Bond Indexes

Pure Index/ Full Replication Approach

Pure indexing is the strictest form of indexing, requiring the exact same securities in the portfolio as in the index, with the same weights. This can be costly due to numerous transactions and associated fees. However, it minimizes tracking risk, and the difference between portfolio and index returns, ensuring closer alignment.

Enhanced Indexing

Enhanced indexing offers flexibility while minimizing tracking errors. It's cost-effective, especially for large or illiquid indexes. Risk factors are matched, with a slight increase in tracking risk to reduce trading costs. Tactics include:

Matching Modified Duration

This method is easy to measure and manage. The disadvantage is that it only minimizes tracking error due to parallel shifts in the yield curve. If bonds with embedded options show up, this will also cause measurement problems, as the modified duration measure alone will not properly capture the optionality of the underlying bonds. For this case, effective duration would need to be used.

Matching Key Rate Durations

Shifting to matching of key rate durations helps to solve the previous problem of modified duration only capturing parallel yield curve shifts. With key rate durations, numerous specific points along the maturity axis of the yield curve are picked out and plotted. As an example, a manager could use bonds with known key-rate durations at 1-, 5-, and 10-year maturities and match these durations to begin to reflect non-parallel yield curve shifts. The more maturities plotted, the more detailed the picture becomes.

Matching Sector/Coupon/Maturity/Issuer Weightings

This method involves examining the various weightings of the index and attempting to replicate those in the portfolio. For example, if the index has a 10% weighting in industrials, use the same weighting for the portfolio.

Matching the Present Value of Distribution of Cash Flows

The final method involves calculating the present value of each cash flow expected to be received from a bond and then calculating the weight of each cash flow as a percentage of total cash flows. The weight of each PV multiplied by its time remaining to be received gives each respective cash flow a contribution amount of duration to total duration. While this method requires lots of calculation, it is also thorough and can be reflective of non-parallel yield curve shifts.

Alternative Methods of Obtaining Passive Bond Market Exposure

Stratified Sampling

The complex and heterogeneous nature of the bond market often makes full replication cumbersome. Another potential answer to this problem is to use stratified sampling, which relies on manager determination to choose the most relevant characteristics of the index to be replicated. The table below shows an example of how this might look in practice:

$$ \begin{array}{c|c|c|c}
\textbf{Index} & \textbf{1–3-year} & \textbf{3–5-year} & \textbf{5–8-year} \\
& \textbf{Duration} & \textbf{Duration} & \textbf{Duration} \\ \hline
\text{Treasury} & 12\% & 18\% & \\ \hline
\text{Corporate AAA} & 24\% & 3\% & \\ \hline
\text{CDOs} & & & \end{array} $$

The manager would use the index to calculate the respective weight of 1 to 3 year duration treasuries. This would be the number of similar treasuries to hold in the underlying portfolio being managed, although the exact bonds need not be held. So long as the weighted characteristics are in line, the manager is free to pick and choose bonds that would be more cost-effective to buy and hold, thus lowering total transaction costs.

Question

Which of the following is least likely to properly capture the risk of a steeping yield curve?

1. Key rate duration.
2. Modified duration.
3. Present value of distribution of cash flows.

Solution

The correct answer is B.

Modified duration is a measure of a bond’s sensitivity to changes in overall interest rates, typically represented as a parallel shift in the yield curve. It does not specifically account for the differential movement of short-term and long-term rates, which is a characteristic of a steepening yield curve. Therefore, modified duration is less likely to properly capture the risk of a steepening yield curve because it doesn’t focus on the specific dynamics of such a curve

A is incorrect. Key rate duration measures the sensitivity of a bond’s price to changes in specific key interest rates at different maturities along the yield curve. It provides a more granular view of how a bond’s price will react to changes in different parts of the yield curve. Key rate duration can be very useful for capturing the risk of a steepening yield curve because it allows for a more detailed analysis of how different segments of the curve affect the bond’s price.

C is incorrect. The present value of the distribution of cash flows considers all the expected cash flows from a bond or portfolio of bonds and discounts them to their present value based on current market interest rates. While this approach is comprehensive in assessing bond price risk, it doesn’t explicitly address the unique interest rate movements associated with a steepening yield curve. It provides a broad view of risk but doesn’t directly capture the specific risk of a steepening yield curve.

Reading 20: Liability-Driven and Index-Based Strategies

Los 20 (g) Discuss bond indexes and the challenges of managing a fixed-income portfolio to mimic the characteristics of a bond index