Last Updated on 14 October, 2021 by Samuelsson

Developed by derivatives trader and statistician Lars Kestner, the K-ratio is a performance metric that tries to address the problem of how returns and consistency of returns are analyzed. Although the K-ratio has been around since 1996 — with some modifications though — do you really know what the K-ratio is and how it is used?

The K-ratio is a statistical metric that is used to measure the growth of return and the consistency of that growth over a specified period. It measures return versus risk by analyzing how steady a security’s, portfolio’s, or manager’s returns are over time using the value-added monthly index (VAMI).

Now, we’ve added the K–ratio (also known as the Zephyr k–ratio) to our discussion. In this post, we will discuss the following:

• What the K-ratio is
• How to calculate it
• What the ratio signifies
• How to use the K-Ratio

## What is K-ratio?

The K–ratio is a return vs. risk ratio that measures the growth of return and the consistency of that growth over a certain period. It takes into account both the returns themselves and the order of those returns. The calculation is performed by plotting a linear trend for the return data and estimating the slope/variability (standard error of the slope) of the data. Hence, the K–ratio not only measures the return of a security over time but also examines the consistency of that return over that period.

The data for the ratio is derived from a value-added monthly index (VAMI). VAMI is a metric that uses linear regression to track the progress of a \$1,000 initial investment in the security being analyzed. The K-Ratio’s calculation requires creating a time series of data that is being analyzed. Because it takes the return trend into account, the ratio is a good tool to measure the performance of equities.

## How to calculate the K-ratio

The K-ratio is calculated by running a linear regression on the logarithmic cumulative return of a Value-Added Monthly Index (VAMI) curve. Here is how we do it:

• We generate a scatter plot of log[VAMI] verses (Number of periods).
• Then, the return per period (days, weeks, months, whatever) is measured by the Slope. For example, we may use the monthly returns of XOM stock over 10 years.
• Finally, the deviation of points from the regression line is measured by the Standard Error. This Error is a measure of “risk” associated with the stock.

The ratio: Slope / Standard Error may be interpreted as Return / Risk, just like in the Sharpe Ratio.

That would give:

K-ratio = (Slope of logVAMI regression line) / (Standard Regression Error)

Or

Where there are n return periods in the monthly return data, the formula would be given as:

K–Ratio (Kestner) = (Slope of logVAMI regression line) / n (Standard Error of the Slope)

## The Significance of the K-ratio

Since investors are often interested in returns and consistency, the K–ratio is a return vs. risk ratio that was created to measure both. Calculated by plotting a linear trend for the return data and estimating the slope/variability (standard error of the slope) of the data, the slope measures the return, while the standard error of the slope represents the risk.

Thus, the K-ratio will increase when the slope increases (cumulative P&L increasing faster) and will decrease when there are outsized gains or losses (increasing inconsistency). A higher k-ratio implies a better performance both in positive returns and consistency. A K-ratio value greater than 2.0 is considered good.

## How to use the K-ratio

K–ratio tests the consistency of an equity return over time, but it isn’t created to be a unique measure. You should use it in combination with other key accounting and financial ratios to measure the viability of an investment.

You can use the K-ratio to compare cumulative returns for different equities over a given time so as to determine the ones that are worthy of your hard-earned money. But it is not used for stocks alone; you can use the ratio to analyze other assets, fund managers, and trading strategies.

## The history of K-ratio

The K-ratio was created by Lars Kestner in 1996. In a book called Quantitative Trading Strategies, he introduced the K-ratio as an alternative to the Sharpe Ratio. It goes something like this:

Slope / Standard Error, where the slope component accounts for return, and the error component accounts for risk.

The formula has undergone two modifications over the years: one in 2003 and another in 2013. In one of his papers, Kestner made this comment:

“I introduced the K-ratio in 1996 as a reward to risk measurement to compliment the popular Sharpe ratio. The K-ratio is calculated by fitting a linear trend series to cumulative returns and estimating the slope and variability of the slope. Over the years there have been comments on adjustments factors needed to account for a varying number of return observations and return periodicity. In this paper, I show that the correct adjustments to the raw K-ratio include dividing by the number of return observations and multiplying by the square root of expected observations in a calendar year.”