The Euler theorem has found extensive applications in finance, particularly for decomposing homogeneous risk measures of degree one. However, a limitation of this approach is that it doesn’t adequately isolate the true sources of risk within an investment portfolio, thus creating a gap in risk analysis.

The Minimum Torsion Bets (MTB) method offers a compelling solution to this challenge. Leveraging spectral decomposition, MTB selectively identifies uncorrelated factors that are as close as possible to the original variables among all possible matrix rotations. This approach ensures a refined understanding of the underlying risk structure.

The results of the MTB method yield a diversification distribution with several noteworthy properties:

• It is always positive, reflecting a constructive aspect of risk management;
• The distribution sums to