In another thread, Lieutenant.Columbo asked the following questions:

viewtopic.php?f=2&t=196768&p=3006499#p3006499
Lieutenant.Columbo wrote:longinvest wrote:For those retiring earlier, I would recommend accumulating more. A rule of the thumb would be **to multiply the ratio of VPW rates between retirement and 65 by 4%**. Example: To retire at 55, I would multiply VPW's ratio of 55-years old and 65-years old percentages by 4% (see lines 55 and 65 of the 50/50 allocation in the VPW table): (4.3 / 4.8) X 4% = 3.6%, or accumulate 28 times residual expenses plus the money required to fill the gap between retirement and the start of lifelong base income payments.

**1.** what's the mathematical reason behind calculating the ratio of the two VPW rates?

**2.** what is the reason for multiplying by 4?

**3.** interestingly, using the calculation you suggested, and for the same two ages (55, 65) the resulting withdrawal rate for someone with an 80% stock/20% bond portfolio is 3.64% (while it was 3.58% for the scenario you described);

I was surprised at how similar both withdrawal rates are for such different portfolios;

what are your thoughts on this?

thank you

Here are my answers:

**1.** what's the mathematical reason behind calculating the ratio of the two VPW rates?

The VPW percentages increase with age. By taking the ratio of VPW percentages between retirement and 65, it gives us an idea of how much less one should withdraw from a portfolio when retiring earlier. It might not be precise, but it should be a

*good enough* approximation.

For example, with a 50/50 portfolio, one would withdraw 4.8% of his portfolio on the first year of retirement at age 65, using VPW.

With the same 50/50 portfolio, one would withdraw 4.3% of his portfolio on the first year of retirement at age 55, using VPW.

So, the person retiring at 55 would withdraw

(4.3/4.8) = 89.6% of what a person retiring at 65 would withdraw from the same portfolio.

**2.** what is the reason for multiplying by 4?

The 4 represents the traditional 4% SWR

planning number, used as a ratio to estimate how much one needs to accumulate to retire. The idea is if it is "safe" to take out 4%, it means that we need to accumulate 100%/4% =

25 times our planned withdrawal needs.

Why use this number? Why not take the initial VPW percentage at 65, instead? Because the VPW will lower withdrawals, during retirement, after bad market years. This means that if one was to retire just before a storm (like 1927-1928 or 2007-2008), one would get lower withdrawals in subsequent years after retirement.

Interestingly, when we backtest VPW with asset allocations ranging between 25/75 to 75/25 stocks/bonds, we discover that the

**median** VPW withdrawal was

higher than 4% of the initial portfolio, in

almost all backtested scenarios. We can see this in the

*Withdrawal Statistics* chart of the VPW spreadsheet:

Note: Look at the

**blue** line.

**25% US stocks / 75% US bonds**
**50% US stocks / 50% US bonds**
**75% US stocks / 25% US bonds**
As we can see, except for a few retirement years in the late 1930s, early 1940s, and mid 1960s with a

low 25% stocks allocation, all the

*medians* were higher than $40,000 (e.g. 4% of the simulated initial $1,000,000 portfolio).

That's what I consider

*good enough*, and it matches well with the

*traditional* number almost everybody uses. I like simplicity, so I won't fight it. I'll accept the 4% SWR as planning number, regardless of asset allocation (assuming the investor is a Boglehead with at least 25% in each of stocks and bonds).

**3.** interestingly, using the calculation you suggested, and for the same two ages (55, 65) the resulting withdrawal rate for someone with an 80% stock/20% bond portfolio is 3.64% (while it was 3.58% for the scenario you described);

I was surprised at how similar both withdrawal rates are for such different portfolios;

what are your thoughts on this?

As I picked 50/50, for my example, the ratio was probably in the middle of possible ratios. If I take the 55 to 65 years old 80/20 stocks/bonds ratio, it is 5.0/5.5 = 91%. If I take the 55 to 65 years old 20/80 stocks/bonds ratio, it is 3.6/4.2 = 86%. The 50/50 stocks/bonds ratio of 89.6% is in between.

**Notes**
Let me remind readers that this is just a simple

**rule of thumb** that I have developed for myself. One should never lose sight that one cannot insure a lifelong base of income using withdrawals from a portfolio of risky assets (stocks

and bonds)*, regardless of the chosen withdrawal method. As a consequence, VPW withdrawals are best combined with lifelong base income such Social Security, pension (if any), and (if necessary) an

inflation-indexed Single Premium Immediate Annuity (SPIA).

*

Yes, bonds have risks, too, not only stocks. Bonds have interest rate risk. Bonds have liquidity risk. Some bonds have credit risk. etc.
The gap between (early-)retirement and the start of lifelong income payments is best filled by setting aside enough money into cash investments (high-interest savings accounts, CDs) which don't fluctuate in value and earn enough interest to match inflation. See:

viewtopic.php?t=102609 for an example of this (to delay Social Security to 70). Of course, this money should not be taken into account when calculating a VPW withdrawal. In terms of early retirement planning, this money should be in addition of whatever money is needed for VPW withdrawals according to the ratio calculated using our rule of thumb.

Bogleheads investment philosophy |
Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds |
VCN/VXC/VAB/ZRR