Week 4

Chapter 16 - Managing Bond Portfolios

Chapter sixteen

Managing Bond Portfolios

Chapter Overview

This chapter discusses active and passive bond portfolio management strategies. The concept and use of duration are explained, as are the various types of portfolio immunization strategies utilizing duration. In addition, it describes various active strategies, or bond swaps.

Learning Objectives

After studying this chapter, the student should have a thorough understanding of duration and how to calculate it for various bond portfolios. Students will be able to construct immunized portfolios appropriate for different investor categories. The student should also understand the difference between passive and active bond portfolio management and the implications of each management style.

PRESENTATION OF MATERIAL

16.1 Interest Rate Risk

The traditional bond pricing relationships and interest rate relationships are discussed in this section. The relationships with respect to maturity are not exact. In discussing the pricing relationships, it is helpful to discuss how maturity and cash flows as measured by coupon rates must be considered together to get exact relationships.

This section continues with a detailed look at duration. The description of duration used here stresses the concept of average life. Since the measurement of duration considers the timing and value of intermediate payments, it is an accurate measure of average life and is more meaningful than maturity for any bond that has coupon payments. Calculation of duration is presented and though an Excel worksheet can be created easily to do the calculations (see the example), it is recommended that the student work through a duration calculation manually to increase understanding. The weight of each cash flow for a fixed income instrument is the present value of the cash flow as a percentage of total value. Duration is the sum of the product of the weights of each cash flow and the period that it is received. The measure is in units of the cash flow payment during the year. For example, with monthly mortgage payments, duration would be in months. For a bond with semiannual compounding, the measure would be in 6-month periods. Spreadsheet 16.1 illustrates the calculation.

Price changes on fixed-income securities are proportional to duration. The financial industry uses modified duration extensively. This section presents some key properties of duration for different fixed income instruments and some useful simplifications of the duration formula. Figure 16.2 displays duration measures for coupon bonds of different maturities and Table 16.3 presents duration calculations for with varying maturities and coupon rates.

16.2 Convexity

Calculating the second order price change, known as the bond’s convexity reduces pricing results in pricing error when used with duration. Convexity creates problems for passive management since duration changes with changes in rates. For target date immunization, this leads to rebalancing problems. The correction for convexity is used to adjust the price-duration relationship.

When bonds have imbedded options, convexity behaves differently. A callable bond has a limit on price appreciation so when rates decline, the likelihood of call increases and the value is capped. Understanding convexity is particularly important for asset backed securities. Mortgage-backed securities are also subject to negative convexity and often sell for more than their principal balance.

16.3 Passive Bond Management

Major strategies for passive management are discussed here. Bond indexing is similar to stock indexing except that it requires more rebalancing and is in many ways more difficult to implement. Many bonds trade in relatively thin markets and indexing for fixed income instruments can be more costly. Figure 16.8 illustrates how stratification is used in bond indexing.

The second passive management strategy is immunization, which attempts to protect a bond portfolio from interest rate risk. Duration can be used for immunization. It is recommended that students immunize a portfolio and then observe changes in interest rate and the subsequent stability of portfolio value. Networth immunization is used by financial institutions to hedge against interest rate risk. Target date immunization is used by institutional investors to lock-in a yield to maturity for a bond or a bond portfolio. Cash flow matching involves selection of fixed income securities that exactly match cash outflow requirements.

16.4 Active Bond Management

Bond swapping strategies are presented here. Swapping strategies are used when the fixed income portfolio is actively managed. Substitution, intermarket and rate anticipation swaps require some level of market disequilibrium. With a substitution swap, two bonds that are substitutes offer different rates of return. The strategy involves purchase of the bond that is offering the higher rate of return and selling the bond that has the lower rate of return. The intermarket swap requires some disequilibrium in the markets as well. In an intermarket swap, the bonds could be of different credit risk but the interest rate differential is not correct. The rate anticipation swap involves changing the duration of the fixed-income portfolio to profit from a change in interest rates. The change in interest rates must not be anticipated by the rest of the market for the swap to result in superior profits. A pure yield pick-up involves a risk/return trade-off decision by an investor. A tax swap involves a purchase and sale of fixed income securities to take advantage of an individual investor’s tax position.

Horizon analysis selects a particular holding period and then predicts the yield curve at the end of the period. Contingent immunization involves both an active and passive component. The strategy allows active management with a constraint of portfolio immunization if return falls to a target level.

Excel Models

The Online Learning Center (www.mhhe.com/bkm) contains spreadsheets for calculating duration and for immunization. One is constructed to help students understand the concepts related to holding period immunization. The spreadsheet is built with closed-end equations that make it easy to work with bonds of any maturity. Students can compare return with different holding periods and understand how returns are affected by interest rate change. The other spreadsheets calculate duration using 1) the individual cash flows and 2) the closed-end equation. The models are also very useful in-class teaching tools.

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