Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections?

Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections?

The most common criticism of using Monte Carlo analysis for retirement planning projections is that it may not fully account for occasional bouts of extreme market volatility, and that it understates the risk of “fat tails” that can derail a retirement plan. As a result, many advisors still advocate using rolling historical time periods to evaluate the health of a prospective retirement plan, or rely on actual-historical-return-based research like safe withdrawal rates, or simply eschew Monte Carlo analysis altogether and project conservative straight-line returns instead.

In this guest post, Derek Tharp – our Research Associate at, and a Ph.D. candidate in the financial planning program at Kansas State University – analyzes Monte Carlo projection scenarios relative to actual historical scenarios, to compare which does a better job of evaluating sequence of return risk and the potential for an “unexpected” bear market… and finds that in reality, Monte Carlo projections of a long-term retirement plan using typical return and standard deviation assumptions are actually far more extreme than real-world historical market scenarios have ever been!

For instance, when comparing a Monte Carlo analysis of 10,000 scenarios based on historical 60/40 annual return parameters to historical returns, it turns out that 6.5% of Monte Carlo scenarios are actually worse than even the worst case historical scenario has ever been! Or viewed another way, a 93.5% probability of success in Monte Carlo is actually akin to a 100% success rate using actual historical scenarios! And if the advisor assumes lower-return assumptions instead, given today’s high market valuation and low yields, a whopping 50% to 82% of Monte Carlo scenarios were worse than any actual historically-bad sequence has ever been! As a result, despite the common criticism that Monte Carlo understates the risk of fat tails and volatility relative to using rolling historical scenarios, the reality seems to be the opposite – that Monte Carlo projections show more long-term volatility, resulting in faster and more catastrophic failures (to the downside), and more excess wealth in good scenarios (to the upside)!

So how is it that Monte Carlo analysis overstates long-term volatility when all criticism has been to the contrary (that it understates fat tails)? The gap emerges because of a difference in time horizons. When looking at daily or weekly or monthly data – the kind that leveraged investors like hedge funds often rely upon – market returns do exhibit fat tails and substantial short-term momentum effects. However, in the long run – e.g., when looking at annual data – not only do the fat tails entirely disappear, but long-term volatility actually has a lack of any tails at all! The reason is that in the long-run, returns seem to exhibit “negative serial correlation” (i.e., mean reversion – whereby longer-term periods of low performance are followed by periods of higher performance, and vice-versa). Yet by default, Monte Carlo analysis assumes each year is entirely independent, and that the risk of a bear market decline is exactly the same from one year to the next, regardless of whether the market was up or down for the past 1, 3, or 5 years already. In other words, Monte Carlo analysis (as typically implemented in financial planning software) doesn’t recognize that bear markets are typically followed by bull markets (as stocks get cheaper and eventually rally), and this failure to account for long-term mean reversion ends out projecting the tails of long-term returns to be more volatile than they have ever actually been!

The bottom line, though, is simply to recognize that despite the common criticism that Monte Carlo analysis and normal distributions understate “fat tails”, when it comes to long-term retirement projections, Monte Carlo analysis actually overstates the risk of extreme drawdowns relative to the actual historical record – yielding a material number of projections that are worse (or better) than any sequence that has actually occurred in history. On the one hand, this suggests that Monte Carlo analysis is actually a more conservative way of projecting the safety of a retirement plan than “just” relying on rolling historical returns. Yet on the other hand, it may actually lead prospective retirees to wait too long to retire (and/or spend less than they really can), by overstating the actual risk of long-term volatility and sequence of return risk!


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