Reframing The Question

"We may consider ourselves lucky when, trying to solve a problem, we succeed in discovering a simpler analogous problem."

- George Polya, How to Solve It

In his book entitled Beyond Greed and Fear: Understanding Behavioral Finance and the Psychology of Investing, Hersh Shefrin poses the following question:

The Dow Jones Industrial Average closed 1998 at 9,181. As a price index, the Dow does not include reinvested dividends. If the Dow were redefined to reflect the reinvestment of all dividends since May 1896, when it commenced at a value of 40, what would its value have been at the end of 1998? In addition to writing down your best guess, also write down a low guess and a high guess, so that you feel 90 percent confident that the true answer will lie between your low guess and your high guess.

I took a wild guess: 40,000. For a low and a high, I chose 20,000 and 60,000. This turned out to be totally wrong - not even in the right ballpark. The correct answer is 652,230. (!)

Apparently I am at least in good company, as the author goes on to state that "virtually nobody finds that the true answer lies between his or her low and high guesses." The author cites this as an example of overconfidence. People generally overestimate their knowledge and abilities, and thus they are frequently surprised by events.

While I think it's a very interesting example, I really felt that the question itself was a much better example of framing than overconfidence. It turns out that the human brain does not work very well with exponential functions like compound interest, so it's not really too surprising that the average person has no clue where the Dow index would be 100 years after inception.

So I propose that we state the problem a different way:

From 1896 through 1998, what has been the annualized total return of the Dow, including reinvested dividends? Again, pick a low and high number that makes you feel 90% confident the true number lies in the interval.

This is a much easier question to answer than the first. You might very well have heard the long run average return for stocks reported as 12%, or 9%, or 10.5%, or various other numbers, depending on the time period and the index involved. You might also have heard that 5% or 6% or 7% plus inflation is a good ballpark number. You might also intuitively know that GDP growth + inflation + dividend yield is a reasonable proxy for long term returns, and you might calculate something like 10% that way. Personally, I've also read that the worst 30-year period for the S&P 500 returned 8%.

So it was fairly easy for me to pick 10% as my guess and 13% and 8% as my high and low. Now let's resolve the original question using the new answers.

Average guess = 40 * (1.10 ^ 102) = 666,982
Low guess = 40 * (1.08 ^ 102) = 102,632
High guess = 40 * (1.13 ^ 102) = 10,376,647 (!)

Interesting, right? First, note that the guess for the average is very, very close to the right answer. Second, note the bounds that are produced by 8% and 13%. Hardly anyone would pick those numbers the way the original question was framed. But in the second framing of the question, you only had to include 10% in your interval. I'll bet a fair number of people would get the question right that way. In fact, I'm nearly certain that the percentage of correct answers would be dramatically better if the question were asked the second way.

Can we learn anything practical from this exercise? I think so. If nothing else, try to reframe questions that appear confusing. A person can very easily be duped by salespeople in the financial arena - not necessarily because they are gullible or uninformed, but because statements and questions are (often deliberately) framed to make it appear that your interests are being served when in fact they are not.

Never let a car salesman or a mortgage broker reduce everything down to a monthly payment and nothing else. Your brain will tend to think you are getting a good deal the way the information is presented. Similarly, don't try to attempt variants of the Dow question above. For example, don't say to yourself: "It looks like I spend about $50K per year. After about 30 years of inflation, that would probably be...oh...I don't really know...probably about $70K." You are likely to make severe financial errors this way. Instead, reframe the question and ask yourself what is a realistic yearly inflation rate given everything you know. Then use a tool (such as a financial calculator, Microsoft Excel, or even a compounding table) and solve the original question. If you choose 3.5% per year, for example, then your original estimate of $70K was less than half the actual number!

Personal finance is hard to master because it involves knowledge, insight, and personal discipline. At the very least, make sure your decision making framework is on a level playing field by insuring that you frame your financial questions in a way that you can realistically make good choices.

Emerging Markets

"A hidden connection is stronger than an obvious one."

- Heraclitus of Ephesus

There has been much talk lately about emerging market equities. Are they overvalued or not? Is a P/E of 14 or 15 too low because of the (potential) growth rate of earnings? Or is the P/E too high because it is now similar to more developed markets and does not provide adequate compensation for the additional risks of emerging markets? Or are emerging markets currently fairly valued?

I confess I don't know the answer to that question.

But let me shift the focus to a related question. Regardless of your opinion of the current valuation, it cannot be denied that (in hindsight) 4 or 5 years ago, emerging market indexes were very undervalued. Now someone might counter that the only reason for the recent stellar returns is that emerging markets have risen way too far and are in a bubble. Hence, the argument would be that perhaps emerging markets were simply fairly valued in 2003 and are overvalued now.

Mathematically, however, this argument does not ring true. Suppose we concede that emerging markets are currently grossly overvalued and we peg "fair value" at half the current price. This would put the current P/E at about 7. While some may argue that such a P/E ratio would be appropriate to discount risks, I seriously doubt that many would claim such markets would definitely be overvalued at that level. So for sake of argument, let's say fair value is one half the current price. Even if emerging market equity indexes were currently 50% less, the appreciation during the last 4 1/2 years would still have been more that 20% annualized.

So it seems to be the case that in the Spring of 2003, emerging markets were quite undervalued, yet there was little recognition of that. The recent returns have been staggering. The total return of the Vanguard Emerging Markets Stock Index Fund from 2003 Q2 to present exceeds 350%, or more than 40% annualized over the past 4 1/2 years.

I tried to search the web for articles and analysis of emerging markets in 2002 and 2003. (The web is probably not the best medium for findings historical articles. A trip to the library to examine the archives for Barron's and Business Week would probably yield better results.) From what little information I've uncovered and pieced together, I don't really find that the attitude about emerging markets was all doom and gloom back then. Rather, it appears that emerging markets were simply totally off the radar screen for most people - unnoticed rather than unloved.

So the example of emerging markets five years ago prompts the question: What asset class is unnoticed and undervalued now? If such an asset currently exists, it's very likely that it's NOT being heavily written about in your newspaper and discussed on the web.