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### TIPS Equivalent Safe Withdrawal Rates

Posted: Sat Dec 28, 2002 7:11 am
TIPS Equivalent Safe Withdrawal Rates

A. Context
1. The larger question is how to handle three investment classes, each with its own goals. This is a blend of hocus's separation of portfolios along the lines of required levels of safety (necessities, normal requirements and luxuries) and types of investments (TIPS or cash equivalents), high-income low-risk (high dividend stocks and REITS) and growth (stocks in general).
2. One way to look at this is to convert a (historical) safe withdrawal rate to a cash-only equivalent. For example, you can safely withdraw 3.33% from an all cash portfolio over 30 years just so long as it grows enough to match inflation. Treasury Inflation Protected Securities (TIPS) and Inflation Bonds (ibonds) match inflation and add some real growth as well.
3. It is straightforward to determine how much interest TIPS must provide to match a (historical) safe withdrawal rate of another investment. With TIPS the balance is guaranteed to be zero at the end of the withdrawal period. With alternative investments the final balance would be zero only under worst case conditions. Under normal circumstances the final balance would be much higher.
B. The formula
1. For the mathematically inclined the formula that relates withdrawal rate, investment growth rate (TIPS interest rate) and duration is:

withdrawal rate = (g-1) / [1 - (1 / g^N)]

where g is the growth multiplier and N is the number of years or duration. For an interest rate of r, expressed as a fraction, the growth multiplier is g = 1+r. For example, if the TIPS interest rate is 3%, then g = 1.03.
2. To derive this formula, you make some simplifying assumptions. The growth multiplier (or real interest rate) is assumed to be constant. The balance at the end of the duration is taken to be zero. You make use of the finite form of the geometric mean formula: if SUM = 1 + x + x^2 + ...+ x^N, then (1 - x )*SUM = (1 - x^(N+1)). For a more general derivation, visit the gummy stuff site http://home.golden.net/~pjponzo/gummy_stuff.htm. (You will still have to convert it to the form that I have shown.)
C. TIPS Equivalent Safe Withdrawal Rates
1. I have taken the following (historical) safe withdrawal rates from the Retire Early Safe Withdrawal Rate study at www.retireearlyhomepage.com. Using an optimal stock/commercial paper mix, 0.20% annual expenses and CPI-U for inflation adjustments, the (historical) safe withdrawal rates are 4.26% over 30 years, 4.08% over 40 years, 3.86% over 50 years and 3.70% over 60 years. These rates apply to the initial balance and withdrawals are increased annually to match inflation. In each case there was one historical sequence that would have resulted in a zero or negative balance before the end of the period. In other years there was growth. The stock allocations are 74%, 77%, 82% and 85% respectively.
2. TIPS with the following interest rates would have matched the (historical) safe withdrawal rates: 1.6% over 30 years, 2.7% over 40 years, 3.0% over 50 years and 3.1% over 60 years. A large fraction of each withdrawal would be a return of capital. The final balance would be zero in all cases.
3. TIPS are currently available at real interest rates of up to 2.8% in the secondary market. Today's TIPS can provide a 40-year withdrawal period with true safety. They keep open the option of investing elsewhere in the future with little, if any, penalty.
4. The volatility of the stock market brings the historically safe withdrawal rate down substantially. The 4.08% historically safe withdrawal rate over 40 years is much less than its 6% to 7% long-term (real) rate of return. It is not quite as good as using today's TIPS.
5. The traditional argument for buying stocks is that they offer growth. But when you consider the return of capital, TIPS come very close to matching stocks when you demand a high level of safety.
6. Stock valuations remain at historical highs. The safety of the historically derived rates is in doubt. Alternative choices look attractive. It is reasonable to expect (the equivalent of) a 3.0% or 3.1% real interest rate from high dividend stocks and REITS at a high level of safety. Historically, stock dividends have grown about 1% faster than inflation over long periods of time (decades). Those increases have occurred at erratic intervals. However, earnings have been growing steadily recently while pay out ratios have fallen. Dividends are relatively secure today and growth is likely. Penalties imposed by volatility should be much less than for stocks in general.

Have fun.

John R.