The Imaginary Line

December 6, 2005 — Leave a comment

[Updated Data February, 2011]

Note: This article refers specifically to the portfolio Long-Term Component by Quality Asset Management, but may be applied to certain other portfolios, as described in the end of the article

How would you like to never worry again about your investments? You already know that your portfolio grows at a pace that is hard to believe, doubling its value every 4-5 years. This is based on the simulated average yearly returns of 17.2% since 1970. This is the average pace. How would you like to put a minimum to the rate of growth? Let’s see how this can be done:

Stretching the Imaginary Line : You can view your long-term portfolio as growing at all times at the higher of the following two rates:

1. Its actual growth rate.

2. The all-time highest peak value of the portfolio plus 4% of this value, adjusted for inflation, for each year that passed since reaching it. Your portfolio is likely to keep up with this Imaginary Line of growth within a few years, as explained below. Since this is a long-term investment, you shouldn’t care about temporary disparities.

Why does this work?

  1. It stood the test of time . In the worst possible scenario since the portfolio was simulated (beginning in 19701), the portfolio value outperformed the Imaginary Line within little over 4 years when measured from the highest peak. Most cases were much better.
  2. It’s logical . This portfolio represents ownership of thousands of companies all over the world. The companies provide the products and services that we need, more cheaply and efficiently than we do on our own. Companies are expected to stick around and grow unless we will prefer to work harder for our needs. The diversification reduces the decline periods and the inclusion of rapidly developing countries and companies increases the average growth.
  3. High average growth . The average growth of the portfolio (17.2% as simulated since 1970) includes all of the worst recessions. In order to keep such a high average, the portfolio has to rise steeply after any significant or prolonged decline. The longer and steeper the decline the quicker the recovery is expected to be.
  4. Conservative measure . The Imaginary Line was intentionally chosen to be conservative, letting the portfolio keep up with it in a few years, even in recessions worse than the worst we’ve seen in simulated history.

Example : Assume that you invested $1,000,000 in the portfolio Long-Term Component, in 1970. The graph below presents the portfolio value and the Imaginary Line from 1970 to 2010. In most of the years, the portfolio has the same value as the Imaginary Line, meaning that it grows faster than the 4% inflation adjusted additions of the Imaginary Line – normally much faster. In the few years when the Imaginary Line grew faster than the portfolio, it was limited to less than 2 years in most cases, and about 4 years in the worst case.

By expecting a minimum of 4% annual additions at all times, you were right most of the time, and, when measured over more than 4-year periods, you were right at all times!

By tracking the Imaginary Line, you stayed positive at all times, while your portfolio grew from $1,000,000 to $669,000,000 , doubling on average every 4 years and 6 months.

2005-12 The Imaginary Line Graph

Let’s view the details of the worst recession period since 1970. The following data is highlighted:

  1. Portfolio value: actual portfolio value.
  2. Total Value: the value of the Imaginary Line.
  3. Distance: the percent gains needed for the portfolio to match the Imaginary Line.
Year Portfolio Inflation Imaginary Line
  Value Annual Change   Additions (5%+inflation) Total Value Distance
1972 $2,228,743 $2,228,743
1973 $1,845,867 -17% 8.8% $89,150 $2,317,893 26%
1974 $1,356,934 -26% 12.2% $96,977 $2,414,870 78%
1975 $2,056,840 52% 7.0% $108,808 $2,523,678 23%
1976 $2,538,223 23% 4.8% $116,436 $2,640,114 4%
1977 $3,911,859 54% 6.8% $3,911,859
1978 $5,837,433 49% 9% $5,837,433
. . . . . . .
2008 $364,546,436 -45% 0.09% $26,699,364 $694,183,453 90%
2009 $553,399,717 52% 2.7% $26,723,660 $720,907,113 30%
2010 $668,827,830 21% 1.50% $27,445,199 $748,352,312 12%

As you can see in the table, the portfolio declined by 39% over 2 years (1973-1974), while the Imaginary Line grew over 8%. In order to reach this target, the portfolio has to grow by 78%! You might say, “It would never recover plus keep up with 4% inflation-adjusted annual additions!”

But since the average growth of the portfolio including the decline years is so high (17.2% simulated since 1970), it is most likely to grow at a very high rate. In 2 years it nearly recovered and kept up with the Imaginary Line. In 2 more years it doubled again!

Bonds for security? If you consider an investment offering about 4% per year on average just to avoid losing money, think twice. Investments like government bonds and fixed annuities may be great for short-term security but do not offer real long-term security.

Can the approach work for other portfolios? The approach presented can be applied only to portfolios that lack stock picking or market timing, are highly diversified and have long-term historic performance data (at least a 30-year simulation).

If a portfolio fits this profile, it will require adjusting the imaginary growth according to its long-term behavior. Many portfolios are more volatile and have lower average growth, and will require lower imaginary additions. Please contact QAM regarding specific portfolios.

Note that past performance does not guarantee future returns. Each individual should have a personal plan to deal with cases worse than those seen in the past.


1 The 2008 decline was worse, but was too recent for tracking its long-term effects. Given that it was very limited in time and nearly recovered by the end of 2010, you can anticipate results consistent with the 1970’s decline.

Disclosures Including Backtested Performance Data

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Gil Hanoch


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