The widespread acceptance of the 4 percent rule within the investment management industry is only overshadowed by the sheer number of its shortcomings. The 4 percent rule was introduced by Larry Bierwirth in 1994 (*Investing for Retirement: Using the Past to Model the Future*) and expanded on by William Bengen in the same year (*Determining Withdrawal Rates Using Historical Data*).

In the conclusion of his paper, Bengen states that a client of age 60-65 planning for a 30-year retirement should withdraw 4 percent of the initial portfolio value, adjusted for inflation, each year. While many variations of the rule exist, the basic idea remains the same:

1) Make assumptions for security return distributions, inflation, life expectancy, risk tolerance, taxes, transaction costs, etc.

2) Determine the fixed withdrawal percentage that minimizes the probability that the portfolio will fail to fully fund spending over the retirement horizon.

Most criticisms of the 4 percent rule focus on the impact that assumption changes have on the optimal withdrawal percentage (i.e. a 15-year vs. 30-year retirement horizon, a conservative vs. aggressive asset allocation, etc.). It is not surprising that if we change basic assumptions relating to the investor or test the withdrawal strategy over a different time horizon, the optimal withdrawal rate (with the benefit of hindsight) will differ. In fact, Bengen acknowledges in his original paper that 4 percent is specific to a 30-year retirement horizon and a 50/50 stock/bond allocation.

The problem with the 4 percent rule lies not in the specific assumptions used for a given investor or its specific implementation, but in its underlying theory. Most important, the 4 percent rule fails because it attempts to fund a static spending rule (fixed withdrawals adjusted for inflation) with a dynamic funding source (financial returns).

In most aspects of our life, we try to match static (dynamic) spending rules with static (dynamic) funding sources. If my house burns down, I will need to pay to have it rebuilt. This is an example of a dynamic spending rule since I cannot predict if and when my house will burn down. To deal with this risk, most people buy a home insurance policy. The home insurance policy is a dynamic funding source since it also only pays off when my house burns down. By matching the correct dynamic funding source to the dynamic spending need, I have largely mitigated my risk.

Nobel laureate William Sharpe discusses this problem in a critique of the 4 percent rule (*The 4% Rule – At What Price?*). Specifically, Sharpe argues that the 4 percent rule was developed with the objective of minimizing the probability of failing to fully fund retirement withdrawals and ignored other important metrics that should be used to evaluate a withdrawal strategy.

The most important of these metrics is the cost of surplus. The cost of surplus measures the value of unused funds at the end of retirement after accounting for any inheritance objectives. This remaining portfolio balance is considered a cost because the excess funds could have been used to increase withdrawals during retirement. Investors can on average spend more during retirement with a lower probability of prematurely exhausting retirement savings by eschewing the 4 percent rule (or a similar static variant) for a dynamic withdrawal policy that is dependent on the realized market path.

A simple example can illustrate both the importance of considering multiple metrics and the valued added by employing simple dynamic withdrawal policies. Consider a 65-year-old retiree with $1 million in the bank to fund retirement. The retiree would like to plan for a 30-year retirement and figures that he needs $40,000 for living expenses per year. The real interest rate is assumed to be 2 percent and the retiree’s financial advisor has invested in a portfolio with an expected return of 6 percent and volatility of 13 percent.

We used Monte Carlo methods to simulate 100,000 potential market paths. Although we make some simplifying assumptions in the simulations (normally distributed returns, constant correlations between assets, etc.), the results are still useful in comparing various withdrawal strategies. Using these paths, we can compute the failure probability, cost of surplus and total risk-adjusted present value of withdrawals.

**• Probability of Failure: 5 percent.** There is a 95 percent chance that the retiree will be able to withdraw an inflation adjusted $40,000 for all 30 years of retirement.

**• Cost of Surplus: 20.8 percent. **On average, 20.8 percent of the initial portfolio value ($208,000) ends up as excess funds that were not used during retirement. Looked at another way, the retiree could have spent $208,000 more in today’s dollars over the course of retirement if he had utilized an optimal withdrawal strategy.

**• Risk-Adjusted PV of Withdrawals: $795,000.** The value of all withdrawals adjusting for the time value of money and the higher relative value of cash in future states of the world where security returns are lower.

We applied a number of simple dynamic spending rules and then recomputed the three statistics to show the improvement relative to the 4 percent rule. One potential rule is to withdraw 4 percent of the current, instead of original, portfolio balance, subject to a floor. For more conservative retirees willing to live on $30,000 in down markets, we can set the floor at $30,000. This reduces the probability of failure from 5 percent to 1.1 percent while maintaining a similar cost of surplus (21.1 percent) and risk-adjusted present value of withdrawals ($790,000).

For investors who are willing to take more risk in return for higher potential withdrawals, we can set the floor at $40,000. This reduces the cost of surplus from 20.8 percent to 14.6 percent and the risk-adjusted present value of withdrawals from $795,000 to $856,000, while leaving the probability of failure nearly unchanged at 5.3 percent.

We can get even better results by making our rule more dynamic. One way of achieving this is to choose the percentage of the current portfolio value withdrawn based on the ratio of current portfolio balance to years of retirement remaining. For example, if we have less than $30,000 per year of retirement in the portfolio, we will withdraw 4 percent, if we have $30,000-$40,000 per year of retirement we will withdraw 5 percent and so on. With this strategy we improve on all three metrics: The probability of failure is 1.8 percent, the cost of surplus is 6.1 percent and the risk-adjusted present value of withdrawals is $940,000.

These dynamic withdrawal rules improve on the 4 percent rule because they are reactive to the realized market path, not predictive. Predictive models are most effective when current market conditions mirror history. The traditional 4 percent rule depends strongly on the assumption that future markets will look like past markets.

## Login in order to post a comment