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Basis Points

Basis Point Gain in Realized Compound Yield

-Year Workout 30-Year Workout

386.5 12.8

Table 31 shows how the gain in effective yield grows with additional pickups in basis points of yield-to-maturity on the initial swap. For example, if the P-bond can be picked up at 7.20% rather than at 7.10%, the resulting gain in realized compound yield in one year increases from 129 to 258 basis points. In this case, doubling the initial yield pickup doubles the gain. This rule of proportionality holds to a very close approximation, as Table 31 demonstrates, for both the 1-year and the 30-year workout times.

Up to this point, we have been assuming that our Substitution Swap worked out exactly as anticipated, with the P-bond realigning itself with the H-bond's price (assumed constant) at the end of the workout period. This will often not be the case and there are, of course, various risks present even in this simple swap category.

The risks arise from four sources: 1) a slower workout time than anticipated; 2) adverse interim spreads; 3) adverse changes in overall rates; and 4) the P-bond not being a true substitute.

Major changes in overall market yields will, of course, significantly affect the price and the reinvestment components of both the H-bond and the P-bond. The resulting changes in the realized compound yields will vary greatly depending on the workout period. Thus, an upward movement in rates may lead to a low total realized yield (principal plus interest) over the first year because of the sudden price drop while the same higher rate will result in an increased yield over life because of the greater reinvestment component. However, in the Substitution Swap, these effects tend to run in parallel for both the H-bond and the P-bond. For this reason, the relative gain from the swap is insensitive to even major rate changes. In Table 32, a sudden yield move is assumed, and (for purposes of simplicity) the bonds are priced and the coupons are reinvested at the same specified new rate. For the 30-year workout period, the swap provides the same gain of 4.3 basis points for reinvestment rates ranging from 5% to 9%. Over shorter workout periods, the P-bond—because of its slight discount—is slightly more volatile than the H-bond and so performs better than the H-bond as rates drop. However, even if the yield-to-maturity on both bonds surged to 9.00% by the end of one year, the investor could still obtain a relative gain of 116 basis points by having executed the swap. This is, of course, a relative gain only, as the table shows. Obviously, on an absolute basis, the investor with hindsight would have preferred not to be holding any 30-year bonds at all.

TABLE 32

Effect of Major Rate Changes on the Substitution Swap (30-Year 7's Swapped from 7.00% to 7.10%)

Realized Compound Yields-Principal Plus Interest

TABLE 32

Effect of Major Rate Changes on the Substitution Swap (30-Year 7's Swapped from 7.00% to 7.10%)

Realized Compound Yields-Principal Plus Interest

Reinvestment Rate

1-Year Workout

30-Year Workout

and YTM at End of

B.P.

B.P.

Workout Period

H-Bond

P-Bond

Gain

H-Bond

P-Bond

Gain

5%

34.551

36.013

146.2

5.922

5.965

4.3

6

19.791

21.161

137.0

6.445

6.488

4.3

7

7.00

8.29

129.0

7.000

7.043

4.3

8

- 4.117

- 2.896

122.1

7.584

7.627

4.3

9

-13.811

-12.651

116.0

8.196

8.239

4.3

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