The Imaginary Line in Retirement

January 6, 2006 — Leave a comment

[Updated Data February, 2011]

The previous article, “The Imaginary Line” (Hanoch, December 2005), demonstrated how to never worry again about your investments. This article assumes that you have read the previous one, and presents a modified approach for retirees making annual withdrawals.

How would you like to achieve growing security throughout your retirement? You already know that your portfolio grows at a pace that is hard to believe: simulated average yearly returns of 17.2% since 1970. How would you like to see your portfolio constantly growing? Let’s see how this can be done:

Stretching the Imaginary Line : Assume that you are retired and hold the portfolio Long-Term Component by QAM. Based on the portfolio value on your retirement date, you withdraw 4% annually, adjusted for inflation. You can view this as your 4% inflation-protected dividend.

Take the highest peak of the portfolio, and imagine that your portfolio never declines below that level, despite any recessions and despite the growing annual withdrawals. No matter how much the portfolio declined recently, view it as if it did not decline at all.

Your portfolio value is likely to keep up with the imaginary line of growth within a few years, for reasons explained in the previous article.

Example : Assume that you retired with $1,000,000 in the portfolio Long-Term Component, in 1973, at the beginning of the worst recession in the 40-year simulated history 1. Also, assume that you withdraw $40,000 per year, growing with inflation. The graph below presents the portfolio value and the Imaginary Line from 1973 to 2010. In most of the years, the portfolio has the same value as the Imaginary Line, meaning that it keeps growing despite the 4% inflation adjusted withdrawals – normally very fast. In the few years when the Imaginary Line was higher than the portfolio, it was limited to less than 2 years in most cases, and 4-5 years in the worst case.

By expecting the portfolio to never decline, you were right most of the time, and, when measured over periods longer than 4 years, 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 $125,000,000 , doubling on average every 6 years, while you lived off it!

2005-12 The Imaginary Line Graph in Retirement

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 Income (5%+inflation)   Total Value Distance
1972 $1,000,000 $1,000,000
1973 $778,210 -22% $40,000 8.8% $1,000,000 29%
1974 $517,688 -33% $43,512 12.2% $1,000,000 93%
1975 $725,756 40% $48,820 7.0% $1,000,000 38%
1976 $827,753 14% $52,243 4.8% $1,000,000 21%
1977 $1,207,266 46% $54,761 6.8% $1,207,266
1978 $1,728,445 43% $58,468 9% $1,728,445
2008 $68,322,052 -46% $198,389 0.1% $125,551,660 84%
2009 $103,468,080 51% $198,570 2.7% $125,551,660 21%
2010 $124,794,538 21% $203,931 1.5% $125,551,660 1%

As you can see in the table, the portfolio declined by 48% over 2 years (1973-1974). In order to reach the recent peak, the portfolio has to grow by 93%! You might say, “It would never recover, especially considering the growing annual withdrawals!”

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 less than 3 years it fully recovered, despite the growing withdrawals, and by the 4 th year, the portfolio tripled its value!

How can you make things even better?

  1. Short-term security : Hold money outside of the portfolio for short-term security, and use it during severe recessions. This would reduce the decline level and duration.
  2. Other income : use social security income, pension payments and available annuities to reduce the portfolio withdrawals, the decline amount and its duration.
  3. Deferral of expenses : defer some expenses during severe declines to reduce the impact of withdrawals.

Don’t try this with bonds! A 5-year government bond portfolio never survived 4% inflation adjusted withdrawals – it was depleted completely!

Can the approach work for other portfolios? Please review the previous article for limited applicability to other 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.

To Summarize

The portfolio Long-Term Component has a combination of global diversification and rapid growth that result in the combination we all dream about: relatively short declines and rapid recoveries. It allows the portfolio to withstand 4% annual withdrawals that grow with inflation. Instead of the portfolio decreasing with your age, it grows out of hand as the years go by. Instead of consuming your capital in your retirement, or preserving it, it keeps growing indefinitely!


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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