Function SecurityPeriodicDuration(SettlementDate, MaturityDate, ParValue, Redemption, Frequency, CouponRate, Yield, Basis)

SecurityPeriodicDuration

The function SecurityPeriodicDuration returns the Macauley duration of a security that pays interest at the end of each coupon period. Duration is defined as the weighted average of time it takes to receive a positive cash flow. The present values of the cash flows are used as weights. The duration can be used as a measure of a bond price’s response to changes in yield.

SecurityPeriodicDuration(
    SettlementDate, ! (input) scalar string expression
    MaturityDate,   ! (input) scalar string expression
    ParValue,       ! (input) numerical expression
    Redemption,     ! (input) numerical expression
    Frequency,      ! (input) numerical expression
    CouponRate,     ! (input) numerical expression
    Yield,          ! (input) numerical expression
    [Basis]         ! (optional) numerical expression
    )

Arguments

SettlementDate

The date of settlement of the security. SettlementDate must be in date format.

MaturityDate

The date of maturity of the security. MaturityDate must also be in date format and must be a date after SettlementDate.

ParValue

The starting value of the security at issue date. ParValue must be a positive real number.

Redemption

The amount repaid for the security at the maturity date. Redemption must be a positive real number.

Frequency

The number of coupon payments in one year. Frequency must be 1 (annual), 2 (semi-annual) or 4 (quarterly).

CouponRate

The annual interest rate of the security as a percentage of the par value. CouponRate must be a nonnegative real number.

Yield

The yield of the security. Yield must be a nonnegative real number.

Basis

The day-count basis method to be used. The default is 1.

Return Value

The function SecurityPeriodicDuration returns the Macauley duration of a security that pays interest at the end of each coupon period. Duration is defined as the weighted average of the time it takes to receive a positive cash flow.

Equation

The Macauley duration \(D\) is computed through the equation

\[D = \frac{ \displaystyle \left(N-1+ \frac{f_{SN}}{f_{PN}}\right) \frac{R}{\left(1 + \frac{r_y}{f}\right)^{N-1+\frac{f_{SN}}{f_{PN}}}} + \sum_{i=1}^N \left(i-1+ \frac{f_{SN}}{f_{PN}}\right) \frac{v_{\textit{par}}\frac{r_c}{f}}{\left(1 + \frac{r_y}{f}\right)^{i-1+\frac{f_{SN}}{f_{PN}}}} } { \displaystyle \frac{R}{\left(1 + \frac{r_y}{f}\right)^{N-1+\frac{f_{SN}}{f_{PN}}}} + \sum_{i=1}^N \frac{v_{\textit{par}}\frac{r_c}{f}}{\left(1 + \frac{r_y}{f}\right)^{i-1+\frac{f_{SN}}{f_{PN}}}} }\]

where all other variables have the same interpretation as in the general equations for securities with multiple coupons.

Note

• This function can be used in an objective function or constraint and the input parameters ParValue, Redemption, CouponRate, and Yield can be used as a variable.

• The function SecurityPeriodicDuration is similar to the Excel function DURATION <https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038>_.

Example

The code:

_p_spd := SecurityPeriodicDuration(
        SettlementDate :  "2024-01-01",
        MaturityDate   :  "2044-01-01",
        ParValue       :  100,
        Redemption     :  100,
        Frequency      :  1,
        CouponRate     :  0.08,
        Yield          :  0.08,
        Basis          :  1);
block where single_column_display := 1, listing_number_precision := 6 ;
        display _p_spd ;
endblock ;

Results in:

_p_spd := 10.603599 ;

References

• Day count basis methods.

  • General equations for securities with multiple coupons.