## The Impact of Severe Drawdowns on Safe Withdrawal Rates

### by Lloyd Nirenberg, Ph.D.

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A Google search for “safe withdrawal rates” produces 30 million results, but none answers a question that is critical to advisors and investors: How would a sudden market downturn – a “return shock” – impair a retiree’s forecast withdrawals?

Substantial return shocks, or drawdowns, have occurred twice in the last six years. Consider this table of closing prices for the S&P 500 index:

 Date Close One-year return 10/1/2007 154.3 10/1/2008 116.06 -33% 1/3/2008 144.86 1/2/2009 92.96 -36%

The financial crisis left investors more risk-averse than before. But the copious literature on safe withdrawal rates (SWRs) does not explicitly account for the possibility of a substantial financial shock.

My formula for calculating the SWR when one explicitly states expected future returns and inflation is published here. I also published a simpler, descriptive version on Advisor Perspectives. But I didn’t include the effect a financial calamity such as that of 2007-2008 would have on SWRs.

In this article, I’ll explain how a market-return shock would affect SWR accounting. The mathematical derivation is given here.

The assumptions are easy to specify. The SWR protocol calls for the investor to withdraw a fraction of the initial account balance and continue to withdraw that amount, adjusted for inflation, each year. This initial fraction is the SWR. The account balance grows with the return rates. If the SWR is too high, the account will be depleted before the planning horizon is reached, and if it is too low, the account will be left with money that could have been spent in the retiree’s lifetime.

What distinguishes my approach to the SWR analysis from others’ is that I do not comingle investment history and portfolio asset allocations with the analysis of SWRs, returns, inflation and time horizons. I assume investors and advisors make their own assumptions about variables such as inflation, projected returns and asset allocations, and I show exactly what those assumptions bring.

I provide a solution for the SWR under a general set of assumptions about the probability distributions of future returns and inflation. Then I greatly simplify the result by using expected future return rates and expected future inflation rates. This expected-value analysis leads to the simplified SWR formula. The key analytical idea is that the investor or advisor selects the appropriate assumptions based on their own investment approach, which may (or may not) rely upon particulars of historical results.

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