The Non-Linear World of Intra-EMU Credit Curve Spreads

Research evidence excerpt

The Non-Linear World of Intra-EMU Credit Curve Spreads

FoundationMItaly and Spain (3y, 5y and 30y sectors) can broadly be bucketed in three groups:

1) Broadly linear relationship: for instance, the 5s10s Italy-Germany spread ratio (5y Italy

spread to Germany divided by 10y Italy spread to Germany) is broadly linear vs the level

of the 10Y spread ( Exhibit 3 ). Re-arranging the terms, the traditional box vs. spread

relationship is broadly quadratic (with intercept set at zero, Exhibit 4 ).

2) Broadly quadratic relationship: for instance, the 5s10s Italy-Germany spread ratio vs.

level of the 10Y spread ( Exhibit 5 ). From a mathematical point of view, this translates

into a cubic box vs spread relationship, which optically looks fairly close to quadratic

( Exhibit 6 ).

3) Non-linear, monotonic relationship and not suited for a quadratic fit: For instance, the

10s30s Italy-Germany spread ratio shows a bit of a 'hockey stick' behavior ( Exhibit 7 ) and

a quadratic fit would introduce unwelcome non-monotonicity that we address with our

formulation. It is important to highlight how much this approach differs from the

traditional linear regression applied to the 10s30s box vs spread until last year, which in

our view fails to acknowledge that all boxes should eventually bull flatten when spreads

are tight enough ( Exhibit 8 ).

Exhibit 3: The 5Y France-Germany/10Y France-Germany ratio Exhibit 4: … meaning the box vs spread relationship is

is broadly linear vs. 10Y France-Germany spread… quadratic

1.4

1.2 40

30 (ratio) 1.0

(bp) 20

0.8 10 France

0 0.6 France/Germany 5s10s -10

0.4

-20 5s10s

0.2 -30

-40

0.0 0 50 100 150 200

0 50 100 150 200

10y France-Germany (bp)

Source: Bloomberg, Morgan Stanley Research.