RISK! How to measure it like a pro


Quick! What are the best measures of risk and risk-adjusted returns[i] in a portfolio or asset class?

If you asked most financial advisors, financial journalists and those in some form of financial profession, I am guessing you would hear “standard deviation” and “Sharpe Ratio” as an answer to each question, respectively. And those answers would be WRONG!

These measures, by far, are the industry standard metrics when people talk about risk and risk adjusted returns -- despite the fact that they are actually fairly poor evaluations of risk in a portfolio on their own.

While many think that standard deviation and the Sharpe Ratio measure risk and risk adjusted returns, what they actually measure is volatility and volatility adjusted returns. While related, these are decidedly NOT the same.

A quick primer on standard deviation and the Sharpe Ratio:

Standard deviation, as you may remember from your statistics classes, is simply a measure of dispersion around an average – kind of like the measure of how different from the average the “average” data point is.

If I have two sets of returns that both average roughly the same return over time, but one has higher “dispersion” of returns (higher absolute variances from the mean), the one with the higher dispersion will have a higher standard deviation. This is best exemplified with a numerical example, as shown below:


In this example, return stream A and B both have the same average return: 0.3% (we are not accounting for compounding here). Return stream B, however, is more volatile since it has a couple data points that are farther from the mean than return stream A. Specifically, data points 6 and 10 are where the differences lie:

            Data point 6:

                        Return stream A: 6%

                        Return stream B: 9%

            Data point 10:

                        Return stream A: -3%

                        Return stream B: -6%

Since all the other data points are the same, these two data points are what account for the higher standard deviation in data set B. Note that the average does not change from return stream A to B, but the standard deviation is higher for return stream B than it is for return stream A.

While both return streams have the same average return (again, not factoring in compounding), return stream B is more volatile.

In evaluating investment systems and allocations, most investors (in theory) seek to maximize the amount of return they receive for a given level of risk or volatility that they are willing to withstand – that is, they seek to maximize the risk adjusted return of their portfolio. As such, investors often look at what is called the Sharpe Ratio to measure risk adjusted returns.

The Sharpe Ratio is simply the compound annual return for a given asset (CAGR), minus the risk free rate (RFR) (usually the rate of Tbills in the home country of the investor), divided by the standard deviation (SD) of the return stream.

Sharpe = (CAGR – RFR) / SD

The Sharpe Ratio does a good job of explaining “volatility adjusted returns” or how much VOLATILITY an investor has historically experienced in a strategy in order to achieve the return offered by the strategy. That said, and this is a key point…


Volatility and risk are not the same thing, because upside volatility and downside volatility are not the same thing.

What is upside volatility and what is downside volatility? Put simply –

Upside volatility occurs when a trading system or asset class is moving aggressively higher. This is the volatility that we want. The more upside volatility, the better, because we are making money.

Downside volatility, on the other hand, occurs when a trading system or asset class is moving aggressively lower. This is the volatility that we seek to avoid. The more downside volatility, the worse off we are because we are losing money when downside volatility occurs.

Unfortunately, the standard risk and risk-adjusted return metrics of the financial services industry (standard deviation and the Sharpe Ratio) do not take into account this nuance – they treat both upside and downside volatility in exactly the same way.

So if you are ever working with a money manager or financial advisor who is seeking to “avoid volatility” on your behalf – make certain that he or she is focused on avoiding downside volatility and focused on maximizing upside volatility. You want the most upside volatility you can capture as possible (within the constraints of the downside volatility that you can afford to endure)!

So if the industry standard risk and risk-adjusted return calculations of standard deviation and the Sharpe Ratio treat both good and bad volatility as “bad,” what options do we have to look at risk in a more intelligent and thoughtful way? How can we evaluate systems and asset classes in light of the fact that we want upside (good) volatility, but we want to avoid downside (bad) volatility?

Fortunately, more sophisticated investors have several options at their fingertips to help with their evaluations. Our favorite risk metrics are (a) the CALMAR ratio (b) the downside deviation and (c) the Sortino Ratio.

First, lets talk about the downside deviation and the Sortino Ratio since they are the cousins of the more prevalently used metrics that we discussed above.

Downside deviation: This is the cousin of standard deviation and is a much better metric of risk. Recall that we said standard deviation penalizes a system or asset class for both upside (good) and downside (bad) volatility. Downside deviation, on the other hand, eliminates upside (good) volatility from the equation, and only measures the volatility that we care about when discussing risk – downside, or bad volatility.

The way this works is to first choose what is called a “minimum acceptable return” or MAR. Some people use the risk free rate or inflation rate, but we simply like to use 0 as the MAR. This is because we manage portfolios for absolute return - we want to make as much money as possible in good times while losing as little money as possible during bad times (and every investment method will go through bad times at some point).

It really doesn’t matter what MAR we use, as long as we are consistent in its application. These metrics are really meant for comparison purposes after all. Given alternative investment options, the question we are evaluating is: “Which option is compensating me BEST for the risk I am taking.” As such, as long as the MAR chosen is uniform across options being evaluated, it really doesn’t matter what value we choose as the MAR.

So now that we have our MAR (0 in this case), we look at our return series and we eliminate all data points that fall ABOVE our MAR from our following calculations[ii]. Since we only want to evaluate risk, or downside volatility, we are only going to evaluate return points that are below our MAR, since this is the true risk that we are trying to measure. We then take the standard deviation of values that fall below our MAR to get the downside deviation.

The downside deviation is a true measure of risk! While the standard deviation tells us what a “normal” data point looks like with regards to an average, the downside deviation tells us what a “normal” downside data point looks like with regard to an average.

Basically, we are calculating how bad a “normal” data point has been historically. How bad is a “normal” bad month for a system or asset class? How bad is a “normal” bad year for a system or asset class? This is what downside deviation tells us. Note that downside deviation is typically expressed as an annualized number.

Sortino Ratio: Since the standard deviation has a cousin that is more effective at evaluating risk (downside deviation), and since the Sharpe Ratio is a function of the standard deviation, it makes sense then that the Sharpe Ratio would have a cousin that is more effective at evaluating risk adjusted returns. It does, and that is the Sortino Ratio.

We earlier defined the Sharpe Ratio as the compound annual growth rate of a return stream minus the risk free rate, divided by the standard deviation, or:

Sharpe = (CAGR-RFR) / SD

The Sortino Ratio simply substitutes downside deviation for standard deviation:

Sortino = (Compound Annual Growth Rate – Risk Free Rate) / Downside Deviation

So while the Sharpe Ratio provides us with insight as to how much return we have gotten from an asset measured as a unit of volatility, the Sortino Ratio provides us with insight as to how much return we have gotten from an asset measured as a unit of downside volatility or risk. Thus we have a true measure of risk-adjusted returns with the Sortino Ratio that we do not have with the Sharpe Ratio!

CALMAR Ratio: Unrelated to standard deviation, downside deviation, and the Sharpe and Sortino Ratios is the CALMAR ratio. This is sometimes also referred to as MAR (not to be confused with the minimum acceptable return mentioned above), since it was brought to prominence by the Managed Accounts Report newsletter back in the 1970s.

The CALMAR ratio is the compound annual return of a program or asset class divided by the maximum historical drawdown. Given sufficient data, this is a good indication of the historical return stream of an asset in the context of the most pain an investor would have had to endure at any one point in order to achieve that return stream.

For those not familiar with the term drawdown, it is actually quite simple. Investors will, unfortunately, spend the great majority of their investment careers in drawdown. “Being in drawdown” simply means that you are not at an all-time high for performance. If the S&P makes an all-time high today and then closes down 2% tomorrow, the S&P is in a 2% drawdown. Since any legitimate trading system or asset class will not make new highs every day, every month, or every year, most asset classes are in drawdown most of the time.

One of the main things we care about when evaluating risk is the maximum drawdown a program or asset class has experienced (given that the asset or system being analyzed has data over many different types of market environments).

This is because if we are invested in the asset, it is at the points of large drawdown where we are prone to feel the most pain and thus be most susceptible to deviating from our stated investment plan.

Below is a chart of the S&P 500 (including dividends) going back to 1995 which shows the growth of $100k (left axis) along with the drawdown percent (right axis). Notice that when we are at a new all-time high, the drawdown is 0 – drawdown is always bound by 0 on the upside. You can see the two major drawdowns since 1995 on this chart (the dot-com crash after the year 2000 and the Great Financial Crisis around the year 2008).


Back to the CALMAR ratio now. The CALMAR ratio is an expression of the returns generated by the system or asset class, divided by absolute value of the worst drawdown. In the case of the S&P 500, including dividends and since 1995, the CALMAR ratio is about 0.2. The compound annual return over this time period has been ~10% and the maximum month end drawdown was about -50%.

Put another way, an investor in the S&P would have at one point lost 5x the average annual gain of the S&P! It’s scary to think about risk this way, but it is also necessary in order to set expectations!

Here at The Intelligent Allocator, these are some of the things we look at when evaluating risk and return. Our favorites include downside deviation, the Sortino Ratio and the CALMAR ratio.

We seek to minimize downside deviation, maximize returns, and thus maximize the Sortino and CALMAR ratios. At The Intelligent Allocator, we believe we have built something that does just that: The Alpha Momentum Strategy. Below are the summary returns and risk metrics for the strategy and the S&P 500 benchmark over the time period from 1995 through the end of 2017.

According to all of the risk and risk-adjusted return metrics that we have discussed, it is clear that, at least historically, The Alpha Momentum Strategy has been a superior strategy to buying and holding the S&P 500.

One particular nuance that we love to see when we look at this analysis is the interaction of the standard deviation and downside deviations of the two strategies. Notice how the standard deviation for the Alpha Momentum Strategy is higher than that of the S&P, but the downside deviation of the Alpha Momentum Strategy is lower than that of the S&P.

This just goes to show that the system has been effective at capturing upside (good) volatility, while avoiding (at least some) downside (bad) volatility associated with the S&P 500.

So next time your advisor or broker wants to put you in a strategy and touts its “low volatility,” ask him what type of volatility he is talking about. Is it the good volatility or bad volatility that he is trying to minimize? They are not, as you know now, one and the same and there indeed are methods to reduce downside (bad) volatility while not necessarily cutting upside (good) volatility by the same amount!

More to come.

[i] Risk adjusted return is a term used to describe the amount of return an asset has historically produced in terms of the risk to which that asset has historically exposed an investor. The higher the risk adjusted return of a strategy or asset class the better – we always want to be compensated more for taking risk than less

[ii] It is important to note that there are two schools of thought about how values at or above the MAR should be treated when doing these calculations. Some choose to set values above the MAR at 0 and include them in the downside deviation calculation (there will be more data points used in the MAR calculation when including the “dummy” 0 values, and the downside deviation will be a better explainer of both frequency and magnitude of downside deviation). We choose to eliminate values that fall above the MAR. The method that we use provides a better feel for true downside deviation, but at the expense of not being as sensitive to frequency. Which method is chosen is a function of what exactly the researcher is trying to evaluate – is he trying to mainly the magnitude of downside deviation (throw out the values that fall above MAR in this case) or is he trying to evaluate a combination of magnitude as well as frequency of down periods (keep values above the MAR in this case, but set them to 0). As long as the data set is sufficiently big, it doesn’t matter much which method is used so long as the calculation method is consistent across return streams being compared. These calculations are meant for comparison purposes above all, so consistency is important. For more on this subject, Tom Rollinger and Scott Hoffman have a paper (https://www.sunrisecapital.com/wp-content/uploads/2013/02/Futures_Mag_Sortino_0213.pdf) as do RCM Alternatives (https://www.rcmalternatives.com/2013/09/sortino-ratio-are-you-calculating-it-wrong/)