Ai = number of accrued days for the ith, or last, quasi-coupon period within odd period counting forward from last interest date before redemption.
DCi = number of days counted in the ith, or last, quasi-coupon period as delimited by the length of the actual coupon period.
NC = number of quasi-coupon periods that fit in odd period; if this number contains a fraction it will be raised to the next whole number.
NLi = normal length in days of the ith, or last, quasi-coupon period within odd coupon period.
Bonds often are referred to as being short-, medium- or long-term. Generally, a bond that matures in one to three years is referred to as a short-term bond. Medium or intermediate-term bonds generally are those that mature in four to 10 years, and long-term bonds are those with maturities greater than 10 years. Whatever the duration of a bond, the borrower fulfills its debt obligation when the bond reaches its maturity date, and the final interest payment and the original sum you loaned (the principal) are paid to you.
Not all bonds reach maturity, even if you want them to. Callable bonds are common: they allow the issuer to retire a bond before it matures. Call provisions are outlined in the bond’s prospectus (or offering statement or circular) and the indenture – both are documents that explain a bond’s terms and conditions. While firms are not formally required to document all call provision terms on the customer’s confirmation statement, many do so.
Bond maturities usually range from one day up to 30 years or even more. But this maturity date must be seen as the last future date (except if the borrower is in default) on which the investor will receive the principal amount from to the issuer. Depending on redemption features, the real reimbursement date can be very different (much shorter). These redemption features usually give the right to the investors and/or the issuer to advance the maturity date of the bond:
This is a provision that allows or require the issuer to repay the bond before the maturity date. The issuer will ‘call’ his bond if the interest rate index is lower than when he issued the bond. On the investor point of view, it means that the bond will be prepaid if the bond brings him too much interest compared to the current market conditions. If you purchase a bond with a ‘call option’, you have to pay less (get a premium) than without call because if the bond is prepaid, you will reinvest the money at a lower rate.
The put is a provision that gives to right to the investors to require from the issuer to redeem the bond before the maturity date. Investors usually exercise this option when the current market rates are higher so that he can reinvest his money at a higher rate. The put feature is a protection for the investor against an increase of the interest rate on the market and, consequently, should pay more (pay a premium) for a bond with a put than without.
Some corporate bonds, known as convertible bonds, contain an option to convert the bond into common stock instead of receiving a cash payment. Convertible bonds contain provisions on how and when the option to convert can be exercised. Convertibles offer a lower coupon rate beacuse they have the stability of a bond while offering the the potential upside of a stock.
Partial Prepayment (Paydown)
This kind of feature is usually seen with mortgage-backed securities. Without entering into details, a mortgage-backed security is anything else but the securitisation of a pool of mortgage loans. In mortgage loans, you have a regular (often monthly or quarterly) payment of principal and also the ability for the borrower the prepay the loan before maturity. Mortgage-backed securities prepay the principal to the investors in parallel the underlying mortgage loans. That’s the reason why mortgage-backed securities are traded on the basis of their ‘average life’.
Mortgage-backed bonds prices are more volatile than fixed rate bonds because the speed of redemption increases when the interests go down (when you have to reinvest at a lower rate) but decreases when interests go up. An increase in interest rates will increase the average life (the real maturity date) of your investment.
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