The Substitution Swap
The Substitution Swap is simple in concept. Both the Hbond and the Pbond are equivalent in quality, coupon and maturity. The swap is executed at a basis point pickup which is expected to be eradicated by the end of the workout period.
It will prove very revealing to determine the value of a concrete Substitution Swap in terms of improved realized compound yield. For this example, take as the Hbond 30year 7's priced at par to yield 7.00%. The Pbonds are, of course, then also 30year 7's but suppose they are priced to yield 7.10% for a modest 10 basis point pickup. For the purposes of the example, assume that the workout period is one year. During this period, the prevailing reinvestment rate for coupons remains unchanged at 7%. At the end of the workout period, both the Hbond and the Pbond are priced at par to yield 7.00%.
The realized compound yield of the Hbond is 7.00%, as we would naturally expect. However, the Pbond has a realized compound yield of 8.29% over the one year workout period. The steps in the computation are shown in Table 29.
In other words, this 10 basis point Substitution Swap with a one year workout period results in a 129 basis point improvement in realized compound yieldbut only for one year.
TABLE 29
Evaluating a Sample Substitution Swap
PBond:
Workout Time: 1 Year Reinvestment Rate : 7% HBond
Original Investment Per Bond
Two Coupons During Year
Interest on 1 Coupon @ 7% for One Hdlf Year
Principal Value at End of Year @ 7.00 YTM
Total $ Accrued
Total $ Gain
Gain Per Invested Dollar
Realized Compound Yield
Value of Swap
 1,000.00 70.00 1.23 1,000.00 1,071.23 71.23
 07123 7.00%
PBond
 70 70.00
 23 1,000.00 1,071.23 83.53
129 Basis Points in One Year
To put these results in a properly qualified perspective, it must be realized that this gain of 129 basis points in realized compound yield is achieved only during the single year of the workout period. To obtain such a realized compound yield over the extended 30year period, the investor must continue to swap an average of once a year, picking up 10 basis points each time or at least averaging such a pickup on balance.
At the very worst, the swap will not "workout" until both bonds reach their common maturity, i.e., 30 years hence. In that case, the realized compound yield gain would be 4.3 basis points. This is even less than the 10 basis point pickup in yieldtomaturity. (See page 98 below for an explanation of this difference.) However, as the workout time is reduced, the relative gain in realized compound yield over the workout period rises dramatically. The following figures assume that the Hbond's price remains stable at parâ€”i.e., no overall change in rate levels is assumed.
TABLE 30
Effect of Workout Time on Substitution Swap 30Year 7's Swapped from 7.00% YTM to 7.10% YTM (7% Reinvestment Rate)
Workout Time
6 Months
Realized Compound Yield Gain
 3 Basis Points Per Year
 4 " " " " ^ 2 g " ** 11 11
25! 7
 4 " " " "
 0 " " M " 258! 8 " H " " 527.2
Table 30 shows that the gain in realized compound yield is approximately inversely proportional to the workout time. For example, if we shorten the workout time from thirty years to one year, i.e., by a factor of 30, then the annual gain jumps from 4.3 to 129 basis points, i.e., increases by the same 30 factor.
TABLE 31
Effect of Initial YTM Pickup on Substitution Swap
(7% Reinvestment Rate)
Initital Pickup in YTM_
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