Why it takes a forensic accountant to measure the stock market accurately
Posted by richwillis in Investing Wisdom, Investor education on March 14, 2013
Imagine a world where our measuring devices were not constant. A ruler would shrink at some times and grow at other times. When you got an annual physical checkup, your recorded body temperature would increase by one degree per year (even though your real temperature would be unchanged). A pound today would weigh less than a pound did five years ago. After several years, the 12-gallon gasoline tank in your car would hold 13 gallons. This would be a very strange world. In the real world, we assume our measuring devices remain constant over time. But this is an erroneous assumption if we are measuring the stock market.
It has been widely reported that the U.S. stock market, as measured by the Dow Jones Industrial Average (DJIA), recently hit a new high. Pundits have pontificated on the significance of this milestone. Some have even questioned the validity of this statistic. But few have detailed the scope of the issue. In order to truly figure out whether the stock market is at a new high, one must take into account sampling error, inflation, dividends, and taxes.
If one were going to sample the entire population of the U.S., choosing only 30 of the biggest cities would not be very representative. It would be even worse if we weighted the influence of each of these cities by the number of letters in their names. This is analogous to the situation with the DJIA, a price-weighted, quasi-representative slice of the U.S. stock market. If a larger and more representative sample is available, why not use that instead? A group of 500 stocks is better, but is still subject to a mismatch in representation if it primarily samples only the biggest companies (S&P 500). 3000 samples (the Russell 3000) are much closer to full representation, but why not use the full sample if available? Several stock index providers furnish an index of the entire U.S. stock market, and numerous ETF providers include a total U.S. market ETF in their offerings. Examples include the Vanguard Total Stock Market ETF (VTI), the SPDR Dow Jones Total Market (TMW), the Wilshire 5000 Total Market ETF (WFVK), and the Schwab U.S. Broad Market ETF (SCHB).
Another contributor to the inaccuracy of index measurement is inflation. Stocks are priced in dollars, which is the measurement device we use when we compare historical prices with today’s prices. However, dollars shrink in value over time, more commonly known as the inflation rate. So today’s 14,000 DJIA is not the same as 2007’s 14,000 DJIA because today’s dollars are worth less. If you use the consumer price index as a proxy for the inflation rate (which is subject to endless debates about its accuracy), today’s 14,000 is about 10% lower than that of 2007.
However, inflation is not the biggest distorter of the measurement device. Today, that characteristic belongs to dividends. Every time a company pays a dividend, the stock price goes down by the dividend amount. Currently, the DJIA loses about 360 points per year due to dividend payments. Said another way, if an investor actually buys the 30 stocks in the DJIA (or its closest ETF equivalent: the SPDR Dow Jones Industrial Average, DIA), and the index level starts the year at one point and ends the year 360 points lower, the investor has actually broken even. If the index ended the year unchanged, the investor would actually be 360 points (roughly 2%) ahead. This same feature applies to the S&P 500 and many other indexes. The S&P 500 currently loses over 30 points per year due to dividend payments.
The distortion created by dividend payments works in an opposite direction to that of inflation. Consider a hypothetical investor who purchased DIA on the day it reached its 2007 high. He would have about 15% more nominal dollars when the DJIA surpassed its old high earlier this month due to dividend payments. After taking inflation into account, the investor would still be ahead, but only by about 5% or so. In prior decades, inflation distorted the index value more than dividends. Therefore, the combined contribution of inflation and dividends to index measurement inaccuracies may be either positive or negative depending on the time period of interest.
If this is beginning to sound a bit complicated, I have bad news. It’s going to get worse. Thus far I have glossed over the handling of the funds received from dividend payments. Should we assume that that money stays in cash (to make the calculations simpler) or should it be reinvested? If the point of the measurement device is to accurately measure how stock prices are behaving and not how a mixture of stocks and cash are doing, then dividends should be reinvested in the same stocks. This could be done on a stock-by-stock basis as each stock in the index pays its dividend, or it could be done in more of a batch mode by reinvesting in a group of stocks after a chunk of dividends have been received. In either case, the calculations are gnarly. Determining the magnitude of the effects of dividend reinvestment is extremely difficult. But it is easy to figure out whether this effect would add to or subtract from the real return, as opposed to a return calculated from a naïve comparison of a change in the index value. In the example cited above, reinvestment would have occurred at prices lower than 14,000 throughout the period from 2007 to 2013, thus boosting the return.
Let the complications continue. Taxes enter the picture. Gains are taxed on nominal differences rather than inflation-adjusted differences. Depending on the rate of inflation, this could wipe out our hypothetical investor’s entire gains. Before inflation he has at least a 15% gain due to dividends. (I am using the term “at least” because I cannot easily calculate the addition return due to dividend reinvestment. All I can say is that it is a small positive number.) Taxes will reduce this amount by 15% or 20% or 32.4% or some other number that is highly dependent on the investor’s income and location (state taxes). And some portion of the gains (dividends) can be taxed at a different rate than other portions (capital gains).
But should tax complications affect the measurement of the index? Not really, because the point of the measurement tool is to inform people about the performance of the stock market, not to measure each individual’s real post-tax, post-inflation return. But tax considerations should not be ignored, because an investor could find himself in the situation of investing in an asset that has the appearance of appreciating nicely over time, but after inflation and taxes are taken into account, he is worse off than he was initially. In this case, the reported measurement of the index would mislead a naïve investor into thinking he is doing better than he really is.
So if we use a broader sample than the DJIA or S&P 500, we find that since the last apparent high water mark, the stock market has actually done better than the popular averages would indicate, since small stocks not included in the DJIA or S&P 500 have outperformed large stocks. Failing to take inflation into account will lead one to overestimate the real return. Failing to take dividends and dividend reinvestment into account will lead one to underestimate the real return. Taxes will muck things up further. If you add all of this together, you will find that the stock market actually hit a new high months ago, when few were watching. Most investors were paying attention to more popular, ever-changing measurement statistics that mislead more than inform.
What the financial world really needs is a widely-reported, precise measurement device that does not require expertise in forensic accounting to decipher. One that would accurately answer a simple question: What would a dollar invested in the U.S. stock market on any given day in the past be worth today?
Is it time to get back in the market?
Posted by richwillis in Investing Wisdom, Investor education on February 26, 2013
Many individual investors panicked during the 2008 market meltdown and have maintained a siege mentality ever since. Reasons to be afraid are abundant: European crises, debt monsters, and a dysfunctional Congress are just a few of the more obvious ones. But the stock market has seemingly ignored these negatives and has erratically rallied for four years and is now at more than twice the value of its low point during the crash. Read the rest of this entry »
What makes investing difficult to learn? (part 4)
Posted by richwillis in Uncategorized on January 16, 2013
4. The process sometimes requires substantive amounts of unlearning.
Learning does not happen in a vacuum. Whenever we learn something, we fit that new piece of knowledge into our existing base of prior knowledge. But what happens if our prior knowledge is flawed? How difficult is it to learn new and better ideas when such ideas contradict existing knowledge? Read the rest of this entry »
What makes investing difficult to learn? (part 3)
Posted by richwillis in Investing Wisdom, Investor education on January 9, 2013
3. It is difficult to maintain objectivity when making judgments about your own investing skill
In the first two parts of this series, I described how the long duration of the feedback process impedes the investment learning process, and how it is difficult to discern whether the quality of our investment decisions is due to luck or skill. In this section I will discuss another obstacle to learning the necessary skills for successful investing: the difficulty of being objective when making self-judgments. Read the rest of this entry »
What makes investing difficult to learn? (part 2)
Posted by richwillis in Investing Wisdom, Investor education on December 18, 2012
This is the second in a series of essays about why investing is difficult to learn. To read the first installment, click here.
2. It is difficult to distinguish the contributions of skill vs. luck.
Imagine that you bought Google stock on December 31, 2011 at a price of $645.90. As of mid-December, the stock is at about 720. This is an increase of about 11.5% in a little less than a year. Was this a good decision? How much of the decision should be attributed to skill vs. luck? Read the rest of this entry »
What makes investing difficult to learn? (part 1)
Posted by richwillis in Investing Wisdom, Investor education on December 12, 2012
The skills required for successful investing are difficult to learn. In the next few essays, I discuss four obstacles that thwart the education process. They are:
- The feedback loop is extremely long.
- It is difficult to distinguish the contributions of skill vs. luck.
- It is difficult to maintain objectivity when making judgments about your own investing skill.
- The process sometimes requires substantive amounts of unlearning. Read the rest of this entry »
How is the stock market performing?
Posted by richwillis in Investing Wisdom, Investor education on November 13, 2012
Some market pundits will tell you that the market has performed unusually well recently. Others will tell you that it has under performed. Still others will tell you that the market’s performance is similar to its very long-term average. All of them are correct.
Judging a market’s performance is highly dependent on the time period you choose.
Examine the table below:
| Measurement period starting date | Time period (in years) | VFINX annualized return |
| 09/30/11 | 1 | 30.02% |
| 09/30/10 | 2 | 14.58% |
| 03/31/09 | 3.5 | 20.79% |
| 09/28/07 | 5 | 0.97% |
| 03/31/05 | 7.5 | 4.76% |
| 09/28/02 | 10 | 7.90% |
| 03/31/00 | 12.5 | 1.48% |
| 09/30/97 | 15 | 4.61% |
| 09/30/92 | 20 | 8.41% |
| 09/30/87 | 25 | 8.44% |
This table shows the performance of the Vanguard S&P 500 Index fund, VFINX, for periods ranging from one year to 25 years, all ending on the most recent quarter-end of 9/30/2012. The historical performance ranges from less than 1% per year to more than 30% per year, depending on the time period you choose. The performance figures include the returns from dividends as well as capital appreciation. Read the rest of this entry »
80 reasons your investment performance is not as good as it should be
Posted by richwillis in Investing Wisdom, Investor education on October 3, 2012
- You think investing is about picking winning stocks.
- You have Internet- or smartphone-induced ADHD and can’t think deeply about this topic.
- You equate investing with gambling. [elaboration]
- You want to get rich quickly.
- You think others have a crystal ball and pay too much attention to their forecasts. [elaboration]
- You oversimplify.
- You misunderstand the relationship between stock markets and the economy.
- You think there is a straightforward relationship between a company’s success and its stock price.
- You are quick to jump to conclusions.
- You focus too much on the short term.
- You don’t understand the feedback loop for measuring results.
- You are unduly swayed by stories.
- You ignore the lessons of history.
- You think that past performance is an accurate guide to the future. [elaboration]
- You focus on the trees instead of the forest.
- You overemphasize the importance of yield.
- You don’t understand the mathematics of investing.
- You see patterns in random data and draw erroneous conclusions from them.
- You don’t understand why stocks go up and down. [elaboration]
- You pay too much attention to irrelevant numbers.
- You confuse a decline in price with a permanent loss (and a rise in price with a permanent gain).
- You believe that risk can be turned up and down like the volume on your radio.
- You misunderstand the nature of market volatility and overvalue stability. [elaboration]
- You think a rising stock market is always better than a falling stock market.
- You underestimate the impact of inflation.
- You want more certainty than is possible.
- You let others do the thinking and you follow their actions.
- You underestimate your own ability to successfully invest.
- You overestimate your ability to pick winning investments.
- You have unrealistic expectations about the market’s behavior and your own performance.
- You overestimate the extent of your knowledge about a particular investment. [elaboration]
- You are too optimistic about the investments you make.
- You overvalue what you own.
- You spend too much time hoping and dreaming. [elaboration]
- You attribute your winning investments to your own brilliance and attribute your losing investments to bad luck.
- You pay much more attention to information which supports your assumptions and beliefs than information that contradicts or challenges them.
- You are afraid to make a decision that might turn out poorly.
- You think too much about proceeds and not enough about process.
- You are scared to make fundamental changes to your investing process.
- Your mental model of how to invest has fundamental flaws. [elaboration]
- You spend too much time and attention on items you cannot control.
- You focus far too much on what to buy and whether now is the right time and not nearly enough about how much to invest. [elaboration]
- Your financial assets are concentrated in too few categories.
- You try to control risk by security selection.
- You think the house you own is an investment.
- You borrow money to invest without fully understanding the risks involved.
- You hold too much cash.
- You think that investing your money outside this country is a foreign idea.
- You invest in asset classes that have a negative expected return.
- You let your asset allocations drift. [elaboration]
- You buy assets without paying attention to their value.
- You only buy stocks of familiar companies.
- You equate average with mediocre.
- You are too concerned about the impact of taxes.
- You are not concerned enough about the impact of taxes.
- You own too many bond investments.
- You own too few bond investments. [elaboration]
- You are afraid to buy when markets are declining because they might go lower.
- You are afraid to buy when markets are rising because you fear it is too late.
- You take actions to avoid losses and forego large gains as a result.
- You don’t ever want to sell anything.
- You freak out and sell out at market bottoms.
- You wait until markets appear “safe” before buying.
- You trade too much.
- You don’t trade enough.
- You underestimate the costs of professional management.
- You overestimate the abilities of professional management.
- You spend too much for professional help.
- You don’t organize your finances.
- You don’t measure your progress. [elaboration]
- You don’t compare your progress to a reasonable benchmark. [elaboration]
- You don’t periodically rebalance your portfolio.
- You don’t know what to do when the market makes an unexpected move.
- You don’t know what to do you when your personal situation changes dramatically.
- You pay too much attention to the financial media.
- You pay too much attention to stuff that doesn’t matter.
- You overestimate the time required to manage your portfolio intelligently. [elaboration]
- You overestimate the amount of expertise required to manage your portfolio intelligently. [elaboration]
- You have no good source of unbiased, high quality, well-organized educational investment information, tailored to your knowledge level, circumstances, and learning abilities.
- You make investing decisions like a human.
The importance of mental models (part two)
Posted by richwillis in Investing Wisdom, Investor education on September 11, 2012
In the previous essay, I described the game/contest mental model for making investment decisions and detailed many of the problems that result. The model’s inherent problems are due to how it simplifies an overwhelming choice of options in a manner that ignores too many important aspects of the investment landscape. Let’s revisit the three critical questions and develop a better mental model. Read the rest of this entry »
The importance of mental models (part one)
Posted by richwillis in Investing Wisdom, Investor education on September 5, 2012
Investors face a daunting set of choices. They can be grouped into three general categories:
- What to own
- When to buy or sell
- How much to invest in any single investment
What to own: There are tens of thousands of potential securities to own if you only include those available to the broad public. Including private investments would push the total number into the millions.
When to buy or sell: Securities can be bought and sold almost continuously. They can be held for seconds, minutes, hours, days, months, or years.
How much to invest in any single investment: One can invest any amount from a trivial amount of money to much more than their net worth by borrowing. Read the rest of this entry »
Cognitive Investing 