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.

Bill ConerlySuppose that we have two investments with comparable standard deviations. If we could accurately measure the fatness of the tails (hyperskedasticity), we could determine which of the assets is truly riskier. But there aren’t many observations out at the tails, so we’re never quite sure just what the distribution really is.

Because we don’t know to much, using standard deviation as a first approximation to risk makes sense. However, investors need to understand that standard deviation underestimates risk for most financial assets. Talk to our friends for Long Term Capital Management for the details.

Abobtrader‘There is no free lunch… 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.’

Thanks for this, it is a a great ‘reminder’ article for investors.

Jim PicernoBill,

Excellent point. Long Term Capital Management is a classic (and tragic) example of how financial engineers can design outcomes that statistically appear to be low risk when the reality is the opposite. Clearly, some forms of quantitative risk analysis didn’t/couldn’t pick up the large fat-tails risk that lurked in the shadows of LTCM. In theory, only a qualitative analysis could uncover the real risks.

The lesson for using standard deviation seems to be that the metric is more reliable for looking at the raw, unmanaged results of asset classes. By contrast, when it comes to actively managed products, a clever manager can game the output.

knznLeaving aside the fat tails issue, which you can get around by using options, I have a couple of problems with this empirical correlation between standard deviation and average return. First, the correlation doesn’t show that standard deviation is a good measure of risk, only that it is correlated with measures presumably used by the market, which may not in fact be good measures. Second, if you start with a slightly more sophisticated measure of risk – market beta – it turns out to be highly correlated with standard deviation, but if you just look at standard deviation, you are going to make some fairly basic asset allocation mistakes from which even beta would save you. The class that immediately comes to mind is commodities. Commodities, despite their high standard deviation, probably have a very low (and possibly negative) market beta: they do well when the world economy is hit by supply shocks that are bad for stocks and bonds. On the other hand, the anti-inflation consensus among central banks probably assures that the long-run expected return on commodities is low. If you look at your 3-year standard deviations, you might want to recommend commodities particularly to relatively aggressive investors, but it is probably more conservative investors that most need commodities in their portfolio.

AIRInteresting post. I think it’s probably too early to write off standard deviation as a risk measure, or even to write it off as THE measure of risk. In the context of portfolio management, distortions to the normal distribution of returns are imo probably best interpreted as evidence of poorly implemented or artificial investment strategies.

TomStandard deviation of returns is useful if it dissuades potential short-term (5 or 10 yr horizon) investors who need stability of capital but get greedy and seek higher returns and think they can get them without the chance of losing. For long term investors, however, its not useful. It won’t hurt (help) much if you buy something at the top (bottom) of one of its gyrations about its 5 year mean return, if you’re in long enough to experience its 20 year average return. If you pick individual stocks you aren’t willing to hold for that long, then you’re more concerned with market psychology than about performance of business. And if that’s the case, understanding the historical volatility of a stock doesn’t tell you anything with predictive power.

AnonymousWould be interesting to see how your returns/standard deviation graph looks for an earlier 3 year period, like 2000/2003.