Modeling Risk: A Primer

At the core of modern finance theory is a simple but powerful idea: There’s a price tag for earning a higher return – higher risk.

Defining risk is a slippery concept, although not for want of trying with an ever-lengthening list of quantitative metrics. But more choices don’t always lead to more clarity. If you ask ten different investors (or money managers) to explain investment risk, you could easily hear ten different answers. This is no trivial point since quantifying risk is essential for managing it, even if the best-laid plans for profiling risk have limits and don’t always unfold as expected.

However you define it, risk is forever immune to a one-size-fits-all definition. Like the proverbial blind men touching different parts of an elephant, risk perceptions vary, largely because investors can experience risk in various ways from a behavioral perspective. Risk, then, is reminiscent of Churchill’s famous description of Russia: a riddle, wrapped in a mystery, inside an enigma.

If there’s such a thing as a universally accepted definition of what is meant by financial risk, the potential for principal loss is probably on the short list of possibilities. Unfortunately, such a broad-brush approach is virtually worthless if we’re seeking to compare the level of risk associated with different assets or investment strategies.

The good news is that financial researchers and money managers have developed numerous ways to slice and dice risk and provide something other than guesswork and rules of thumb to distinguish between different levels of risk. No one’s found a silver bullet, at least not yet. But even flawed risk metrics have value – especially if we look at several that are, to some extent, complimentary.  Let’s take a brief tour of five risk measures that lay a foundation for assessing how much danger is potentially lurking in a portfolio.

Five for the Road

For a bit of real-world perspective, let’s compare two popular large-cap U.S. equity factor ETFs (targeting momentum and minimum variance) against everyone’s favorite U.S. large-cap stock benchmark (S&P 500 Index) via a publicly traded proxy: SPDR S&P 500 (SPY).

For the sake of brevity, let’s engage in a round of reductio ad absurdum and assume that the only relevant question is whether there’s a case for favoring one or both factor ETFs over the plain-vanilla S&P 500 fund from the vantage of risk.

To star, note the annualized five-year returns through June 13, 2019. SPY earned 10.6% over that stretch. A solid performance, but it trails USMV’s 13.1% and MTUM’s 15.2%. The question is whether the equity factor ETFs look as impressive after filtering the results through a risk-adjusted lens?


Consider how the portfolios compare via one-day return volatility (a proxy for risk-based on the dispersion of returns). This indicator shows that USMV enjoyed a modestly smoother ride (lower vol) than its competitors.

Next, take a look at Sharpe ratio for additional context. This metric adjusts returns based on volatility – a higher Sharpe ratio indicates a higher risk-adjusted performance. By this standard, USMV and MTUM outperformed SPY.

The Sortino ratio also filters returns through a risk-adjusted lens, but in this case the focus is on downside deviation rather than the full range of return volatility. As such, some analysts consider the Sortino ratio to be an improvement over the Sharpe ratio, which considers all volatility to be “bad” volatility. In any case, the Sortino ratio tells us that USMV and MTUM delivered stronger risk-adjusted performances relative to SPY.

We have two metrics that are telling us that SPY’s performance looks relatively weak in risk-adjusted terms. Add to that the fact that SPY also trailed USMV and MTUM before correcting for risk suggests we may have a trend unfolding.

But, wait – there’s more.

Enter Estimated Shortfall (ES), a tail-risk measure. The idea here is to model the worst-case scenario for loss. For this toy example, the data above reflects one-day returns at the 95% confidence level. USMV offers a kinder, gentler profile: the expected worst-case scenario is a one-day slide of 1.9% — somewhat milder vs. SPY’s 2.4% decline. Note, however, that MTUM’s ES is a deeper 2.6% loss.

Finally, the worst historical drawdown shows how the real-world corrections stack up, albeit for the trailing five-year period in this example. On this front, SPY’s risk (per the deepest drawdown) is middling, although all three funds lost a substantial amount of altitude via peak-to-trough declines. That’s a reminder that you can dress up an equity portfolio but it’s still hard to immunize it from the worst-case scenarios that plague all stock markets from time to time.

The bottom line: the numbers present a bit of a mixed profile. That’s not unusual in risk analysis. Clear-cut results are rare. This is finance, not physics, after all, and so science and hard numbers only bring you so far. Nonetheless, we’ve learned quite a bit—certainly far more than if we limited our review to the return histories.

As this simple risk profile reminds, there’s a strong case for analyzing assets and portfolio strategies from several vantage points. While the five risk metrics above barely scratch the surface of possibility, they do offer a reasonable starting point for modeling risk and pulling back the curtain, if only slightly, on potential dangers down the road.

If the only information available was the trailing performances, an investor might reason that MTUM’s substantially higher return for the past five years gives it an obvious advantage and makes it the clear choice. But considering the performances through a risk-adjusted lens (Sharpe and Sortino ratios) suggests that USMV’s track record is stronger, at least for an investor with a relatively low risk tolerance. That’s also the message in the drawdown data: USMV’s peak-to-trough tumble was relatively modest vs. the other two funds.

It’s important to also recognize that the risk metrics mentioned above are determined based solely on historical data.  Unfortunately, the past provides an imperfect view, at best, of the future. The lesson is that when evaluating risk, it’s essential to go deeper, such as using stochastic modeling’s ability to provide insights on how an asset investment strategy may be impacted by changing economic and financial conditions and random events. Monte Carlo analysis (which draws on thousands of simulations with randomly varied inputs to estimate the probability of different outcomes) is perhaps the most common tool used to fill this void.

First Do No Harm

To be fair, the profile above doesn’t suffice to make a final decision. Rather, the point is that building a robust investment portfolio starts with intelligently selecting funds that are likely to satisfy performance and risk expectations/targets over a particular time horizon.

Alas, there are no short cuts. But as Charlie Ellis long ago advised, investing is a loser’s game and so the first order of business is dodging unforced errors. That’s a multi-step process, but at least we know where to begin: Going deep on profiling risk.

By James Picerno, Director of Analytics

Important Disclosures:  Please remember that past performance may not be indicative of future results.  Different types of investments involve varying degrees of risk, and there can be no assurance that the future performance of any specific investment, investment strategy, or product made reference to directly or indirectly from The Milwaukee Company™, will be profitable, equal any corresponding indicated historical performance level(s), or be suitable for your portfolio.  Due to various factors, including changing market conditions, the content may no longer be reflective of current opinions or positions.  Moreover, you should not assume that any discussion or information contained in The Milwaukee Company™ serves as the receipt of, or as a substitute for, personalized investment advice from The Milwaukee Company™.


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