Yield-Curve Volatility and Bond Selection Risk

Summary

The document frames a bond-selection problem in which several fixed-rate bonds appear to offer the same forecast return over a short horizon. Their durations and convexities differ, and the forecast assumes the issuer's yield curve will retain roughly the same shape. The author identifies yield-curve movements as a source of forecast error and highlights level, slope, and curvature as principal components whose volatility can change over time.

The proposed considerations include bond duration and the volatility of each curve component, but the document does not supply a combined objective function or answer the question. A practical criterion would need to map factor shocks into each bond's price sensitivity, account for covariance among the curve factors, and specify how forecast uncertainty is balanced against the expected return. Duration alone captures only a limited rate-risk approximation; convexity and issuer-specific curve behavior may also matter. The discussion is therefore a useful problem statement, not a complete selection method, and it gives no empirical comparison or calibrated factor-risk estimates.

Key ideas

• Yield-curve changes can make a bond's forecast return uncertain even when the forecast is correct under a stable curve.\nLevel, slope, and curvature movements are identified as important sources of yield-curve variation.\nDuration offers a way to compare sensitivity to interest-rate moves, but it does not capture all bond-price risk.\nA combined selection criterion would need factor sensitivities and the covariance of factor changes.\nThe document poses the optimization question without specifying or evaluating an objective function.

Tags

# Yield Curve Volatility


# Yield Curve Volatility












Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds.

Each yield curve has its slope and its curvature, and they obviously change over time (if the yield curve didn't change its shape over time, you would be able to predict with great accuracy the price variation of each bond which belongs to the yield curve).

Now let you have few bonds that (you think) will gain +1% during the next month, and you produce this forecast according to the yield curve assuming it won't change much its shape over the next month.

Let your forecast is correct and let you have to choose just one of these bonds: they have different durations and convexity, but it's rational to choose the one with the smallest duration in order to minimize mark-to-market risk due to interest rates volatility.

Now let your forecast is affected by estimation error: the main noise source here is the yield curve volatility, that is changing over time of its three principal components (level, slope and curvature according to literature).

If I asked you to choose one of those bonds to gain +1% over the next month, you would probably answer me you have to consider:

- the smallest duration

- the smallest yield curve level volatility

- the smallest yield curve slope volatility

- the smallest yield curve curvature volatility

What a suitable criterion to consider all of these factors would be? That is: what a global to-be-minimized function would be?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.