Friday, November 4, 2016

Calculating Required Retirement Savings Rates: Part 5

In Part 1 of this series on calcluating required retirement savings rates, I stated this assumption:
  • The remainder of your retirement living expenses will be covered by annual, inflation-adjusted withdrawals of 4% of your retirement savings.
In this post I'll explain what this means, evaluate whether or not this assumption is reasonable, and discuss a few different ways to think about this.

The statement about the 4% withdrawal rate can be interpreted in different ways, but the most common interpretation is that you withdraw an inflation-adjusted 4% of your original retirement savings each year. So if you had $1,000,000 of retirement savings when you first retired, your withdrawal in the first year would be $40,000 (4% x $1M). If inflation was 2% in your first year of retirement, your withdrawal in the second year would be $40,800 (1.02 x $40,000), regardless of the size of your portfolio at the beginning of year two. The purpose of withdrawing a constant, inflation-adjusted amount is to allow you to maintain a similar lifestyle throughout retirement, regardless of the change in purchasing power of your dollars due to inflation.

This approach for retirement income planning is widely used and written about by financial planners. The approach has its origins in studies published by various financial planners and academics in the 1990s. These studies showed that this approach would have enabled a balanced portfolio of US stocks and bonds to have survived the worst 30-year period since 1926. In other words, 4% would have been a safe withdrawal rate (SWR) for a 30-year retirement starting in any year since 1926, and you would not have run out of money even if you retired at the beginning of the worst 30-year period of real returns for stocks and bonds. At least 50% of the retirement portfolio had to be in stocks; failure rates were higher at lower stock allocations.

A second school of thought about retirement planning is that it is imprudent to rely on historical stock and bond returns for retirement planning purposes, and that you should not depend on returns from risky assets, like stocks, for retirement income. Instead, you should either keep your retirement savings in safe assets, or purchase an annuity that guarantees a set level of income for life. Of course the safe assets or annuity should ideally be inflation protected.

In Part 1 of this series I explained that an initial withdrawal rate of 4% implies that your initial retirement savings equals 25 years of residual retirement expenses (retirement expenses not covered by Social Security benefits or a pension). This means that if you earned a steady 0% real return in safe assets, and withdrew an inflation-adjusted 4% annually, you would run out of money in 25 years. What real rate of return on safe assets would be required for the portfolio to last 30 years? We can answer this with the following spreadsheet RATE formula:

=RATE(30, 4, -100, 0)

In this formula, 30 is the number of years, and you can interpret the 100 as 100% of your retirement savings at the beginning of the 30-year period, the 0 as 0% of your retirement savings at the end of the 30-year period, and the 4 as a withdrawal rate of 4% per year. This formula returns 1.2% as the required real rate of return (you can copy the formula and paste it into a Google Sheets or Excel spreadsheet to verify it for yourself).

You can change the number of years in the formula to determine the required real rate of return to support different length retirements. Plugging in 25 as the number of years gives a required real return rate of 0%, as expected. Plugging in 40 years gives a required real return rate of 2.5%. What guaranteed, real rate of return can you earn in the current economic environment with historically low interest rates?

The only investments I know of that guarantee a real (inflation-adjusted) rate of return for US investors are TIPS (Treasury Inflation Protected Securities). You can look up the current TIPS interest rates (yields) here: Daily Treasury Real Yield Curve Rates. Currently I see a rate of 0.75% for the 30-year TIPS, with lower rates for shorter maturities, and negative real rates for maturities of 7 years or less. So currently you cannot earn even 1% real with TIPS, which means that you cannot count on TIPS for a 30-year retirement at a 4% withdrawal rate.

Just as we easily calculated that a 0% real rate of return would support a 25-year retirement at a 4% withdrawal rate (since 1/25 = 4/100 = 4%), we can easily calculate the withdrawal rate that will support a 30-year retirement at a 0% real rate of return as 1/30 = 3.33/100 = 3.33%. We can verify this with the spreadsheet PMT formula:

=PMT(0%,  30, -100, 0)

This returns a value of 3.33, which we can interpret as the expected 3.33% withdrawal rate. We can replace the 0% in the formula with different return rates to determine withdrawal rates that would support a 30-year retirement. For example, assuming we could earn an average real rate of 0.5% from a 30-year TIPS ladder, with one TIPS maturing each year to cover our residual living expenses. we can use this formula to calculate the withdrawal rate

=PMT(0.5%,  30, -100, 0)

This returns 3.6, which we can interpret as a 3.6% withdrawal rate. We already used the spreadsheet RATE formula to determine that a 1.2% real rate of return would support a 30-year retirement at a 4% withdrawal rate, and we can plug 1.2% into the PMT formula to verify this; it returns 4.0 as expected.

Of course to support longer retirements requires either lower withdrawal rates or higher rates of return. For example, to retire at age 50 with the expectation of living until age 90, we could use this PMT formula to determine the supported withdrawal rate for 40 years at a 0.5% real rate of return:

=PMT(0.5%,  40, -100, 0)

This formula returns 2.8, which we can interpret as a 2.8% withdrawal rate. This means that with an initial retirement savings amount of $1,000,000, residual living expenses would be funded with annual retirement savings withdrawals of $28,000, adjusted for inflation.

The conclusion is that using only safe assets for retirement income for a 30-40 year retirement implies safe withdrawal rates of closer to 3% than 4%.

Some financial planners and investment experts suggest that with current, historically low real interest rates, it is imprudent to assume that even a balanced portfolio of stocks and bonds will support the historically-justified 4% safe withdrawal rate, and that it is more prudent to use something like 3% as a safe withdrawal rate for retirement planning purposes. So although I used a 4% withdrawal rate in the calculations in the prior posts in this series, it may be prudent to re-run the savings calculations with a 3% withdrawal rate, which will result in higher required savings rates.

As an example, let's consider a 25-year old earning a constant, inflation-adjusted salary of $60,000, retiring at age 65, and earning a real return of 4% during the working years. Assuming $20,000 of annual Social Security benefits in today's dollars, at a retirement savings safe withdrawal rate (SWR) of 4% I calculate a required savings rate of about 14%. Lowering the SWR to 3% increases the required savings rate to about 17%.


  1. Thanks for the great article. This closely matches my situation but I am fortunate to need only 2% withdrawal due to pension and FRA SS payments. I enjoyed the math for determining the actual return needed.

  2. The calculation you are doing is much better to survive after retirement. Thanks to share this blog which are very useful to all people .Retirement Living in Florida