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Wouldn't fitting a spline curve against 300+ Treasury bonds be similar across the street? I know there's different ways to fit/interpolate points to create a spline curve and I understand that every firm has slightly different models for creating a spline and from that the zero coupon curve for pricing as well as forward and par curves. In the end, splines are used for RV trade ideas but if splines generate similar results, how does this give one firm an advantage over another? In other words, wouldn't everyone see the same RV opportunity?

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The reality is that fitted curves can vary significant from one firm to the next. The chart below shows the fitted par curves as of June 19, 2018, using two very different models. The differences are quite stark:

enter image description here

Even if two firms adopt the same model, they can still end up with vastly different curves (and therefore curve spreads), because curve fitting is quite an art. There are numerous decisions involved: which bonds should we include; do we want smoother curves or do we want smaller spreads (these are two competing objectives); if the model involves knot points, where should the knots be placed (infinite combinations); do we change knot points over time or do we use the same knots forever; how should we weigh the bonds; do we minimize price errors, yield errors, or a combination of both; and so forth. These are difficult trade-offs, and different institutions have different priorities.

More importantly, fitted spreads give only one (incomplete) view of relative value. As others have pointed out, some bonds can be persistently rich or cheap. Further, a cheap (rich) bond can easily get cheaper (richer). For a somewhat dramatic example, here's a chart showing the fitted spread of an old bond:

enter image description here

Uncovering potential RV opportunities is not difficult, and fitted curve is one of many (imperfect) tools that can help, but understanding the reasons behind these dramatic dislocations is far more important, and that's the difficult part. Mechanically trading fitted spreads is unlikely to work...

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That's a reasonable question. I would say most of the time, participants will agree which bonds look 'cheap' and which look 'expensive'. This is because usually the forces of supply and demand have caused the dislocation. Typically , a certain bond or bonds have been in demand for some reason, so they become expensive. These dislocations can persist , even if everyone sees the same opportunity, if the specific demand is large.

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There are many considerations when fitting a curve that will add to variability across analysers;

  • Weights of bonds,
  • Knot points,
  • Smoothing constraints,
  • Other complex constraints like minimising curvature over time.
  • Minimising function used for residuals,
  • Etc.

I don't profess to know which is best, different analyses are better served by different ones I suspect.

Then you have the question of RV. Some bonds are perpetually cheap or expensive, relative to others and therefore not a real trading opportunity. It often takes a second layer of analysis to determine whether they might be more or less cheap/ expensive than normal. And this creates further subjectivity.

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