Choosing a Yield Measure for a Basket of Coupon Bonds

Summary

The document frames a benchmark construction problem for a basket of coupon bonds denominated in the same currency but differing in maturity, face value, coupon, and outstanding amount. It asks how to summarize the basket with an index yield, and considers a straightforward weighted average of the constituent bonds’ yields to maturity. The author is concerned that this average may lack a strong theoretical basis and could produce misleading results.

No response or worked method is included, so the document does not resolve how to calculate a basket yield or establish that any weighting scheme is appropriate. It serves as a useful statement of the measurement problem: an index yield must account for heterogeneous cash flows and bond characteristics, while the meaning of the index itself and its constituent weights need to be specified. Readers should treat the weighted-average proposal as an open question rather than a validated method or recommendation.

Key ideas

• A bond basket can contain instruments with different coupons, maturities, face values, and outstanding amounts.
• A weighted average of individual yields to maturity is proposed as a simple index measure.
• The document questions whether that average has a sound theoretical interpretation.
• It does not provide an answer, calculation method, or evidence comparing alternative yield measures.

Tags

# Different methodologies of building indices


# Different methodologies of building indices












Say have a basket of coupon bonds $B_i$ with $i \in \{1, ..., n\}$. Those bonds have different characteristics one from another. For example they differ in maturity, face value and coupon outstanding. But they are in same currency.

The problem I am facing is quite theoretical: how can I come up with a benchmark index of those bonds. In particular, I want to find the "yield" of the index which is composition of all $n$ bonds.

The most trivial thing I could think of is the following ($P_i$ is the $i$-th bond price in 100s, $F_i$ its outstanding face):

- For each bond I calculate YTM$_i$



- I define YTM of the index as YTM$_I = \sum_{i = 1}^n$YTM$_i \cdot w_i$

Basically a weighted average of YTM. To me, this doesn't have so much theoretical background and may lead to misleading results. Does anybody have any idea on a way to find YTM of the basket of bond (possibly computationally efficient).

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.