD of two sets of numbers to see which set of numbers has more variability.

To see how this concept might apply to the world of personal finance, take a look at the graph below.  It shows the monthly return on investment for a popular Exchange-Traded Fund, SPY, for the last twenty years.  SPY represents an investment in the common stock of the 500 largest US companies, known as the “S&P 500.”  The blue bars show the actual data; the higher the bar, the more monthly returns were in the range shown.  The smooth red curve shows the idealized bell curve with the same average and SD as the return date for SPY.  As discussed above, SPY looks approximately, but not exactly, like the bell curve.


Here are some things to notice about SPY over the last 20 years.  The average monthly return was about 0.8% per month, meaning that in an average month, the value of an investment in SPY would have been 0.8% higher at the end of the month than at the beginning.  Any monthly return between negative 3.57% and positive 5.16% would have been within one SD of the average; any return between negative 7.94% and positive 9.52% would have been within two SDs.  This movement around from month to month is called “volatility” in the world of investment research.  Remember, these are monthly results.  Daily numbers would have been much more volatile!

What do these numbers tell us about how much money you would have made by investing in SPY?  As it turns out, not much.  That’s because an actual investor’s return would have been influenced not only by the average return, but the specific pattern by which the average result was achieved.  It turns out that if someone had invested $100 in SPY on September 1, 1993, re-investing all dividends and leaving the account alone, that account would have been worth $429 on September 3, 2013.  This works out to a monthly return of 1.09%, or an annual return of 13.87%.

Here’s another question: what do these numbers tell us about what SPY is expected to do in the future?  Well, these numbers tell us nothing about why SPY performed the way it did; they don’t predict anything about future economic conditions, future interest rates, or anything else that could influence stock market performance.  However, in the absence of a crystal ball, most investors use numbers like these to make decisions about future investments, realizing that caution is in order.

Remember that in order to interpret these numbers, we have to know what “population” we are talking about.  The statistics shown above apply specifically to the S&P 500.  A different SD would be observed for small company stocks, or stocks from another country, or other types of investments.

Standard Deviation is the core statistic used in almost all definitions of “risk” for financial purposes.  It’s an imperfect but extremely useful number.  Since the bell curve itself is a partial lie, SD is too.

The conventional wisdom is: given two possible investments with the same potential return, the one with the lower SD is the better choice; and, given two possible investments with the same SD, the one with the higher average return is the better choice, because you are getting a bigger reward for the amount of risk you are taking.   Investors are expected to require a higher return to compensate them for taking on more volatility in the value of their stocks.

This post is not an endorsement of SPY or any other specific investment.  I chose SPY for this discussion because it is a widely traded ETF and there is a lot of information available about it.  And it does illustrate a central point:  over the long run, the S&P 500 has delivered respectable returns, accompanied by significant volatility.   If you are investing for the long run, it makes sense to hold stocks as part of your portfolio, but only if you are investing for the long run, and only if you are prepared to weather the bell curve.


Forrest Gump and Your Finances

This little pep talk is brought to you by two famous lines from the movie “Forrest Gump:”

  • You never know what you’re gonna get.
  • S**t happens.

Recently, the Governor of Maryland, Jack Martell, wrote a great article about the need for financial education in the US.  In it, he points out that “half of all Americans say they could not pull together $2,000 in 30 days to fix a car or pay an unanticipated medical bill…”  (You can read his article here:

This is really sad.  These folks didn’t know what they were gonna get when they experienced their financial emergency.  The didn’t know that their transmission was going to conk out, or their kid was going to fall off the monkey bars and break her arm.  I don’t know what your emergency will be – and I certainly don’t with it upon you!  But it’s a sure bet that something unexpected is going to happen at some point. Even Forrest knew this, and we all know he wasn’t the sharpest crayon in the box. 

I would like every reader to make it a goal to belong to the other half: the one that does have a financial cushion for unexpected emergencies.  Future blog posts will talk about investing, retirement savings, and stuff like that; none of this will do you any good unless you have something put by.  Certainly Gov. Martell’s example of $2,000 would be a reasonable place to start.  Something like three months’ living expenses is a good long term savings goal.

I can’t tell you how to free up cash from your budget, but I hope to convince you that it’s necessary to do so. Credit card companies and payday lenders make a fortune out of transmission problems and playground accidents, but it doesn’t have to be that way.  Once you experience a minor emergency and realize you can handle it from your savings, it will feel good, and motivate you to keep on saving.

Money is always tight, and everybody’s budget is different.  I don’t know where you are going to find room in yours.  But if you want to brainstorm, here are just a few ideas to get you started:

  1. Learn how to cook if you don’t know how.  I don’t mean the gourmet stuff.  I’m talking premade hamburger patties, spaghetti with Ragu, grilled cheese and tomato soup.  Then substitute a home cooked meal (or a brown bag lunch) for your usual restaurant habit, a few times a month.
  2. Resale shops:  nearly everyone can benefit from them as a seller, buyer, or both. 
  3. If you haven’t been to your public library recently, you might be surprised at what you can get there: music downloads, Kindle books, audiobooks, movies, and much more.
  4. Instead of letting your expenditures grow to match your cash on hand, bank a portion of your next pay raise, or a few months of payments after your car is paid off, or that check your Aunt Edna wrote you for your birthday. 
  5. Boring but true: keep your tires properly inflated and change your oil regularly.

It’s not easy, but it’s simple.  You never know what you’re gonna get.  So take some steps.


A Little of This, A Little of That

John owns a business that sells umbrellas and galoshes.  Jane’s business sells sunscreen and bathing suits.  Both of these business owners are profitable, over all; but they both experience broad fluctuations in their business revenues, depending on the weather.  One day they decide to merge their businesses.  Now their income is more steady.  This is called diversificationJohn and Jane now have a more robust business than they would have had separately, because a major factor – weather – has a much smaller effect than previously.

John and Jane are glad that they diversified.  You should also diversify your investment portfolio, and for the same reason.  Almost all investors are happier when their portfolios grow more steadily.

Let’s talk some more about John and Jane.  The following things are true for them, and for you:

  1. They are well diversified with respect to weather, but there are more steps that they can take: they can diversity geographically, by opening stores in new cities; by market size, by offering more different products in various price ranges; by distribution channel, by operating a web site or a toll-free phone number; and in many other ways.  And they probably should, if they want their business to grow.
  2. Diversity does not guarantee profitability.  If they merge two mediocre businesses, they will just get a bigger mediocre business.  Diversification is more of a risk management strategy than a profit maximization strategy.  They may not be the most successful business around, but at least they can put food on the table whether it’s rainy or sunny!  So they can sleep better while they explore ways to improve their business.
  3. Poorly chosen diversification is worse than none.  Suppose the next branch store they decide to open is located in Saudi Arabia.  It doesn’t rain much there, and very few people wear bathing suits, for religious reasons.  Do you think this will improve their business results, or reduce their risk?  I don’t.
  4. Business cycles still happen, and still affect their results.  Long term weather patterns, government regulations, tax policies, consumer sentiment, and many other things will still happen.  Sensible diversification does not eliminate all risks; it just tempers the effect of certain ones that you can do something about.

It’s not terrible to have business results (or investment results) that vary from month to month or year to year, especially if you have a long time horizon.  If you are not going to need the money for 30 years, who cares what wild gyrations happen in the meantime, as long as the end result is good?

If you really, in your heart of hearts, agree with the above paragraph, then you have what is known as a “high risk tolerance.”  You are psychologically capable of ignoring short term cycles and fluctuations while keeping your focus only on long term results.  For you, the main job is to identify long-term profit opportunities.

Most of the rest of us need to be honest with ourselves: we don’t have the stomach for large changes in our portfolios[i].  When we open our statements and see that our balance has dropped 25% in the last month, we freak out, and lose sleep worrying about whether the market will ever recover!  Next thing you know, we’ve panicked, and sold everything. Repeat this behavior over the years, and we’re eating cat food during our retirement years.

Everyone has a different risk tolerance.  It’s critically important to know yours.  Once you have, use intelligent diversification to design a portfolio that mitigates the risks that are out there.  You, John, and Jane will all sleep better for it.

[i] When I say “large changes,” I really mean “large drops.”  Most investors would be ecstatic at a 25% increase in their portfolio value in a month.  If you can figure out how to have upside volatility without a corresponding downside, please let me know!


The Infinite Dangers of Life

“I don’t own any stocks.  The stock market is too risky.”

I have heard these or similar words many times over the years.  Or even worse:  “I had my money in the stock market, but then it went down, so I sold it all.  So I lost money.  Never again for me.”

People who think this way are not thinking about risk in the proper way.

You are probably familiar with the general characteristics of the stock market.  The market goes up, the market goes down; this is known as “short-term volatility.”  Long term, prices of US common stocks have risen.  Common stocks have outpaced inflation in the long run.  Individual companies have gone bankrupt, but stocks in general have been good long-term investments.  If you own only stocks, or only the stock of a few companies, you are at the mercy of these fluctuations.  Most people don’t have the stomach for this kind of volatility.

If you want to avoid risk, don’t avoid stocks!  Instead, own several different types of investments, including stocks.  There are many different kinds of risks to worry about.  Instead of hyper-focusing on just one kind of risk, consider the big picture:

Own stocks, as part of the picture, to control for inflation risk, or the possibility that your money will lose purchasing power.

Own stocks of different companies in different industries to control for business risk, or the possibility of an individual company performing poorly.  Or, own a basket of different stocks by purchasing mutual funds or Exchange Traded Funds.

Keep part of your funds in lower volatility investments, like bonds and cash, to control for volatility risk.  The less volatile  components will reduce the overall swings in portfolio value, so you will be less likely to panic and sell during the inevitable market downturns.

Consider protecting yourself against longevity risk, or the possibility of outliving your assets, by including Social Security, pensions, and annuities in your long range planning.

Own life insurance to protect your heirs against mortality risk, or the possibility that you won’t be around long enough to collect your pensions and annuities.

Use different forms of ownership (conventional IRAs, Roth IRAs, taxable accounts) to protect against  tax risk.

There are other risks out there.  The title of this post is from a quote by Johann Wolfgang von Goethe, 1749 – 1832.  He lived in a time before quantitative easing, Social Security, biological warfare, and the other things that we worry about in 2013, but he still faced risks and recognized their power.  In Goethe’s time as well as our own, the task is not to obsess over one particular form of risk, but to take a balanced approach that accounts for many different kinds of risk.

In the world of financial planning, this approach is called a “balanced portfolio.”  If you don’t have one, you need one.  And once you get one, stick to your plan.  Stop reacting to the latest headlines and start thinking systematically.  Turn off the TV if you have to.  Recall the previous post, in which we realized that everybody is trying to sell you something.  Fear and panic on your part may be somebody else’s financial advantage, but it is not yours.

Comments on this blog (or any related topic) are welcome.


Everybody’s Got an Ax to Grind: Fees and Charges

There is nothing wrong with going in to business to make a profit.  It’s the basis of the American financial system.  For many of us, it’s why we enjoy a paycheck.  And how else would we pick up a loaf of bread, or have our cavities filled, or go to the movies, if we couldn’t patronize a business set up for the purpose?  On the other hand, just because we appreciate the benefits of a market economy, that doesn’t mean we shouldn’t shop around for the best product at the best price.

Unless you keep all of your money under your mattress, somebody is getting paid to take care of it for you.  Investment fees vary widely, depending on the investment type and how you buy it.  Excessive fees can jeopardize you financial solvency, and no fee is worth paying unless you are getting something of value in return.

In general, the financial products that are the most heavily promoted are those for which the salespeople receive healthy commissions.  Get in the habit of asking how the person offering the service is compensated.  If they can’t, or won’t, explain it, maybe that investment is not for you.

What are some of these fees? Here is a partial list:

  • Banks may charge fees on a monthly basis and/or a per-transaction basis.  Banks also make money on the difference between the interest rate that they pay their depositors and the interest rate that they charge their borrowers.
  • Stockbrokers charge commissions on securities trades, and they may charge fees for services such as moving money into or out of an account.  They may reduce or waive some of these fees based on the size of your account balance or the products that you purchase.
  • Mutual Funds and Exchange Traded Funds charge management expenses.  Some also charge a front-end fee or “load” when you purchase the fund.  There may be additional fees if you hold the fund for only a short time.  Funds with “active mangement” tend to charge more than those with “passive management.”  (More on this in a later blog post.)
  • Employer pension plans, like 401(k) and 403(b) plans, charge management fees which typically vary depending on what specific investments you choose.  Some also charge transaction or service fees.  Fees on these accounts vary from extremely reasonable to absolutely ridiculous.
  • Annuities and other insurance-like products often charge sales commissions and annual service fees.   Many of these products are particularly expensive because they charge a fee for the underlying mutual fund and an additional fee for the “insurance contract” that is part of the product.
  • Financial planners operate under several different fee plans.  They may charge by the hour for the financial plan itself; they may charge a percentage of assets under management for ongoing management; they may charge commissions for the products that they sell you; or maybe a combination of all of these.

One thing that almost all of these fees have in common is: they get paid whether you make money or not.  

I am not against fees.  The financial products industry provides many necessary services.  And clearly, some things should cost more than others.  For example, mutual funds that concentrate on obscure market sectors (developing country Treasury bonds, Bolivian copper mining futures) typically have higher fees because they have higher expenses.  Small accounts generally pay larger fees on a percentage basis than large accounts.  No surprise there.

But sometimes the fees are clearly ridiculous!  For example, at my broker, Charles Schwab, there are 17 mutual funds that I could buy that track the S&P 500 Index, a popular index of large company stocks.  Expense ratios for these funds range from 0.05% to 1.55% for what is essentially the same product.  The least expensive fund had an investment return of 7.30% over the past five years.  The most expensive fund had a return of 5.66% for the same time period.  Which would you rather have?

Financial products are just like other products, except the fees are less transparent.  Sometimes it makes sense to pay more because you get more.  Other times, the more expensive product is just more expensive.  The point is, know what you’re getting!

I look forward to your comments about this article.  Also what would you like to see here in the future?




Fighting Financial Fear

According to common wisdom, the biggest mistakes investors make stem from two sources: fear and greed.  This blog is going to cover ways to overcome the first problem.  Fear is a factor in everybody’s life, but it can be overcome with knowledge, forethought, and practice.

Many people are afraid of investing.  They either avoid it completely, or they avoid opening their statements and acting on them, or they just hand the reins over to somebody else.

In the coming weeks, I will discuss some aspects of investing and financial planning.  I will  try to make my posts clear, entertaining, and concise.  If you like them, or don’t like them, let me know.