Return

Excess Return

The simplest of the benchmark-relative statistics, excess return measures the difference between the manager return and the benchmark return.

How Is it Useful?

Excess return is simple to understand and doesn’t require any sophisticated statistical knowledge. One calculates excess return using nothing more complicated than subtraction.

What Is a Good Number?

One would hope to outperform the benchmark, resulting in an excess return greater than zero. Negative excess return indicates the investor would have been better off investing in a low-cost index product. The higher the excess return, the better.

Math Corner: 

Excess return is one of the simplest metrics to calculate. Its simplicity is both an advantage and a disadvantage. It is easy to understand but does not take into consideration any form of risk.

Upside / Downside Omega

Upside omega measures the count and scale of returns above a minimum acceptable return (MAR). Downside omega measures the count and scale of returns below the MAR.

How Is it Useful?

Upside omega and downside omega are simply the numerator and denominator of the omega ratio separated into individual parts. While the omega ratio is useful for quantifying the trade-off between upside gains and downside losses, sometimes the details get lost because both the good and the bad are rolled into one number. By breaking omega into its constituent parts, one can focus only on the return or only on the risk element.

Math Corner: 

The upside omega is an integral, defined by the minimum acceptable return (MAR) on one axis and the count and scale of observations above the MAR at the upper bound. Downside omega is the same, but counting the observations below the MAR.

Batting Average

An indicator of consistency, batting average measures the percentage of time an active manager outperformed the benchmark.

How Is it Useful?

Batting average is conceptually easy to understand. It is simply the percentage of periods when the manager outperformed the benchmark. The higher the batting average, the more consistent the outperformance.

Math Corner: 

The calculation for batting average is quite simple. Its relative simplicity is both its strength and weakness. It is easy to understand but limited in what it tells you.

Skewness

Skewness measures to what direction and degree a set of returns is tilted or “skewed” by its extreme outlier occurrences.
PDF version: 

How Is it Useful?

One way of thinking about skewness is that it compares the length of the two “tails” of the distribution. Another way of thinking of skewness is that it measures whether or not the distribution of returns is symmetrical around the mean. The two are related, because if the distribution is impacted more by negative outliers than positive outliers (or vice versa) the distribution will no longer be symmetrical. Therefore, skewness tells us how outlier events impact the shape of the distribution.

Math Corner: 

Skewness is also known as the third moment of the distribution. By cubing the differences of the individual observations away from the mean, positive or negative values are possible, which indicate the tilt of the distribution. The process of cubing exacerbates the deviations from the mean, which is why skewness is used for measuring tail risk.

 
 

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