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

# SecurityPeriodicDurationModified

The function SecurityPeriodicDurationModified returns the modified Macauley duration of a security that pays interest at the end of each coupon period.

SecurityPeriodicDurationModified(
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 SecurityPeriodicDurationModified returns the modified Macauley duration of a security that pays interest at the end of each coupon period.

## Equation

The modified duration $$D_{\textit{mod}}$$ is computed through the equation

$D_{\textit{mod}} = \frac{D}{1+\frac{r_y}{f}}$

where $$D$$ is the Macauley duration.

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 SecurityPeriodicDurationModified is similar to the Excel function MDURATION.

The function SecurityPeriodicDuration. Day count basis methods. General equations for securities with multiple coupons.