CHAPTER FIFTEEN

Passive Fixed Income Portfolio Management

The term passive means one of two things; the investors want to:

Let’s look at how each is constructed, its advantages, disadvantages, and any special issues.

TIE THE MARKET: LADDER PORTFOLIOS

In a ladder portfolio, equal quantities of bonds are purchased that mature at set intervals along the yield curve. For example, a ladder could have $20K worth of bonds that mature each December for the next 15 years. Each year when the bonds mature, the principal is reinvested in a new 15-year bond. In effect, the portfolio is an endless conveyor belt. The variables in a ladder portfolio include:

The advantages of this approach include:

The disadvantages of this approach are that it is strictly regimented. Does it really make sense to roll over maturing debt into new 30-year bonds if interest rates are at all-time lows? Probably not, but this approach offers no flexibility.

TIE THE MARKET: MIRROR INDEX

Another way to tie the market is mirror a fixed income index. The most popular index is the Barclays Capital US Aggregate Bond Index (formerly known as the Lehman Aggregate). The index is composed of more than 8,700 bond issuers, including:

Mirroring an index used to be very difficult. Today, however, any investor can mirror an index with as little as $500. This became possible with the advent of exchange-traded funds that mirror the index. Here are some examples:

BND Vanguard Total Bond Market ETF

AGG iShares Core Total US Bond Market ETF

LAG SPDR Lehman Aggregate Bond ETF

SCHZ Schwab US Aggregate Bond ETF

FUND LIABILITIES: ZERO COUPON BONDS

Regardless of whether an investor is looking to fund one liability or a large series of liabilities, one way to fund them is by funding each liability with a zero coupon bond that matures on the day the liability is due (or shortly thereafter). Because the bonds are ZCBs and the principal is spent as soon as it comes in, there is no reinvestment risk. Provided the bonds have a high credit quality, the position has little risk. The cost of funding the liabilities is known. The cash flows offset each other, and so the duration of the assets equals the duration of the liabilities.

FUND LIABILITIES: DEDICATED PORTFOLIO

A dedicated portfolio is another way to fund a set of liabilities. In a dedicated portfolio, you start by funding the longest liability with the last payment of a long-term coupon bond—not a zero coupon bond. In each of the earlier years, the bond’s coupon payments are used to partially pay an earlier liability. Thus, when the bond’s 1-year coupon is paid, it is immediately used to pay a part of a 1-year liability. When the 2-year coupon is paid, it is immediately used to pay part of a 2-year liability. When the 3-year coupon is paid . . .

By using this methodology, short-term liabilities are partially funded with long-term higher yielding assets. Then, the remaining balance of the next to longest liability is funded, and its coupons also reduce the earlier liabilities. Then, the next liability is funded until all the liabilities are funded.

An example will help illustrate.

PROBLEM 15A

Suppose a business owner buys out his partner and agrees to pay him $1MM a year for 20 years. The business owner wants to buy a portfolio that will fund the liabilities. The current yield on eurobonds is as depicted in Figure 15.1.

FIGURE 15.1

New Issue Eurobond Yields

ANSWER:

As is usually the case, the long-term bonds yield more than the short-term bonds, so we want to use as many on longer-term bonds in funding as possible.

Figure 15.2 depicts the dedicated portfolio worksheet used to work through the requirements:

($935,000 Principal + ($935,000 × .0695 × 360 / 360)) = $999,983

This loop continues until the first (1-year) liability is paid off.

FIGURE 15.2

Dedicated Portfolio Worksheet

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The main issues with the construction of a dedicated portfolio are:

FUND LIABILITIES: IMMUNIZED PORTFOLIOS

An immunized portfolio is another passive approach to managing a portfolio. However, unlike the last two approaches, while the duration matches, the cash flows don’t. Let’s start by considering a single $10MM liability due in 10 years. As a single cash flow, the duration of the cash bond is also 10. For this example:

The easiest way to fund this liability would be with a 10-year ZCB. A 10-year ZCB has a duration of 10 years. The cash flows and durations are a match, so the funding approach works. It is, however, the most expensive way of financing the liability because the return is only 3%. Another way to fund the liability is to use longer-term, higher yielding bonds to fund the liabilities. Because the bonds will have maturities longer than 10 years, the coupons will have to be higher than 0 to keep the duration at 10. Figure 15.3 looks at three alternatives.

FIGURE 15.3

Three Alternatives for Funding a 10-Year Liability

Maturity

10 Years

12 Years

14 Years

Coupon

0.00%

3.50%

6.97%

Yield

3.00%

3.50%

4.00%

Frequency

1

1

1

Duration

10

10

10

Funding Cost

$7,440,939

$7,089,102

$6,755,406

Funding the liabilities with the 14-year coupon bonds is the least costly of the three alternatives, but there is a catch. To illustrate the catch, let’s start by using the 10-year zero coupon bond as a funding vehicle. In this case, as of today the liability and the asset both have durations of 10 years, as shown in Figure 15.4.

FIGURE 15.4

Initial Duration of 10-Year ZCB and 10-Year Liability

As time passes, the duration of the liabilities declines in a linear manner—that is, in 1 year, the liability has a duration of 9; in 2 years, 8; in 3 years, 7; and so on. Because the asset is a zero coupon bond, its duration also declines in a linear manner. Therefore, if the liability is funded with the 10-year zero, the durations not only start out equal—but stay equal over time, as shown in Figure 15.5.

FIGURE 15.5

Duration of 10-Year ZCB and Liability over Time

If instead, the liability is funded with the 14-year coupon bond, the durations start off equal but decline at different rates as time passes. After 10 years, the liability is due, but the bond would still have 4 years to maturity and a duration of approximately 3.5, depending on the yield. Clearly, while the durations start out equal, they decline at different rates, and the hedge breaks down, as shown in Figure 15.6.

FIGURE 15.6

Duration of Liability and Duration of 14-Year Bond over Time

In order to use the 14-year bond as a hedge, it is necessary to periodically rebalance the hedge. This means shortening the duration of the asset so it equals the duration of the liability. There are two ways to shorten the duration: Periodically swap into lower-duration bonds or periodically add short T-note futures positions to the portfolio to lower the duration. Either will cost some money, but using the futures usually costs much less. Using the 14-year funding vehicle instead of the 10-year initially saved $685,533 ($7,440,939 − $6,755,406), as shown in Figure 15.7. If the costs of rebalancing the hedge plus the hedging error caused by a less than perfect hedge totals less than $685,533, it makes more sense to use the 14-year bond. If the costs are higher, use the 10-year.

FIGURE 15.7

Using the 14-Year Bond and Rebalancing