A leading complaint is that standard deviation doesn’t reflect the true risk that threatens investors. The woman investing for retirement 20 years on faces a variety of risks, starting with the possibility that she will spend all of her savings before dying. Standard deviation, as a result, is of no consequence to someone trying to avoid outliving her savings.
There are technical complaints as well. The basic calculation of standard deviation assumes a normal distribution. Normal distributions work great in physics and general statistics, but are flawed when it comes to picking up the tendency of investment returns to suffer distributions that are less than normal. The so-called fat tails distribution forever haunts the world of investing, a risk that effectively means that dramatic events can and do happen every once in a while, and that risk isn’t captured in a normal distribution world that defines the basic concept of standard deviation.
True enough. Standard deviation isn’t a real-world risk in saving for retirement, and it doesn’t fully reflect what happens in the capital markets in terms of how returns are distributed around the mean. But after accepting the wisdom of the observation, the analysis shouldn’t end there. Standard deviation, or the volatility of prices around the mean, still offers a reasonably valuable tool for comparing one type of risk (although hardly the only type) among various asset classes. It’s less than perfect; in fact it’s flawed. But it’s still useful for getting a general sense of the risks that loom.
Should investors use standard deviation exclusively and ignore all other measures and definitions of risk? Absolutely not. But neither should one dispose of standard deviation simply by recognizing that the metric can’t be all things to all investors at all times. If that’s the bar by which risk measures must reach, then nothing would suffice. Something, we submit, is better than nothing. In fact, the imperfections of the real world demand that we use a collection of flawed risk measures to piece together an outline of the overall risk that looms.
Here now begins our admittedly underdog attempt at defending and, perhaps, partially restoring standard deviation’s once-good name in the world of risk analytics. The effort consists of simply showing that price volatility, while flawed, is nonetheless valuable still for assessing the nature of a particular asset class relative to another.
Exhibit A is the table below, which ranks the major asset classes by their respective 3-year annualized standard deviation, based on monthly total returns through last month. Note that the asset classes that rank highest in volatility are indeed, by most accounts, the riskier of the bunch. Meanwhile, those at the bottom, including cash, are the least risky by this measure.
To restate the obvious, there’s a world of difference with the low risk of cash to the high risk of emerging market stocks. High risk isn’t inherently bad, nor is low risk inherently good. In fact, mixing risks together with a strategic purpose is the only way to fly. But we digress.
The pairing of standard deviation against trailing 3-year annualized total return shows that the relationship between the two is eminently logical. Consider the graph below, which plots the trailing 3-year returns for each of the asset classes listed above against their respective standard deviation. The key revelation is that returns generally rise along with risk, even when the risk is measured as standard deviation. There is no free lunch, as the graph reminds. This iron law of the investment universe is sometimes thrown out of whack in the short run, but as a long-term proposition it’s virtually impervious to change.
Obviously, standard deviation is only one risk measure in an ever-expanding sea of competing metrics, both quantitative and qualitative. No single measure fully encompasses the concept of “risk” in all its nuance and variety. An accurate profile of the risk that inhabits the investment landscape requires more than crunching the numbers by any one gauge.
But for our money, we begin with standard deviation, and do so regularly. Price volatility, after all, ebbs and flows, just as returns do. The ongoing shifting sands of return and risk warrant keeping a close eye on the relationship between the two. The moral of the story: Enlightenment in the investment game comes one metric at a time.