Here's an interesting series of questions and answers with a surprising conclusion at the end.

I'm sure that many would not have believed me if I simply stated the conclusion without first showing the complete calculations.

Enjoy!

Q-1: What is the inflation-indexed amount that must be invested yearly, over a period of 30 year, to accumulate an inflation-adjusted $1,000,000 portfolio, at a nominal growth rate of 10.1% and a 3% inflation rate?

A-1: $10,778.40

This was calculated as follows:

- Inflation-adjusted growth rate = (1 + 10.1%) / (1 + 3%) - 1 = 6.9%
- Using a financial calculator: n=30, i=6.9, PV=0, FV=1000000 => PMT = -10778.40

Q-2: What is the inflation-indexed amount that must be invested yearly, over a period of 30 year, to accumulate an inflation-adjusted $1,000,000 portfolio, at a nominal growth rate of 8.7% and a 3% inflation rate?

A-2: $13,805.39

This was calculated as follows:

- Inflation-adjusted growth rate = (1 + 8.7%) / (1 + 3%) - 1 = 5.5%
- Using a financial calculator: n=30, i=5.5, PV=0, FV=1000000 => PMT = -13805.39

Q-3: How much more must be invested yearly, over a period of 30 year, to accumulate an inflation-adjusted $1,000,000 portfolio, at a growth rate of 5.5% real instead of 6.9% real?

A-3: 28%

This was calculated as follows:

- Using the answers of Q-2 and Q-1: $13,805.39 / $10,778.40 - 1 = 28%

Q-4: If future annual returns in the upcoming 30 years were exactly 6.9% real for a 100% stocks portfolio, and 5.5% real for a 60/40 stocks/bond portfolio, how much more should an investor save, assuming he makes an inflation-adjusted $80,000 yearly salary and will be getting an inflation-adjusted $25,000 yearly Social Security pension during retirement?

A-4: 21%

This was calculated as follows:

- Our objective is for work-years salary minus savings to be equal to total retirement income. We're assuming that savings are invested into a tax-deferred account, and that tax rates will be similar on equal taxable total-income during work years and retirement.
- Assuming that a portfolio at retirement supports approximately 4% in withdrawals, our objective is to split the excess in work-years salary over future Social Security income, that is ($80,000 - $25,000) = $55,000, between savings and taxable income such that work-years excess taxable income is equal to retirement-years excess taxable income (on top of Social Security).
- At a growth rate of 6.9%, every $1 of annual savings accumulates to $92.78, 30 years later, supporting $92.78 X 4% = $3.71 in retirement spending.
- As a consequence, we split the excess $55,000 according to the ratio 1:3.71 between savings and taxable spending. This results into $11,674.49 in tax-deferred yearly savings. This leaves $80,000 - $11,674.49 = $68,325.51 for paying taxes and spending.
- At a growth rate of 5.5%, every $1 of annual savings accumulates to $72.44, 30 years later, supporting $72.44 X 4% = $2.90 in retirement spending.
- As a consequence, we split the excess $55,000 according to the ratio 1:2.90 between savings and taxable spending. This results into $14,111.90 in tax-deferred yearly savings. This leaves $80,000 - $14,111.90 = $65,888.10 for paying taxes and spending.
- The additional ratio of savings is thus: $14,111.90 / $11,674.49 - 1 = 21%

Q-5: What is the impact of the additional 21% in tax-deferred savings on after-tax net spending, for the example shown in Q-4?

A-5: 3.3% or $153.17 per month

This was calculated as follows:

- We approximate after-tax income using the 2017 marginal tax rates in this Wikipedia table.
- The first $9,325 of income attract 10% in taxes. That's $9,325 X 10% = $932.50.
- Additional income up to $37,950 attracts 15% in additional taxes. That's ($37,950 - $9,325) X 15% = $4,293.75.
- Additional income up to $91,900 attracts 25% in additional taxes.
- The 100/0 investor has a pre-tax after-savings income of $68,325.51. It attracts ($68,325.51 - $37,950) X 25% = $7,593.88 in additional taxes. He is left with: $68,325.51 - $932.50 - $4,293.75 - $7,593.88 = $55,505.38 for spending.
- The 60/40 investor has a pre-tax after-savings income of $65,888.10. It attracts ($65,888.10 - $37,950) X 25% = $6,984.53 in additional taxes. He is left with: $65,888.10 - $932.50 - $4,293.75 - $6,984.53 = $53,677.32 for spending.
- The impact on net spending, in terms of ratio, is thus: $53,677.32 / $55,505.38 - 1 = -3.3%.
- As an absolute amount, this is: ($55,505.38 - $53,677.32) / 12 = $153.17 per month.

Yes, that's it. By reducing total spending by a mere 3.3%, an investor could use a less volatile 60/40 portfolio all lifelong and still retire with dignity.

Added (1): Forum member #Cruncher has developed an awesome little spreadsheet encoding the calculations of this post, along with improvements and additional flexibility. It can be found here: viewtopic.php?f=10&t=225497&start=50#p3491294.

Added (2): Forum member #Cruncher has provided a summary of how the "cost" of the 60:40 portfolio computed in this post compares to other ways of computing its "cost": viewtopic.php?p=3494999#p3494999