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Yield curves

Can I mix yield curve types in the same analysis?

Yes. You may want to do this if, for example, you have some securities that are priced using a par curve, and others that use a zero curve. FIA allows you to assign yield curves on a per-security basis, so it is straightforward to mix and match.

You can even change the yield curve a security uses over time, using FIA’s effective date functionality.

Par curves or zero curves - does it matter which ones I use?

It depends on the attribution model.

For first-principles attribution, FIA prices secuurities using discount rates read off each security’s yield curve. In this case, only a zero curves will generate correct prices.

For perturbational attribution, one can use either as the yield curve is only used to measure changes in yield. At any given maturity, changes in the par curve are usually close to changes in the zero curve, so it makes little difference which you use.

What is the right way to measure parallel shift?

Despite its importance in attribution, there is no single standard way to measure parallel shift of a yield curve. Some widely used techniques are

(i) Measuring the movement in the curve at a given maturity, and setting that change to be the parallel movement;

(ii) Measuring the movement in the curve at the benchmark’s maturity, and setting that change to be the parallel movement;

(iii) Forming an average of the curve’s level at each sample point, and taking the difference over time;

(iv) Calculating the area under the curve, dividing by the longest maturity, then taking the difference over time;

(v) Selecting part of the curve such as maturities longer than 1 year, forming an average of these rates, and taking the difference over time.

Each of these has advantages and disadvantages. For instance, (iii) might seem the ‘obvious’ way of measuring changes in the overall level of the curve, but in practice yield curves tend to be more heavily sampled at lower maturities, and so this method over-weights shorter maturities at the expense of longer maturities.

What is the longest maturity a yield curve should measure?

As far as there are market movements.

It depends on the market to be modelled. For instance, there are relatively few European corporate bonds with a maturity of more than 10 years, so a yield curve to model these assets probably does not need to be specified past this maturity, and any longer yields can just be set to the 10 year yield - so the part of the curve past this points is flat.

On the other hand, the UK has issued 50 year gilts, so the UK risk-free curve needs to be specified out to at least 50 years. If the curve is only supplied out to 30 years, and there is significant market activity past this point, then the attribution analysis may miss some important activity. (We have seen this happen).

What is the shortest maturity a yield curve should measure?

For the bulk of fixed income portfolios, curve levels at maturities less than six months or so are unlikely to have much impact on the overall return. However, if you are storing cash rates or short term reference rates as part of the yield curve, then this data will be stored at shorter maturities.

What is sector curve allocation and sector curve selection?

Consider a portfolio that generates part of its return from credit spread.

For each security, the manager assigns a sector curve. The same sector curve can apply to more than one security.

The change in the security’s credit spread (the difference between the market yield and the risk-free yield) can now be broken down into two changes:

  • Change in the sector curve for the current security
  • Change in the spread between the security’s yield and the sector curve

The first effect generates sector curve allocation return, and the second generates sector curve selection return.

Sector curve allocation returns indicates the return generated by investing in a particular sector, since it measures the return of that sector’s curve as a whole.

The second effect measures the manager’s skill at picking individual stocks that outperformed their sector.

Note that these returns are entirely different to asset allocation and stock selection returns in the Brinson model, despite the superficial resemblance in terminology.

What is country curve attribution?

In some circumstances a currency may have multiple yield curves that are equivalent in status. A common example is the existence of sovereign yield curves for each country in the Euro zone. Although they all share the same base currency, they have distinct yield curves and are not all rated AAA. Country curve attribution measures the return generated by changes in the spread between these curves.