Executive Summary
Since the turmoil of the financial crisis in 2008, financial planners have become increasingly obsessed about so-called "black swan" and "fat tail" events. As we witnessed one "impossibly rare" volatile day after another that fall, the fact that financial planning models its uncertainty using Monte Carlo analysis with normal distributions suddenly became not a virtue, but a liability. Yet for most clients, who don't invest with leverage, even a black swan event does not result in immediate destitution, but merely sets them on an unsustainable path that must be adjusted in the years that follow to prevent a subsequent depletion of assets. Which means in reality, it's not about more accurately modeling the probability of a black swan... it's about having a plan for dealing with it when the time comes.
The inspiration for today's blog post is some analysis of black swans that I have been working on as a part of my recent series on Monte Carlo analysis in the January and pending February issues of The Kitces Report. In exploring the increasingly common criticism of Monte Carlo analysis - that it is typically based on normal distributions that fail to accurately model black swan scenarios because the tails of the distribution are actually "fatter" and more leptokurtic than the normal distribution implies - I realized that in truth, we're spending far too much time worried about the wrong thing.
In the case of some engineering and physics problems (where the use of Monte Carlo was popularized early on), the results of Monte Carlo must be incredibly accurate up front because they will be used to determine the consequences of a nuclear reaction or the potential for a structural failure - which cannot be fixed after the fact. For example, an engineering scenario with a 98% probability of success and a 2% chance that a bridge could collapse would be deemed intolerable; the consequences are severe, and you can't adjust the strength of the bridge components once it's built. So the bridge is constructed to make the risk of failure as close to 0.00% as possible, and any exposure to black swans presents a real concern.
On the other hand, in the case of a financial planning scenario, a 98% probability of success actually just means a 2% likelihood that some change will have to occur to get the plan back on track before the end of the time horizon. The client is not bankrupt the day an "impossible" 10% market decline occurs; it's simply a financial loss that requires a future adjustment to the plan. In other words, 2% is not a measure of absolute failure; it's a measure of the probability of needing to make a future adjustment to get back on track. And the fact that the path can change along the way and that black swans are not automatically and instantaneously catastrophic means that we must view them differently.
Notably, in the case of many investment institutions, the problem is more serious, for one simple reason: leverage. In the case of a hedge fund or an investment bank, a precipitous short-term decline can be catastrophic. For instance, with 10:1 leverage, a 10% one-day "black swan" really can wipe out 100% of a fund's equity, leaving it worthless and leading any lenders to promptly call in their loans. The investment arrangement ends, permanently. In point of fact, this is exactly what happened to many hedge funds in 2008. But the difference is leverage; for a client, a 10% decline may literally be negligible to the long-term plan if the market recovers before the next withdrawal is due in a month or a year, while for a leveraged hedge fund, it means the fund is out of business at the end of the day, and next month or year will never come. Just ask Long-Term Capital Management (LTCM), who collapsed in 1998 when "black swan" events decimated its leveraged equity, even though the reality is that when the fund assets were ultimately wound up two years later, they had generally recovered their losses.
For instance, the graphic to the right from Lowenstein's book "When Genius Failed: The Rise & Fall of Long-Term Capital Management" shows a comparison of 5 years invested in LTCM (with extensive leverage) vs "just" being fully invested in the Dow Jones Industrial Average. As the graphic clearly shows, when the "black swan event" finally did occur in mid 1998, it was genuinely catastrophic for LTCM, whose account balance essentially went to $0. The black swan event was unrecoverable. On the other hand, the decline for the unleveraged investor, as shown by the red line for the stock index, was little more than a tiny blip; at worst, the pullback meant cutting expenses modestly for a limited time, but it was not an immediate and total catastrophe by any stretch! The bottom line is that for an unleveraged investor, even a market black swan isn't that much of an immediate and permanent catastrophe, whether it's 1998 or 1987 or 2008.
Moreover, the reality is that because the risk of black swans is still rare - even though they are far more common than a normal distribution suggests - they still have a negligible impact on the plan up front. For instance, if the probability of success for a client's plan is 94%, but due to a more accurate analysis of potential black swan events "that proper takes into account fat tails and leptokurtic distributions" the client's probability of success is really only 92% (because an event that was supposed to be a once-in-a-billion-years event now has a 2% probability), the reality is that the client likely will not actually do anything different at that point! It's not a reason to make a dramatic change to spending or saving or to work another year. 92% is still awfully close to 94% (or 76% instead of 78%, or 86% instead of 84%, or any other 2% difference). In this scenario, "proper" accounting for black swans simply means a somewhat elevated likelihood (from 6% to 8%) that something will have to change down the road. In turn, this also means that getting the probability of success down to the last decimal point by using fancier, more robust distributions is somewhat unnecessary; knowing a client's probability of needing a plan adjustment is 8.1562% instead of 8% may be a more precise measurement, but it doesn't necessarily lead to a more accurate or materially different decision or actions.
In other words, with black swans in particular - given the fact that they are still rare - the real issue is ultimately not about the probability the client will have to make a change (which increases from impossible to "still pretty rare"), but about having a real plan in place for how the client's goals or actions will in fact be changed if the world begins to take the client down that improbable-but-concerning path (and doesn't recover in a timely manner). And of course, the reality is that such a plan for dealing with bad returns is equally relevant anytime the client's performance results lag too far behind - whether that's due to a black swan event, or a "white swan event" such as a mere decade of entirely probable below-average returns that gets the client dangerously far behind the original projection.
