Executive Summary
Standard financial industry practice builds retirement portfolios using mean variance optimization and validates them using Monte Carlo simulations that assume asset returns are a random walk. To put a finer, more brutal, point on it, managers construct portfolios using anachronistic technology from 1952 and then have the temerity to check the results using assumptions from 1970. The unsurprising result of a process stuck over 50 years in the past is portfolios that burden future retirees with an unnecessarily high risk of financial ruin.
However, in contrast to the oft heard “TINA defense,” 1 there is an alternative: we suggest a more modern portfolio construction approach that puts the key problem of having sufficient assets to support investors’ required spending in retirement front and center. We believe an approach to retirement investing that better models and understands the ways in which financial markets differ from the outdated academic assumptions of market efficiency and random walks will result in substantially superior portfolios.
Framing and aligning the portfolio construction process with the actual problem an investor is attempting to solve (as opposed to some willow-the-wisp time-varying coefficient of risk aversion) also helps to avoid the troublesome guesswork as to how a client’s portfolio should change if needs and circumstances or, indeed, market conditions, shift from the advisor’s original assumptions.
If you don’t have orange and brown shag carpets or an avocado green bathroom suite or wear bell-bottom jeans or sport pork chop sideburns, why on Earth would you choose to believe that a random walk is a good description of the reality of asset returns? Similarly, the unclear (and unhelpful) framing of a coefficient of risk aversion is far from client friendly. It is high time financial planners stopped being “the slaves of some defunct economist” (to borrow Keynes’ words) and instead joined the 21st century. We propose that planners adopt a needs-based approach coupled with an up-to-date understanding of the way in which portfolio returns are generated.
Introduction
If the financial planning industry had an anthem, it would probably be “Let’s Do the Time Warp Again” from the Rocky Horror Picture Show (thank us when that tune plays randomly in your head). By using mean variance analysis and Monte Carlo simulations that assume a random walk, many planners are (perhaps implicitly) adopting a portfolio construction technology from the 1950s and combining it with a world view that passed as conventional wisdom in the 1970s. The usual rationale for this approach is either that everyone else is doing it or that it has always been done this way. Neither of these excuses is valid or, frankly, laden with intellectual vigor. For the sake of their clients, it is high time financial planners updated their beliefs, assumptions, and processes.
Questioning Your (Hidden) Assumptions: Why Your Monte Carlo Is Wrong!
All too often assumptions lie in the background, driving results but unquestioned or even hidden from view. In the best case, assumptions made are a reasonable approximation to reality or, even better, aren’t driving the results. In the worst case, they may be widely at odds with reality and small perturbations can lead to wildly differing outcomes.
In the field of retirement planning, the problem of assumptions and their impact is particularly pervasive and potentially pernicious. At what age will you retire or die? How much income will you need? These questions highlight the vital role time horizon plays. Unfortunately, conventional approaches to dealing with these issues are based on single-period analysis. This is an odd marriage of multi-horizon problems with single-period “solutions.” It is little wonder that this pairing often produces sterile offspring.
We will show these assumptions have a meaningful impact on retirement portfolios, even under equilibrium forecasts. As an example, assuming asset prices follow a random walk 2 leads to bond-heavy portfolios, causing negative impacts on long-term outcomes in a world in which expected returns vary over time.
Some will try to blind and baffle you with pseudo-science by saying something along the lines of “We use Monte Carlo simulations to help determine the best portfolio or test the viability of your plan.” However, this is really not addressing the issue. It is akin to saying you took a touted performance car for a test drive but failed to check out what was under the hood. Ultimately, when it comes to investing you need to ask about the “deep structure” of the return generation process. Are returns driven by a random walk or a process driven by mean reversion? Only by specifying a sensible empirically consistent model for the return generation process can Monte Carlo simulations be of any real use or relevance. Of course, if your assumptions are at odds with reality, you run the risk of reaching dangerously incorrect conclusions with potentially disastrous consequences.
It is well known that if asset prices follow a random walk, then mean variance optimization generates portfolios that do not depend on the horizon of the investor. However, if expected returns vary over time, then this is no longer the case and portfolios depend critically on the horizon of the investor. 3 4
The choice you make for your assumption of the “deep structure” (or return-generating process) can radically alter the outcomes generated. So, how do you go about choosing a deep structure?
As ever, looking at the evidence is a pretty good place to start. At a minimum, you want whatever deep structure you choose to at least be consistent with the empirical evidence. In terms of modelling your asset return streams, this amounts to examining whether returns are mean reverting or more akin to a random walk. But simply replicating the statistical properties of a series is not enough. Rather, understanding the economic intuition and mechanisms behind the empirics are essential in generating greater confidence and comfort in capturing the return generating process.
Signatures of Random Walks vs. Mean Reversion
However, before we turn to the empirics, we ought to outline how we will examine the issue of random walks versus mean reversion. There are many ways to think about this topic, but the one we have chosen as most apposite for our purposes with respect to retirement planning is the variance plot. This measure makes sense to us because it captures the essence of one important aspect of modelling asset return streams: the uncertainty around the outcome. (N.B. We aren’t using volatility or variance as a measure of risk. As we discuss later in the context of our approach to retirement planning, risk is best thought of as not having enough capital when you need it. However, the range of likely outcomes that any given asset can generate is going to be of interest when it comes to the modelling of the assets you own, especially how this uncertainty evolves over time.)
In the random walk scenario, changes in the series have no memory. An implication of this “no memory” characteristic is that the variance of multi-period returns scale linearly with the horizon of returns, e.g., two-period variance is simply twice the one-period variance.
In contrast, if a series has a tendency to mean revert, then its multi-period variance will scale less quickly than the one-period variance multiplied by horizon, as the series will tend to return to its long-run value over time.
In Exhibit 1 we show the volatility profiles of two series we created. One is constructed to be a random walk, the other to be a mean-reverting series. From the time series plot alone it is obviously very hard to tell these two series apart. However, the second chart in the exhibit shows how the volatility (the standard deviation, or square root of the variance) evolves as the time horizon (or holding period) is altered. As you can see from the plot, the random walk series has a volatility profile that scales with the square root of time (because the variance scales linearly with time) and the mean-reverting series has a volatility that scales less rapidly than the random walk.
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