Zephyr K-Ratio: Measure Wealth Creation Consistency

By Marc Odo, Swan Global Investments

The objective of this ongoing educational series of blog posts is to sort through, explain, and organize all of the various performance metrics that are available to the financial analyst, but most investors really want just two things:

1. They want their wealth to appreciate at a rapid rate
2. They do not want to deviate from that path of wealth appreciation

Luckily, there’s a ratio for that: Zephyr K-Ratio^[1]. This ratio measures the consistency of wealth creation over time.

The Steeper the Slope, The Faster the Climb

Let’s begin with an illustration to help understand this new metric.

Below we see a cumulative return graph for the S&P 500 over the last 20 years^[2]. Superimposed over the actual data is a straight, best-fit line.

Source: Zephyr StyleADVISOR, Swan Global Investments.

The slope of the line is the return measure, so the steeper the slope of that line, the better. A steeper slope indicates a more rapid pace of wealth appreciation.

Obviously in real life the path of wealth appreciation is not a straight line. There are many ups and downs along the way. However, a straight line of wealth appreciation can be thought of as an ideal. If an investment offered a consistent rate of

wealth appreciation with no deviations on a month-to-month or year-to-year basis, it would likely find an enthusiastic pool of investors.

Calculating & Evaluating the Zephyr K-Ratio

The K-ratio is the slope of the best-fit line that measures capital appreciation divided by the standard error of the mean, which it uses as its measure of risk.

The standard error of the mean is subtly but importantly different than the standard deviation used in most performance and risk statistics. While standard deviation measures how much individual observations of data tend to be dispersed from the mean value, standard error of the mean is a test of the mean itself—it is a way to indicate how precise or accurate a mean value is.

Using the standard error of the mean as a measure of risk allows us to see just how closely an actual return pattern matches that idealized straight line. The smaller the standard error of the mean, the closer the actual return series is to the idealized straight line. Conversely, a large standard error of the mean indicates that the actual path the investment takes meanders far and wide off the straight line.

With this ratio, the larger the number the better, and a comparison to peers is necessary to determine whether a number is “good” or “bad.”

K-Ratio Addresses a Standard Deviation Flaw

As an added benefit, the K-ratio addresses one of the long-standing complaints regarding the use of standard deviation as a risk measure: it does not and cannot take into account the timing of bad returns. If there are a dozen very bad monthly returns over the span of ten years, standard deviation cannot tell whether those bad months were randomly scattered throughout a decade or if they were all clustered in a small period of time. Anyone who remembers the dark days of late 2008/early 2009 can recall that some of the worst months in memory were tightly clustered within a few quarters.

The standard error of the mean and the K-ratio remedy this. A financial crisis pushes the investment from the idealized straight line, so you can clearly see where that cluster of bad months happened.

The Zephyr K-Ratio in Action: A Comparison

For the K-ratio to have meaning, it must be compared to other investments’ K-Ratios. Using the Defined Risk Strategy (DRS) as an example, we compare the K-Ratio for the DRS Select Composite to the S&P 500.

The DRS Select Composite looks strong when analyzed in terms of consistency of wealth creation in contrast to the S&P 500. First of all, the slope of the best-fit line is steeper than that of the S>&P 500, meaning the DRSSelect Composite does a better job of creating wealth.


Source: Zephyr StyleADVISOR, Swan Global Investments. All S&P 500 data based on historical performance of the S&P Total Return Index. All historical performance of the Swan. Select Composite is net of fees. Prior performance is not a guarantee of future results.

Secondly, and more importantly, the actual data line tends to hug the idealized best-fit line much more closely than the S&P 500 fits its ideal line. This is the consistency part of the equation.

A strong return metric divided by a smaller risk metric will certainly lead to better overall ratios. That is what we see with the K-ratio metric—the DRS winning on both the wealth creation and consistency fronts.

Defined Risk Strategy: Smooth & Consistent Wealth Creation

The DRS was devised with this goal in mind: to provide a nice, smooth, constant rate of wealth creation. The K-ratio illustrates how well the strategy was able to achieve that goal.