Measuring Volatility and the Cost of Retirement

By Frank Armstrong III

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NOVEMBER 2005 - Few investors know whether they will be able to retire with any level of comfort, and studies indicate that most Americans choose to ignore the subject. The amount of investment capital required to replace preretirement income is more than most people think. Annual withdrawal rates of 4% to 6% require that there be $16 to $25 of capital at work for every dollar of income a portfolio must produce.

An individual’s income needs depend partly upon expectations for a retirement lifestyle. Many retirees find that they need as much or more than before retirement; a retiree probably should not expect to be satisfied with less than 75% of preretirement income. People more than a few years from retirement must also account for inflation. A plan that doesn’t account for inflation is doomed to fail. The highest risk factor a retiree faces, and the only decision directly under his control, is the withdrawal rate.

The Volatility Effect

A tool called the Monte Carlo simulation, along with a straightforward computer spreadsheet, is enough to start focusing on solutions. A Monte Carlo simulation uses random draws of numbers from pools constructed with specified rates of return and volatility (risk). Much like a lottery, values are drawn at random from a pool of numbers to construct a single test. The process is repeated many times, and a summary of the results provides a quantitative estimate of the range and distribution of the possible returns. Varying the construction of the pools of numbers allows the planner to examine different strategies to see which ones give a higher probability of success.

For example, one could construct pools of numbers that have an average rate of return of 10% and a standard deviation of 10%. Using random draws from those pools, one can test the survival rates of 4%, 5%, 6%, and 7% annual withdrawals. The findings will generally confirm the pioneering 1990s study by Phillip L. Cooley, Carl M. Hubbard, and Daniel T. Walz that tracked failure rates against withdrawal amounts, commencing in 1926 (using the S&P 500 and bonds in various combinations over varying time periods). The study results revealed that portfolio failure rates are directly related to time horizon and withdrawal rates and are influenced by asset allocation. One could run the simulation again using a pool of numbers with a 10% return but a standard deviation of 10%, 15%, and 20%, and assume a annual withdrawal rate of 6%. At 30 years, only 1% of the trials with a 10% standard deviation fail, but 23% fail at a standard deviation of 20%. Failure rates soar with higher volatility. The point is that all 10% returns are not equal (see the Exhibit).

The simulation reveals a clear link between volatility and survival of the portfolio at any given time horizon. Anything that reduces portfolio volatility (given the same rate of return and withdrawal rates) significantly enhances the probabilty that a retiree’s nest egg will survive.

Totally Skewed

In the traditional analysis referred to above, one might have assumed that half of all trials would result in greater than expected returns, and half less. But the only case where each trial yields the average result occurs where there is no volatility. In that special case, every trial survives and gets the identical result.

With volatility, outcomes become skewed. Although one obtains the expected rate of return across the sample, the median return is less than the average. The higher the volatility, the greater the sample becomes skewed at any time horizon. So, although the average return meets expectations, the median result is less than expected. As the number of failures goes up, the number of extraordinary results also goes up. A small number of portfolios will deliver much higher than expected results, while a large number of portfolios either fail or obtain lower than expected results.

For example, assume an target terminal value of $100,000 for a particular withdrawal rate, rate of return, and time horizon. If one result yields $1 million, and nine results yield $0 at some particular risk level, then the average return has been achieved but nine out of 10 results are portfolio failures.

The importance of selecting a realistic withdrawal rate cannot be overestimated.

  • If capital is insufficient, the retiree may be tempted to increase the withdrawal rate.
  • A high withdrawal rate increases the probability of portfolio failure.
  • Reaching for higher investment returns increases volatility, which in turn increases the probability of portfolio failure.

Constructing an Investment Strategy

Every step of a financial plan must support the retiree’s objectives. The ideal investment plan supports the required withdrawal rate while maximizing the probability of success. The first problem facing the retiree is that “guaranteed” investment products are unlikely to provide sufficient total return to meet reasonable needs. Meanwhile, equities are too volatile to provide a reliable income stream. A combination of stocks and bonds will probably best meet the need.

Because at least part of the portfolio will be volatile, the issue of risk management moves to the forefront. The first step is to construct a “two-bucket” portfolio. Bucket 1 would consist of adequate liquid reserves. Recognizing that equity investments are too volatile to support even moderate withdrawal rates safely, investors must temper their portfolios with a near-riskless asset that will lower the volatility at the portfolio level and be available to fund withdrawals during down-market conditions. As a minimum liquidity requirement, high-quality, short-term bonds are generally sufficient to cover five to seven years of income needs at the beginning of retirement. While chasing higher yields with longer-duration or lower-quality issues may be tempting, the enormous increase in risk often swamps the small additional yield benefit.

An individual who expects to draw down 6% of capital each year for income needs should plan to have 30% to 42% of assets in fixed investments. When the market takes a downturn, the investor will have plenty of time for it to recover while drawing down the bonds. This strategy protects growth assets during market declines.

Bucket 2 would be the world equity market bucket. The design philosophy here is to construct the equity portfolio with the highest possible return per unit of risk. This investment policy recognizes the impact of volatility and employs standard portfolio construction concepts to reduce it. These well-known modern portfolio theory techniques include the use of multiple asset classes with low correlations to one another. Some planners use nine distinct global equity asset classes, each with high expected returns at tolerable risk levels and relatively low correlation to the others.

Withdrawal Strategy: Preserve Volatile Assets in Down Markets

A rational withdrawal strategy recognizes that equities are volatile and short-term bonds are not. Therefore, a sound strategy is one designed to protect volatile assets during down-market conditions to avoid consuming excessive equity capital.

Most financial advisors have been content to treat retirement assets as a single portfolio with a targeted allocation, say of 60% stocks and 40% bonds. This conception of a portfolio, however, would lead to withdrawals on a pro rata basis from both equity and fixed assets, regardless of market experience, and does nothing to protect volatile assets during down markets.

A far superior strategy would treat the equity and bond portfolios separately, then follow a rule for withdrawals that protects equity capital during down markets by liquidating only bonds during bad years. During good years, withdrawals are funded by sales of equity shares, and any excess accumulation is used to rebalance the portfolio back to the desired asset allocation. Again, using spreadsheet models with Monte Carlo simulations, this simple rule can be shown to result in substantial incremental improvement in overall results.

Implementation and Evaluation of Alternatives

A policy of implementation via no-load institutional-class index funds spreads risk as widely as possible in some of the world’s most attractive markets while controlling costs, preventing “style drift,” minimizing taxes, and eliminating “management” risk.

The Monte Carlo simulation is a powerful tool to evaluate alternative strategies. For example, should an investor needing a 6% withdrawal rate invest in a portfolio with a 10% return and a 12% standard deviation, or one with an 11% return with a 15% standard deviation? Does this answer depend on the time horizon? Does the answer change if the withdrawal rate changes? Monte Carlo simulations can guide an investor to the best choice, based on personal requirements and goals. The correct choice is the one that is most likely to succeed.

Frank Armstrong III is the founder and principal of Investor Solutions, Inc. (, a fee-only, SEC-registered investment advisor. He is also the author of The Informed Investor: A Hype-Free Guide to Constructing a Sound Financial Portfolio (AMACOM).













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