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How Babe Ruth Can Help 401k Plan Sponsors Teach Employees the Most Important Thing They Need to Know

May 28
03:57 2011

(The following is one of a special five part series meant to be shared by professionals and non-professionals alike. This particular series covers only one of the 7 Deadly Sins Every ERISA Fiduciary Must Avoid.)

What’s the real reason why total return investing far exceeds investing for income? While the typical professional fiduciary and ERISA plan sponsor have grown familiar with this concept, the reason behind it remains controversial 149741_9016_alarm_clocks_stock_xchng_royalty_free_300within the “inside baseball” of university finance departments. Worse, 401k investors possess certain cognitive biases which lure them to the false siren of investing for income. How can 401k plan sponsors overcome both the ivy covered theory of the academic world and the apparent “common sense” of the employee’s real world? It’s easy. All they need is a little baseball sense.

As late as the 1960s, by which date the academic world had had enough time to digest the stochastic concepts of Modern Portfolio Theory, the idea arose that longer holding periods can actually mute the volatility – or risk – of short term (annual) equity returns. Harold Evensky, in his book Wealth Management, attributes the concept of time diversification to Peter Bernstein, whom he credits with these two adages:

  • “The longer the investment horizon, the larger the percentage of the portfolio that should be invested in stock and other high-return assets.”
  • “In the long run, an investor can be reasonably sure that a higher volatility portfolio will earn more than a lower volatility portfolio.”

Said another way, time diversification means, over the long haul, investment returns regress to the mean. In other words, the good years tend to offset the bad years and the longer our holding period, the greater the chances this offsetting will occur.

And the data (at least the data offered by Ibbotson 2010 Yearbook) bears this out. We took the post-World War II large company returns and analyzed them over holding periods cover one year, 5 years, 10 years, 20 years and 30 years. Per the recommendation of the Ford Foundation report, we used a 5% annual return target. We then tested to see how many return periods met or exceeded our annual return target. The table below shows our results.

The Impact of Time Diversification on US Large Cap Equities using Annualized Return Data (1946-2009)

Holding Period

1 Year

5 Years

10 Years

20 Years

30 Years

Total Number of Periods






% Periods Meeting or Exceeding 5%






























Delta (Max-Min)






Standard Deviation






The data seems quite consistent with the theory of time diversification. The number of periods meeting or exceeding our annual return target of 5% increases as we increase of holding period. The median, average and difference between the maximum and minimum decrease as we increase our holding period. Finally, the traditional measure of risk – the standard deviation of the returns – reduces significantly as we increase our holding period. All these statistics suggest we are converging towards some mean, as the theory of time diversification predicts.

But all did not remain well in the hallowed halls of academia. Some felt it was heresy to suggest “risky” assets (i.e., stocks) were, in reality, less risky than Modern Portfolio Theory requires. Almost immediately after time diversification came about, Robert Merton and Paul Samuelson independently wrote papers (in 1969) attacking the premise. In 1985, Richard McEnally published a scathing refutation of the concept in The Journal of Portfolio Management. Ten years later, Zvi Bodie wrote against the idea in Financial Analysts Journal. Much like the active vs. passive debate among financial professionals, there remains no clear consensus on the merits of time diversification among finance professors.

Why? It turns out those against time diversification argue we should be looking at the standard deviation of annualized returns (like the above table does), but the standard deviation of cumulative returns. Indeed, it is true. When looking at cumulative returns, the standard deviations do not converge as you increase the holding period, they increase at a nearly exponential rate. For example, using the same base data from the above table, our standard deviations rise from 17.64% (one year) to 58.62% (five years) to 140.35% (ten years) to 574.97% (twenty years) to 895.16% (thirty years).

Critics of time diversification concede the chances of a loss will decrease over time. They maintain, though, the chances of a catastrophic loss increases. A simple way to view this is flipping a penny thirty times. Each time you flip, if you flip heads you win a penny and if you flip tails you lose a penny. Since the odds of getting heads or tails when flipping a fair coin are even, if you flip only one penny you have a 50% chance of losing a penny. Over time, however, you’ll break even – you’ll win as many pennies as you lose. In this sense, critics of time diversification agree. What they’d argue – and this is a mathematically infallible argument – is by staying in the game for 30 flips, you’ll have bought into a potential loss of 30 pennies. Again, this is true. There is some real probability (about one in a billion) that you will get tails in 30 consecutive flips.

But are these professors merely arguing abstract mathematics? This is where Babe Ruth comes in. In analyzing the Bambino’s career, we’d find in 1927 (the year he hit 60 home runs), the standard deviation of how many home runs he would hit per game was about 0.50. If we looked at monthly data, the standard deviation was about 5 and if we looked at yearly data, the standard deviation was almost 20.

Interesting phenomenon. Just as with the critics analysis of cumulative investment returns, the cumulative home run statistics of the Sultan of Swat produce standard deviations that increase dramatically as you increase the time period. Could it be that this increase in standard deviation is not a significant judgment of risk, but merely an artifact of gathering more data. It’s like comparing the home run record of a 160 game season with the home run record of a 168 game season. Does it really make sense? Quite simply, this is not an apples-to-apples comparison.

Evensky concludes the work of the academics has no practical application in the real world. “The experienced Wealth Manager makes investment recommendations based on real client’s goals and time horizons, not on the intellectual construct of the rational investor.” He says, in the real world, investors “have neither a reason nor a desire to take excess risks to earn returns in excess of their target.” More importantly, he points out “the investor is likely to be relatively indifferent as to whether he is earning one-fourth or one-half his required return. Any return significantly below the required is likely to decimate the client’s standard of living.” Evensky believes this is why time diversification works.

To paraphrase, academic theory proves time diversification does reduce theoretical volatility in exchange for increasing the magnitude of the extremes. The good professors therefore imply no theoretical justification exists for long term investors to invest in higher risk/higher return assets.

This is poppycock. It fails to recognize the realities investors must face both in their choice of investments and the way they set goals. As we demonstrated in the previous installment of this series, an analysis of actual return data proves investors are far more likely to use up their principal when they invest for income (through risk free bonds) than when they invest for total return. There was only one time period where stocks performed more poorly than bonds and that was in the most recent ten years.

Ironically, this is consistent with our time diversification analysis in the table above. We see there that there remains roughly a one in ten chance of missing the 5% return target over ten years. The only way to reduce that likelihood is to extend the holding period. And remember, the study we revealed in the previous part to this series took inflation into account, too.

If there’s one visual the plan sponsor can use to establish the value of total return investment under the concept of time diversification, it’s the Grand Canyon. This natural wonder is 18 miles at its widest point. When you’re trying to jump across the 18 mile chasm of the Grand Canyon, your only goal is to jump a minimum of 18 miles. You’ll still be alive whether you jump 18 miles or 180 miles (this assumes, of course, you’ve learned how to roll when you land).

On the other hand, you’ll still be a splat on the Canyon floor whether you jump two feet or you double the current long jump record of 29.4 feet set on August 30, 1991 by American Mike Powell at the World Championship Games in Tokyo by sailing an incredible 58.8 feet.

Now, imagine this: A gang of alien thugs, recently escaped from Area 51 in nearby Rosewell, New Mexico, are forcing you at laser point to jump across the Grand Canyon. Being somewhat compassionate, they allow you to select between two choices of footwear: You can pick the most expensive pair of athletic track and field shoes (in fact, the one’s worn by Mike Powell when he set the world long jump record); or, You can opt for a pair of experimental rocket shoes which have successful allowed people to jump at least 18 miles five out of ten times.

Remember, you’re at gunpoint.

Which pair of shoes do you choose? The one’s that guarantee you go splat or the one’s where you’ve got only a 50% chance of going splat.

What in the world would prevent you from making the same kind of choice when it comes to your investments? Remember, 401k investors have to plan on having only one chance to pick a right investment strategy to meet their goals. Plan sponsors need to help them focus on the practical, not on the theoretical.

We’ll end this series with one more question. Returning to our penny flipping days, you’ve just flipped 29 straight tales on a fair coin. What’s the probability of flipping a tail for a 30th straight time? (Remember, the odds of flipping 30 straight heads are one in a billion.)


Got the answer yet?

I’ll give you just a little bit more time. Incidentally, if you bought $100,000 of 1945S pennies in 1945, they’d be worth about $400,000 today. That’s still less than what your stocks would be worth. And if you flipped one of those 1945S pennies tails 29 straight times, the probability of flipping tails for a 30th straight time would be 50%. Yes, that’s right. Since each individual flip is independent of one another, the odds of each flip always remain 50-50.

So, time may be on your side, but “past performance does not guarantee future results” or, as Babe Ruth once said:

“Yesterday’s home runs don’t win today’s games.”

Part I: What do Robin Hood, Investment Income and Fiduciary Duty have in Common?
Part II: Plan Sponsor Warning: What’s Wrong with Emphasizing Income?
Part III: Is Income Really the Only Way for a 401k Fiduciary to Meet an Objective
Part IV: If Income Doesn’t Matter, What Should Plan Sponsors Look For?
Part V: How the ERISA Fiduciary Can Avoid the 1st Deadly Sin – Whither “Time Diversification?”

About Author

Christopher Carosa, CTFA

Christopher Carosa, CTFA


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