Yield according to ISMA

The yield according to ISMA (formerly “AIBD yield”) is an international measure of the yield on bonds that takes into account the daily effective interest rate .

Irrespective of the time of the actual interest settlement, the accrued accrued interest is added to the invested capital every day and interest is added to the next day.

In the event that the interest period is greater than the pension period, the ISMA method can be used to adjust “pension period equals interest period”. With the ISMA method, the interest period is identical to the time interval between two payments, and the interest surcharge is applied accordingly. The applicable period interest rate i _p conforms to the annual interest rate i.

Example of using the ISMA method:

Given is an eight-time advance installment R with € 500 per quarter (beginning with the payment of the 1st installment on January 1, 2008) and i = 10% pa ( effective ) and the compounding factor q = 1 + i = 1+ 0.1 = 1.1. Find the advance final value E (in €) according to the ISMA method as of January 1, 2010. See also the four basic formulas of the pension calculation .

${\displaystyle i_{\text{p}}=i_{\text{Q}}}$ (the period interest rate corresponds to the quarterly interest rate): therefore m = 4

${\displaystyle q_{\text{Q}}=1+i_{\text{Q}}=q_{\text{p}}}$

${\displaystyle q_{\text{Q}}=q^{\frac {1}{m}}=1{,}1^{\frac {1}{4}}=1{,}02411}$

${\displaystyle E=R{\frac {q_{\text{Q}}^{n}-1}{q_{\text{Q}}-1}}q_{\text{Q}}=500{\frac {q_{\text{Q}}^{8}-1}{q_{\text{Q}}-1}}q_{\text{Q}}=4459{,}29}$

Sketch:

The picture shows an eight-time advance payment with the quarterly rate R = 500 €, starting on January 1st, 2008.

See also

• Annuity yield
• Day loan
• Compounding paper

Individual evidence

1. ↑ See also Jürgen Tietze: Introduction to financial mathematics