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Peer-Group Volatility Boxplot

Peer-Group Volatility Boxplot

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

The boxes span from the first quartile (Q1) to the third quartile (Q3), covering the middle 50% of the community's portfolios for that currency risk level pair.

  • 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.
    Dots located beyond the whiskers correspond to outlier instruments.

    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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