Indexed sinking fund debentures: valuation and analysis - includes appendices - Security Design Special Issue

Financial Management (Financial Management Association), Summer, 1993 by John D. Finnerty

Exhibit 3 shows how the remaining outstanding balance of the 8.70% ISFDs would change over the life of the issue if the average ten-year CMT were to change, relative to the 8.85% base rate, as of the first sinking fund date by the amounts indicated and remain at the new rate for the life of the issue. For example, if the average ten-year CMT is 8.85% on each sinking fund payment date, 20% of the remaining balance would be redeemed on each sinking fund date. The remaining balance would be 80% immediately after the first sinking fund date, 64% of the original balance after the second sinking fund date, 51.2% of the original balance after the third sinking fund date, and so on.(1) The terms of the ISFDs provide that if the scheduled redemption on any sinking fund date would leave a remaining balance less than five percent of the original balance, the FNMA will immediately redeem the entire outstanding balance. Depending on the course of interest rates, the 8.70% ISFDs could be retired as early as January 1992 (3.5 years from the date of issue).

A. Ten-Year ISFDs Versus Five-Year ISFDs

The 9.80% ISFDs, 9.75% ISFDs, 9.95% ISFDs, and 9.15% ISFDs are different from the 8.70% ISFDs and 9.05% ISFDs in several important respects. They have a longer maturity (ten years); the base rate is significantly lower than the offering yield whereas it is higher for the 8.70% ISFDs and only slightly lower for the 9.05% ISFDs; the average life, calculated at the base rate, is greater (5.42 years versus 3.08 years); and the four ten-year issues have a contingent sinking fund structure that is different from that of the two five-year issues. The base annual sinking fund percentage for the five-year issues, which the FNMA sold first, is 40%. In designing the contingent sinking fund for the ten-year issues, the FNMA raised the base annual sinking fund percentage to 50%. But the FNMA set the base rate far enough below the initial offering yield that if interest rates did not change, each ten-year ISFD's annual sinking fund percentage would be 45%. In addition, the FNMA made the annual sinking fund percentage in the ten-year ISFDs relatively more sensitive to a decrease in interest rates and relatively less sensitive to an increase in interest rates than the five-year ISFD's sinking fund. For example, the five-year ISFD's annual sinking fund percentage increases by ten percent if interest rates decrease by 100 basis points but decreases by 20% if interest rates TABULAR DATA OMITTED TABULAR DATA OMITTED increase by 100 basis points. The ten-year ISFD's annual sinking fund percentage increases by 30% if interest rates decrease by 100 basis points but decreases by 15% if interest rates increase by 100 basis points. As discussed further below, the redesign resulted in the interest-rate sensitivity of the sinking fund payments matching more closely the interest-rate sensitivity of mortgage prepayments.(2)

B. Imbedded Options

The contingent sinking fund contained in the ISFDs can be explained in terms of option theory. The issuer of the ISFDs has effectively purchased a strip of European call options and a strip of European put options. The times to expiration correspond to the sinking fund dates; the strike prices are par; exercise is costless; and exercise will occur with certainty if an option is in-the-money on one of the sinking fund dates. The amounts of bonds covered by the options correspond to the amounts shown in the sinking fund percentage adjustment column in Exhibit 2. The options always work to the issuer's advantage and to the investors' disadvantage. If interest rates drop sufficiently relative to the base rate, the call options come into the money and are exercised. If interest rates rise sufficiently relative to the base rate, the put options come into the money and are exercised.