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Portfolio Boxplots

Portfolio Boxplots

This block visualizes the position of a portfolio in relation to the distribution of comparable portfolios from the Performance Watcher community, in order to evaluate not only its level, but also its relative positioning, its consistency and the possible presence of atypical behaviors, according to three dimensions:

  • Performance

  • Volatility

  • Weather (Perfometer score)

The grey boxplots represent the distribution of the portfolios from the Performance Watcher community for the same currency and the same risk level.

The analyzed portfolio is represented by a distinct point, positioned on each of the boxplots.

This allows an immediate visual comparison between the portfolio and its peers.

How to read the boxplot

Each boxplot summarizes the distribution of comparable portfolios in the following way:

  • Box (grey)
    The box extends from the first quartile (Q1) to the third quartile (Q3) and contains the central 50% of the portfolios.

  • Median (horizontal line inside the box)
    The median corresponds to the central portfolio of the distribution.

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

  • Dots
    Each dot represents an individual portfolio.
    The dot representing the analyzed portfolio makes it possible to identify its exact position in the distribution. If it is located beyond the whiskers, this indicates atypical behavior compared to the comparable portfolios.

The comparison between the analyzed portfolio and the community boxplot makes it possible to visually evaluate:

  • the position of the portfolio in relation to the market median,

  • the relative dispersion of the portfolio,

  • the presence of extreme behavior.

About the Weather dimension

In the Weather panel, the boxplot represents the distribution of the Perfometer scores of the comparable portfolios from the Performance Watcher community.

Unlike return or volatility, weather is a derived and bounded indicator, combining performance and risk into a synthetic measure of quality.

The positioning of the analyzed portfolio in this boxplot therefore makes it possible to evaluate the relative quality of its management compared to comparable portfolios, rather than an isolated raw variable.

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.

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