Looking Into The Future With A Rear-View Mirror

How do you know if the stock market (or any asset class) is overvalued and ripe for a fall? Wait a year or two and you’ll have a definitive answer. Real-time decisions, alas, are slightly more complicated. Yes, there are several techniques that you can apply for estimating expected return, but you might start with one metric that easy to compute and always up to date: trailing return. It’s hardly perfect and it’s burdened with all the usual caveats. But it’s a great starting point for developing some context for thinking about what’s overpriced, what’s not, and how to tell the difference.


As a simple example, let’s consider the US stock market by way of everyone’s favorite benchmark: the S&P 500. Let’s say that your time horizon is one year, although we could just as easily use five or ten years, for instance. Sticking with a one-year period, let’s consider how returns stack up through history. For some perspective, here’s how the trailing one-year return compares with three-year results. Not surprisingly, the one-year change bounces around its less-volatile three-year counterpart. The two never diverge for long, of course, since they’re ultimately linked at the hip. But in the short run, as we know, irrational exuberance and its dark cousin can and do dominate.

The key message in the chart above is that trees don’t grow to the sky. Positive returns don’t keep climbing, nor do negative results incessantly fall ever deeper into the performance pit. Granted, it may seem otherwise if you’re holding, say, an S&P 500 ETF. But reversion to the mean ultimately prevails. The timing is always suspect, of course, but in the dark art/science of risk management there are no absolutes in real time for money management.
There are, however, a number of techniques for deciding if trailing returns look excessive, in which case the future may be somewhat less murky than usual for estimating expected return. No one should confuse the connection between ex post and ex ante returns as a branch of physics, particularly in the short run. But no one can ignore this link entirely, volatile as it can be at times. Yet the question remains: How to define extreme?
An obvious way to begin is simply reviewing historical returns through a quantitative lens that provides relative context. For example, here’s how one-year returns (defined here and throughout as 250-trading-day price changes) fit into quartiles through the decades:
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Note that the 50% mark is the median return, which in this case is 9.2% for the S&P in terms of one-year performance over the past half century. This is close to what’s popularly cited as the long-term performance in equities. Naive investors think this is what they’ll earn through time with no effort or anxiety. Maybe, but over shorter periods you can expect to earn or lose quite a bit more than the median.
For a graphical perspective, here’s how the quartiles look in a standard boxplot representation. Note the positive bias in the central rectangle, which spans the first to third quartiles of performance. It’s tempting to focus on this middling tendency and ignore the outliers, but when returns are in the extreme corners of trailing results it’s often the case that nothing else matters in terms of what you need to know.

What can we do with this information? Well, we can start by recognizing that when trailing one-year returns are in the upper quartile (above 18.8%), risk is relatively high. That’s still no assurance that a 20% trailing return will soon give way to steep losses. We could very well be on our way to 30% returns. Momentum, in other words, can’t be ruled out as a short-term factor, for returns and losses. Rather, the point here is that you should be aware that when you’re sitting on relatively high returns (or suffering unusually big losses), the odds are higher that we’re closer to a reversion to the mean. Indeed, we’re always dealing in probabilities when it comes to estimating future returns. That said, not all models for deciding what’s probable, and what’s not, are created equal.
In any case, we rarely if ever have to go off the deep end with interpreting the numbers. If you own a diversified portfolio of the major asset classes, there’s a good chance that you’ll own a mix of investments with trailing returns that are scattered across their respective performance quartiles at any point in time. As a result, monitoring this data provides some basic intuition for identifying rebalancing opportunities. Even then, it’s probably best not to engage in radical actions, particularly if the trailing returns aren’t at the extreme edges of the outer quartiles.
Why should you pay attention to any of this? Because reversion to the mean is likely to prevail… eventually. It’s the “eventually” that makes managing asset allocation so challenging. The market can remain overbought or oversold for longer than you can remain financially solvent. That’s why risk management should be multi-faceted. One of those facets can be, and probably should be, monitoring trailing returns in the historical window that’s appropriate for your strategy.
On that note, what’s the current one-year (250-trading-day) return for the S&P? For the period through yesterday, August 20, 2013, stocks are higher by 16.5%. That’s below the 75th percentile (18.8%), which suggests that trailing returns are relatively high but still well below extreme levels. Does that mean it’s time to rebalance US equity weights down? Maybe, but much depends on how the rest of your asset allocation compares.
The dirty little secret of risk management is that there are no absolutes. Your time horizon, investment objectives, tolerance for short-term volatility and a host of other factors—including your current asset allocation—determine how and when you should rebalance. In other words, the absolutes, such as trailing returns, are a beginning rather than an end to analyzing and managing risk. Yes, it’s a long and winding road, but the first steps, at least, are quick and easy, and to some extent reliable. Just don’t assume that the path to investment success ends here.
Update: For a decent primer on other avenues for developing return assumptions for the equity market, see this research note from Vanguard: Forecasting stock returns: “What signals matter, and what do they say now?” (pdf)

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