## The Substitution Swap

The Substitution Swap is simple in concept. Both the H-bond and the P-bond 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 H-bond 30-year 7's priced at par to yield 7.00%. The P-bonds are, of course, then also 30-year 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 H-bond and the P-bond are priced at par to yield 7.00%.

The realized compound yield of the H-bond is 7.00%, as we would naturally expect. However, the P-bond 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 yield-but only for one year.

TABLE 29

Evaluating a Sample Substitution Swap

P-Bond:

Workout Time: 1 Year Reinvestment Rate : 7% H-Bond

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%

### P-Bond

1. 70 70.00
2. 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 30-year 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 yield-to-maturity. (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 H-bond'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 30-Year 7's Swapped from 7.00% YTM to 7.10% YTM (7% Reinvestment Rate)

Workout Time

6 Months

### Realized Compound Yield Gain

1. 3 Basis Points Per Year
2. 4 " " " " ^ 2 g " ** 11 11

### 25! 7

1. 4 " " " "
2. 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_

+1 0

### Responses

• chilimanzar
How to do a substitution swap?
7 years ago
• William
How to price securitisation swaps?
7 years ago