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Photo: AP
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Investors still believe they can beat the stock market

I recently wrote about the benefits of stock diversification. Some readers still aren’t buying it. Here’s what they said—and my responses.

Last month I offered readers a paean to the virtues of diversified investing—the idea of spreading your money across different kinds of investments so as to reduce a portfolio’s risk without reducing expected returns.

I presented five myths that skeptics often cite, and debunked those myths in an effort to strengthen the case for a diversified portfolio.

Well, judging from readers’ reactions, it seems I still haven’t convinced everybody.

So let me offer some of the common skeptical comments I received from readers, and my responses to those. I’m sure I still won’t convince everybody. But I can’t help but keep trying.

• Average is for losers. A reader wrote: “Diversification will of course mitigate the losses from your bad picks, but it will also strictly limit the rewards from the good picks."

What the reader says is true. Undiversified investors aspire to pick good stocks and avoid bad ones, earning above-average returns. Diversified investors forgo such aspirations. They hold all stocks, good and bad, earning average returns.

Several readers insist they can be above-average investors. My question to them: Are you really an above-average investor?

The facts suggest they aren’t. They just think they are. A study of the members of the American Association of Individual Investors found that they overestimated their own investment returns by an average of 3.4 percentage points a year relative to their actual returns, and they overestimated their own returns relative to those of an appropriate benchmark by 5.1 percentage points.

• OK, but I know what I’m doing. A reader advocated beating the market with undiversified portfolios by acquiring investment skills to avoid losses from bad investment picks. “It’s vital to know investing’s and finance’s language, how to read a financial statement, have run a decent-sized biz, understand how to value a biz, are disciplined and patient and understand the qualities that separate great businesses from good," the reader wrote.

Many amateur investors frame stock picking and trading as the equivalent of playing tennis against a training wall. But picking stocks and trading is properly framed as tennis against a professional on the other side of the tennis net, perhaps Roger Federer. Amateur investors are similarly playing the stock-buying game against professionals, perhaps one with inside information or better ability to combine public information into superior assessments.

Do you really think that you gain an advantage over professional investors by knowing investing and finance language or the ability to read financial statements?

It is a folly for engineers, physicians or professors to believe that they can acquire in their free time the information and skills investment professionals acquire and deploy in their day jobs. As I often note, in every trade there is an idiot. And if you do not know who it is, you are it.

Granted, very good amateur tennis players might beat middling tennis professionals from time to time. Luck helps. The same is true with the investment game—even more so, because luck helps in investing more than it does in tennis. When that happens, though, amateur investors tend to become overconfident in their investment skills and it encourages them to continue trading.

One other point on this: As another reader noted, “Most people in the accumulation phase of their lives are also raising young children and trying to build their careers and do not have the time to perform the day-to-day study necessary for market timing. Diversification and mutual funds are boring but work for most people." Indeed.

• Reward requires risk. A reader wrote: “The whole discussion about mitigating your risk seems to misunderstand the basic reality of buying stocks. There is no getting around the fact that risk and reward are connected. If you want to make real money in the market you have to be able to pick stocks."

It is true that high risk can be rewarded with high expected returns. But not all risk is rewarded.

Risk is of two kinds, diversifiable and undiversifiable. Diversifiable risk is the extra risk that an undiversified portfolio might lose value even if the stock market gains. Undiversifiable risk is the risk that even a diversified portfolio, such as a total index fund, will lose some or much of its value when the stock market loses.

Investors who hold undiversified portfolios bear both diversifiable and undiversifiable risk, but only the undiversifiable portion of the risk is rewarded. Therefore, they bear more risk than is rewarded.

Yes, a combination of undiversification and good luck can deliver fantastic returns. But a combination of undiversification and bad luck can decimate a portfolio and retirement prospects.

One way to understand this is to note that the volatility of the returns of a portfolio of 18 or even 1,800 stocks is greater than the volatility of a portfolio of 3,500 stocks. The extra volatility of the 18 or 1,800 stock portfolio can be eliminated by increasing diversification to 3,500 stocks, and therefore this extra volatility is not rewarded.

• Time itself is diversification. A reader wrote that he follows this rule: “If you can’t own a stock for five years you shouldn’t own it for five minutes."

This is the rule of “time diversification," the belief that the risk of stocks declines as the investment horizon increases. The claim of time diversification is that stocks are risky when held during short periods of five minutes, or even a year, but that risk is lower if held during long periods of five years, and the risk of stocks held for very long period drops to almost zero.

That belief is tempting but unfounded. The risk of a diversified portfolio of stocks does not decline as the investment horizon increases, and the risk of a single stock or an undiversified portfolio of stocks surely does not decline as the investment horizon increases.

Consider the following example. Imagine a portfolio of stocks that has a 50-50 chance to gain 20% each period or lose 10%.

You begin with $1,000.

By the end of the first period, that $1,000 either grows to $1,200 or diminishes to $900. If you are fortunate to have $1,200 by the end of the first period you will have either $1,440 or $1,080 by the end of the second period. If you are unfortunate to have $900 at the end of the first period you will have either $1,080 or $810 by the end of the second period.

The probability of a loss decreases from 50% if held for one period to 25% if held for two periods. This decline in probability underlies the time diversification argument. But the amount of loss increases from $100 if held for one period to $190 if held for two periods.

Holding a single stock for long periods doesn’t eliminate its risk. Its value might decline to zero along the way and never recover. Holding a diversified portfolio for long periods does not eliminate its risk either. A diversified portfolio can sustain a long series of losses and sometimes never recover, as happened in stocks in Germany and Japan in World War.

• Dollar-cost averaging is another form of diversification. A reader recommended that investors lacking skills at picking winning stocks “should invest the same amount of money the same date each month in an S&P 500 fund if they believe in the future of the U.S."

Another reader recommended choosing an investment method “where you don’t put the money in at one time, but average in over 10 years."

This recommended investment method, known as dollar-cost averaging, promises the risk-reduction benefits of time.

Suppose that you inherited $120,000 from a beloved uncle. You intend to invest it in stocks, say in an S&P 500 fund. You can choose to invest it all in the fund today, in a lump sum, or you can choose to invest it in 12 equal $10,000 increments on the 15th of each month during the coming 12 months.

Your risk by dollar-cost-averaging investing during the 12 months is indeed lower than the risk by lump-sum investing, because the risk of cash is lower than the risk of stock. But once the 12 months are past, the entire $120,000 is in the stock fund. You are 12 months older now. Does older age make it easier for you to bear risk?

Dollar-cost averaging is like dipping your toes in the pool one at a time, followed by feet, legs and the rest of you. Lump-sum investing is like jumping into the pool head first.

The real benefit of dollar-cost averaging is in reducing regret. Regret is the painful emotion we feel when we find, too late, that another choice would have brought better outcomes. Pride is the pleasurable emotion that stands at the other end from regret.

Consider the regret potential of investing the entire $120,000 in the stock fund today. How much regret would you feel if the stock fund plunged tomorrow? Regret would be lower if you invested only $10,000 today, because you can contemplate the pride you will feel by investing the next $10,000 at a lower stock price.

• Just pick stocks of good companies. A reader wrote: “Invest in a handful of only the greatest companies."

This is common advice. But it is not necessarily good advice.

Imagine that you are shopping for a car and considering the Toyota Camry and Lexus ES 300h. You face two distinct questions. First, is the Lexus a better car than the Toyota? Second, is the Lexus a better buy than the Toyota?

Even I, a Toyota driver, readily admit that the Lexus is a better car than the Toyota, and more prestigious. But are the better features of the Lexus worth the substantial difference in price? Some buyers say yes, others say no, but they all understand that they must contemplate the two distinct questions.

Somehow, many investors regularly fail to ask themselves the second question. Are great companies better than companies that are not as great? Sure. But are investments in stocks of great companies better than investments in stocks of companies that are not as great? Perhaps, but not necessarily. We must consider the prices of the stocks relative to their value before we answer this question.

Evidence indicates that, if anything, stocks of great companies have been worse investments, on average, than stocks of not-so-great companies. A study of Fortune magazine’s annual list “America’s Most Admired Companies" found that stocks of admired companies had lower returns, on average, than stocks of spurned companies, and that increases in admiration were followed, on average, by lower returns.

The dispersion of returns among stocks is high, however, especially in the portfolio of spurned company stocks. That high dispersion implies that investors who would like to benefit from the return advantage of spurned company stocks must diversify widely among them.

Dr. Statman is the Glenn Klimek professor of finance at Santa Clara University’s business school and author of “Behavioral Finance: The Second Generation" (available free at cfainstitute.org). He can be reached atreports@wsj.com.

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