Ridiculous Pessimism

Rob Bennett of www.PassionSaving.com sent me an email, directing my attention to an article in the September 5, 2005 issue of Barrons, Can You Afford to Retire? He wrote his own comments in his blog entry of September 8, 2005. (Scroll down.)
Comments based on Can You Afford to Retire?

Rob is anything but a pessimist. Although he was willing to accept the notions put forth at face value, he did not fall victim to its negative outlook. Rob’s assessment: ”It sounds depressing on first review. I don't think that the mathematics is as discouraging as Pollock makes it out to be, however.”

Rob readily admits that he is not a numbers guy. He was right to reject the pessimism. He was wrong to accept the mathematics. Only in a very narrow sense do the numbers come close to telling us the truth. This is why I have come up with my own description: Ridiculous Pessimism.

A Narrowly Defined Mathematical Problem

The article has several percentages and rates that confuse matters.

This is the actual calculation:
1) Assume that you want to save enough to be able to withdraw 70% of your annual income for 20 years.
2) If your nest egg grows enough to match inflation exactly, but no more, you can withdraw 5% per year for 20 years before running out of money.
3) Under these conditions, your nest egg needs to be 14 times your annual income. That is, your nest egg equals 20 years of withdrawals times 70% of your annual income, which equals 14 times your annual income.
4) If you invest the same amount annually for 40 years, with the first payment being made at the beginning of the first year, your final balance will equal 100 times (more precisely, 99.82 times) the amount of your annual investment. (If you invest the same amount annually for 40 years, with the first payment being made at the end of the first year, your final balance will equal 95.03 times the annual investment.)
5) If you invest 14% of your income annually, starting at the beginning of the first year, your final nest egg equals 14 times your annual income. That is, 14% of 100 (more precisely, 99.82) times your annual income equals 14 (more precisely, 13.9748) times your annual income.

Big Holes in the Logic

Rob Bennett has seen lots of articles with lots of numbers. He is right when he talks about the extreme sensitivity of percentages. The percentages that he should be mentioning are the rate of return on investments (which was 4% above inflation) and the withdrawal rate (which was zero percent above inflation) in retirement.

Rob was misdirected by the article. He was wrong when he talked about a special sensitivity to the savings rate. The savings rate scales directly. That is, if you double your annual savings, you end up with twice the nest egg and twice the annual withdrawal amount.

The Investment Return

The article’s 4% real return on investments is reasonable for a mixed portfolio of stocks and bonds.

Most articles would mention the 7% long-term historical annualized real return of stocks.

I would qualify both numbers, in view of my own findings. However, I am not overly concerned with this part.

With equal investment amounts made at the beginning of each year for 40 years, the total amount at 4% equals 99.8 times the annual investment amount. At 7%, the total is 214.6 times the annual investment amount. At 4%, it takes an annual investment of $10020 to reach one million dollars. At 7%, it takes an annual investment of $4660 to reach one million dollars. Both amounts are reasonable.

Remember that all of these amounts are in terms of real dollars. You must adjust them to match inflation.

The Withdrawal Rate

We have focused on early retirements. Rob Bennett’s Passion Saving approach will help you build your nest egg much faster. My research shows how you can make your nest egg do more for you.

We must start with a baseline. These are minimal numbers.
1) A zero percent real interest rate produces 5.0% (plus inflation) for 20 years.
2) A one percent real interest rate produces 5.5% (plus inflation) for 20 years.
3) A two percent real interest rate produces 6.1% (plus inflation) for 20 years.

Using these withdrawal rates and applying our findings, we are able to extend this time period into the indefinite future.

Portfolios for Even the Youngest Retirees

Now see what happens if you wait to take advantage of favorable valuations. We can expect such valuations in the intermediate-term (approximately, ten years).

Consider these portfolios. They are relevant even to the youngest of retirees. I have extracted the following from Withdrawal Rates at Favorable Valuations.
Withdrawal Rates at Favorable Valuations

Portfolios CTVR50 and CTVR80 provide 30 years of withdrawals without loss.

Portfolios HFWR50 and HFWR80 provide 30 years of withdrawals with a balance that never drops below one-half of the initial balance.

Interestingly, the CTVR portfolios sometimes drop below one-half of the initial balance before year 30.

CTVR50 (Constant Terminal Value Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 50%. The commercial paper allocation is 50%. At the Calculated Rate, the final portfolio balance equals the initial balance.

CTVR80 (Constant Terminal Value Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 80%. The commercial paper allocation is 20%. At the Calculated Rate, the final portfolio balance equals the initial balance.

HFWR50 (Half Failure Withdrawal Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 50%. The commercial paper allocation is 50%. At the Calculated Rate, the lowest portfolio balance equals (or exceeds minimally) one-half of the initial balance in throughout the entire 30 years.

HFWR80 (Half Failure Withdrawal Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 80%. The commercial paper allocation is 20%. At the Calculated Rate, the lowest portfolio balance equals (or exceeds minimally) one-half of the initial balance in throughout the entire 30 years.

Equations

This is the Calculated Rate of portfolio CTVR50.
y = 0.3279*x + 1.4254 plus 0.72% and minus 0.72%.

This is the Calculated Rate of portfolio CTVR80.
y = 0.7033*x + 0.2133 plus 1.10% and minus 1.10%.

This is the Calculated Rate of portfolio HFWR50.
y = 0.3408*x + 2.0804 plus 0.88% and minus 0.88%.

This is the equation for the Calculated Rate of portfolio HFWR80.
y = 0.6822*x + 0.5298 plus 1.864% and minus 1.864%.

Withdrawal Rates at Favorable Valuations

If we wait for favorable valuations and then invest heavily in stocks, we can withdraw 6% (plus inflation) without losing ground.

These portfolios (CTVR50, CTVR80, HFWR50 and HFWR80) consist of stocks and commercial paper. They would do better with TIPS.

Calculated Rates

When P/E10 = 8:
The Calculated Rate of portfolio CTVR50 is 5.524.
The Calculated Rate of portfolio CTVR80 is 9.005.
The Calculated Rate of portfolio HFWR50 is 6.340.
The Calculated Rate of portfolio HFWR80 is 9.057.

When P/E10 = 10:
The Calculated Rate of portfolio CTVR50 is 4.704.
The Calculated Rate of portfolio CTVR80 is 7.246.
The Calculated Rate of portfolio HFWR50 is 5.488.
The Calculated Rate of portfolio HFWR80 is 7.352.

When P/E10 = 12:
The Calculated Rate of portfolio CTVR50 is 4.158.
The Calculated Rate of portfolio CTVR80 is 6.074.
The Calculated Rate of portfolio HFWR50 is 4.920.
The Calculated Rate of portfolio HFWR80 is 6.215.

Safe Withdrawal Rates

Safe Withdrawal Rates are lower confidence limits relative to Calculated Rates.

When P/E10 = 8:
The Safe Withdrawal Rate of portfolio CTVR50 is 4.8.
The Safe Withdrawal Rate of portfolio CTVR80 is 7.9.
The Safe Withdrawal Rate of portfolio HFWR50 is 5.5.
The Safe Withdrawal Rate of portfolio HFWR80 is 7.2.

When P/E10 = 10:
The Safe Withdrawal Rate of portfolio CTVR50 is 4.0.
The Safe Withdrawal Rate of portfolio CTVR80 is 6.1.
The Safe Withdrawal Rate of portfolio HFWR50 is 4.6.
The Safe Withdrawal Rate of portfolio HFWR80 is 5.5.

When P/E10 = 12:
The Safe Withdrawal Rate of portfolio CTVR50 is 3.4.
The Safe Withdrawal Rate of portfolio CTVR80 is 5.0.
The Safe Withdrawal Rate of portfolio HFWR50 is 4.0.
The Safe Withdrawal Rate of portfolio HFWR80 is 4.4.

High Risk Rates

High Risk Rates are upper confidence limits relative to Calculated Rates.

When P/E10 = 8:
The High Risk Rate of portfolio CTVR50 is 6.2.
The High Risk Rate of portfolio CTVR80 is 10.1.
The High Risk Rate of portfolio HFWR50 is 7.2.
The High Risk Rate of portfolio HFWR80 is 10.9.

When P/E10 = 10:
The High Risk Rate of portfolio CTVR50 is 5.4.
The High Risk Rate of portfolio CTVR80 is 8.3.
The High Risk Rate of portfolio HFWR50 is 6.4.
The High Risk Rate of portfolio HFWR80 is 9.2.

When P/E10 = 12:
The High Risk Rate of portfolio CTVR50 is 4.9.
The High Risk Rate of portfolio CTVR80 is 7.2.
The High Risk Rate of portfolio HFWR50 is 5.8.
The High Risk Rate of portfolio HFWR80 is 8.1.

Summary

This analysis should remove some of the fog caused by the article.

Taking advantage of favorable valuations always works, both during accumulation and during distribution.

If we wait for favorable valuations and then invest heavily in stocks, we can withdraw 6% (plus inflation) for 30 years without losing ground.

The really big holes in the article’s logic are related to building the nest egg. Motivated saving works miracles.

There are other issues as well. For example, why was the requirement identified as 70% of annual income? Rob Bennett has made this clear: you should base your planning on your expenses in retirement, not on your income before retirement.

Rob remained optimistic because he knows better. His own experience and the experience of others on that he has met on discussion boards refute the pessimistic outlook found in the Barrons article.

Have fun.

John Walter Russell
September 23, 2005