### DEFINITION of K-Ratio

K-ratio examines the consistency of an equity's return over time. The data for the ratio is derived from a value added monthly index (VAMI), which tracks the progress of a \$1,000 initial investment in the security being analyzed. K-ratio is calculated as: K-ratio examines the consistency of an equity's return over time. K-ratio is calculated as:

K - Ratio = Slope of LogVAMI Regression Line * Square Root of the Number of Observations Per Year

(Standard Error of Slope * Number of Observations)

### BREAKING DOWN K-Ratio

The K-ratio was developed by derivatives trader and statistician Lars Kestner as a way to address a perceived gap in how returns had been analyzed. Because investor scare about both returns and consistency, Kestner designed his K-ratio to measure risk versus return by analyzing how steady a security, portfolio or manager’s returns are over time. It takes into account not just the returns themselves, but the order of those returns in measuring risk. The calculation involves running a linear regression on the logarithmic cumulative return of a Value-Added Monthly Index (VAMI) curve. The results of the regression are then used in the K-ratio formula. The slope is the return, which should be positive, while the standard error of the slope represents the risk.

### What Does the K-Ratio Show?

The ratio measures the return of the security over time, and it is considered to be a good tool to measure the performance of an equity because it takes the return trend, rather than point in time snapshots, into account. The K-ratio allows for comparison of cumulative returns for different equities (and equity managers) returns over time. It differs from the widely used Sharpe measure by taking into account the order in which returns occur. In practice, the K-ratio is designed to be viewed in tandem with and in addition to other measures of performance.

In addition to their use in analyzing individual stock returns, style categories and fund managers, K-ratios can also be calculated for bonds. K-ratios will differ across asset classes (domestic stocks versus bonds versus emerging market stocks), within asset classes (e.g., large cap versus small cap) and by time period.

In 2003, Kestner introduced a modified version of his original K-ratio, which changed the formula of the calculation to include the number of return data points in the denominator. He introduced a further modification, which added a square root calculation to the numerator, in 2013.