0%

Peer-Group Weather Boxplot

Peer-Group Weather Boxplot

Based on the selected section, a boxplot of the community's weather is displayed for each currency-risk level pair.

The boxes span from the first quartile (Q1) to the third quartile (Q3), enclosing the middle 50% of the community's portfolios.

  • Median (horizontal line inside the box)
    The median portfolio, i.e. the central value of the community's distribution.

  • Whiskers (lines extending above and below the box)
    The whiskers delimit the range of outlier portfolios, as defined by the interquartile range (see methodology below).

  • Dots
    Each dot represents an individual instrument. The colours are based on the legend below the chart.

Dive deeper: how boundaries and outliers are defined

Why do we not assume normal distributions

Portfolio return and risk distributions are rarely normal. In practice, they may exhibit:

  • strong skewness (e.g. misclassified or exceptional portfolios),

  • fat tails,

  • very tight clustering (centralised or highly standardised management).

For this reason, Performance Watcher does not use percentile-based limits (such as 1%–99%) to define boxplot boundaries.

The IQR-based method

Whiskers are computed using the interquartile range (IQR):

[{IQR} = Q3 - Q1]

The boundaries are defined as:

  • Lower bound:
    [Q1 - 1.5 x IQR]

  • Upper bound:
    [Q3 + 1.5 x IQR]

Portfolios outside these bounds are considered outliers.

This classical method has two key advantages:

  • It relies on the central 50% of the data, making it robust to extreme values;

  • It does not require any assumption about the shape of the distribution.

Relation to a normal distribution (for reference only)

If the data were normally distributed:

  • (Q1 ~ -0.6745𝝈)

  • (Q3 ~ +0.6745𝝈)

  • (IQR ~ 1.349𝝈)

This implies that the whiskers would be located at approximately:

  • Lower bound:
    [Q1 - 1.5 x IQR ~ -2.70𝝈]

  • Upper bound:
    [Q3 + 1.5 x IQR ~ +2.70𝝈]

In a normal distribution, fewer than 1% of observations would lie beyond these limits.
This equivalence is provided purely as a reference — normality is not assumed in Performance Watcher.

Why not use a fixed 99% range?

Using fixed percentiles would implicitly assume that:

  • The distribution is stable,

  • tails are well-behaved,

  • Extreme observations are always meaningful.

Portfolio data rarely meet these conditions.
The IQR method instead adapts naturally to:

  • asymmetric distributions,

  • heterogeneous portfolio sets,

  • varying sample sizes.

Capped whiskers

An additional feature of the Performance Watcher boxplot is whisker capping:

  • If no portfolio exceeds the IQR-based boundary, the whisker is drawn at the worst or best observed portfolio, rather than at a theoretical limit.

This ensures that the boxplot remains a faithful visual summary of the data, without artificially extending the range where no outliers exist.


0%