Efficient Frontier
William J. Bernstein
Efficient Frontier
William J. Bernstein
<B>Signal, Noise, and Success</B> Signal, Noise, and Success
A short while ago, I got an email from one of the brightest journalists I know. He asked for my reply to an analyst who observed:
If all these smart guys you quote say investors have to get used to far more modest equity returns for quite a while, that doesn't square with what the S&P, Naz, and Russell 2000 are doing this year.
My journalist’s friend made a startlingly common error of omission: he failed to realize that both expected and realized returns are contaminated by a large amount of noise. Readers of this site know it is just another way of stating the Bogle Partition Theorem—the return of any security or asset class is the sum of its fundamental return (signal) and its speculative return (noise).
Over very short periods, the latter overwhelms the former; only over periods of a decade or greater is the former even vaguely predictive. (For a more formal treatment of this phenomenon, see "Of Risk and Myopia" in the Efficient Frontier Winter 2002 issue.) It turns out, however, that the equity risk premium provides a handy back-of-the-envelope way of understanding this phenomenon.
Let’s divide the world into equity optimists, who believe that the equity risk premium (which we’ll define for discussion purposes as the difference between the stock and T-note returns) is 4%, and the pessimists, who believe it’s only 2%. Let’s further assume that the volatility, or standard deviation (SD), of stocks is 16%.
At a time horizon of one year, it doesn’t matter much whether or not you’re an optimist or a pessimist—the 16% noise is so vastly greater than the 4% or 2% premium that anything can happen over such a short time period. In other words, the fact that it’s 55 degrees outside doesn’t tell you whether it’s a warm day in December or a cold day in June.
Over longer periods, however, the noise washes out in proportion to the square root of the number of years: the annualized SD is halved at 4 years and quartered at 16 years. I’ve summarized this for the optimist case below:
Time Period
Risk Premium
SE
Probability of Negative ERP
Probability of ERP>8%
1 Yr
4%
16%
40%
40%
4 Yrs
4%
8%
31%
31%
16 Yrs
4%
4%
16%
16%
64 Yrs
4%
2%
2%
2%
The second column merely reflects that the expected return is the same each and every year, while the third shows how the noise washes out with time. Still, even after 64 years, the SE (standard error, the term for a multi-period SD) is still 2%. This means that a loss is a 2-SE event, the probability of which is still 2%, listed in the fourth column. The fifth column merely demonstrates that the probability of a very good long-term return, defined as an ERP of >8%, is the same as that of a negative ERP.
Here’s how things shake out for the pessimists:
Time Period
Risk Premium
SE
Probability of Negative ERP
Probability of ERP>8%
1 Yr
2%
16%
45%
35%
4 Yrs
2%
8%
40%
23%
16 Yrs
2%
4%
31%
7%
64 Yrs
2%
2%
16%
0.13%
At the short end, the numbers aren’t that different, reiterating the point that just because it’s pleasant outside doesn’t tell you what month it is—meaning, just because we’ve had good stock returns thus far in 2003, as well as in 1998 and 1999, doesn’t mean that expected returns are high.
At the long end (64 years), things are different; the pessimists can reasonably foresee a significant probability of a poor result, since a negative ERP is merely a one-SE event, which carries a probability of 16%, while the probability of a good (ERP > 8%) result is a 3-SE event ([8-2]/2).
What have we learned from this disarmingly simple exercise? Two things:
Over short time periods, noise overwhelms. Anyone making a judgment about security returns, investment strategies, or fund performance based on data spanning less than ten years should be required by statute to wear a clown’s uniform and sandwich board saying, "I slept through Finance 101."
Even over very long time periods, there are no certainties. Unless securities prices fall dramatically from here, Stocks for the Long Run are no longer a sure thing.
Returning to our weather analogy, if you know that the average temperature for the month was 55, you know for certain it was neither December nor June (unless you live, as I do, on the coast of Oregon).
Some might argue that the above methodology ignores mean reversion, which produces actual SE’s somewhat smaller than those computed above. Unfortunately, today mean reversion cuts both ways—true, it can be counted upon to lower SE somewhat, but it is just as likely to lower expected return as the valuations of stocks mean revert.
This is not to say that investing in stocks is a bad idea—after all, very few people would argue that the ERP today is negative (although it was relatively easy to make such a case four short years ago). You are still more likely to come out ahead with stocks. It’s just they’re not a sure thing any more.
The signal/noise paradigm also provides behavioral insight, since it neatly explains the gap between those who succeed and those who do not. No one describes this cleavage better than senior Vanguard exec James Gately:
[Successful investors] don’t ask us many questions about whether Alan Greenspan will cut interest rates and what that will mean for the stock market. They don’t wonder what tension in the Middle East will mean for their portfolios. The headlines aren’t driving their decisions.
Their questions are much more fundamental or philosophical. We might be asked, "You’re offering a lot of new services. Will that raise fund expense ratios?" It’s clear that these clients are thinking several years ahead, not about what’s going to happen in 2003.
Unsuccessful investors, however, are just the opposite. They get caught up in the moment and have a tendency to chase performance. Once a year, I see a friend who hasn’t enjoyed as much investment success as he could have. He always asks me about the current "hot fund." I can predict what he’s going to ask about by looking at the table of 12-month trailing returns. In 2002, it was the GNMA Fund, which soared as stocks sank. The year before it was something else, and next year it will be something else still.
In short, the winners focus on the signal, the losers on the noise. As investors, we all navigate a stormy sea of random market fluctuation. From day to day and year to year, our returns are for the most part stray waves and wind gusts, not omens.