how to calculate "yield to maturity" using Stored Procedures?

Question

or using Excel sheet.

Answer 1

Yield To Maturity


Overview
Definition:
The constant rate at which the cash flows of a long term interest bearing security (for example a bond) must be discounted to obtain the instrument’s present value.



Equivalently, it is the rate of return an investor will receive if a long term interest bearing security is held to maturity and the interest payments are reinvested at this rate.



Consider the following example. Suppose the value date is 1-Jan-1995 and the future cash flows:

1-Jan-1996 10

1-Jan-1997 10

1-Jan-1998 10

1-Jan-1999 10

1-Jan-2000 110.



Further, suppose that the present value of these cash flows is 100. The annually compounded yield to maturity (using the accrual act/365 (actual)) is 10% since:



100 = 10/(1+.10)1 + 10/(1+.10)2 + 10/(1+.10)3 + 10/(1+.10)4 + 110/(1+.10)5.



FINCAD Functions


aaYTM(price, freq, cfp_table):

Calculates the yield to maturity for a set of future cash flows where time is denominated in number of periods.



aaYTMirr(price, freq, cfp_table):

Same as aaYTM except that negative cashflows are allowed.



aaYTM2(d_v, price, cfp_table):

Calculates the yield to maturity for a set of future dates and cashflows. The yield is annually compounded and the accrual is act/365 (actual).

Note that aaYTM3 is more general and hence may be more useful.



aaYTM2irr(d_v, price, cfp_table):

Same as aaYTM2 except that negative cashflows are allowed.



aaYTM3(d_v, price, cfp_table, acc, stat):

Calculates the yield to maturity for a set of future dates and cashflows. The user may choose the frequency and accrual of the yield.



aaYTM3irr(d_v, price, cfp_table, acc, stat):

same as aaYTM3 except that negative cashflows are allowed.



aaYTM_mmkt(d_v, price, cfp_table, acc, stat):

Calculates the money market equivalent (simple interest) yield to maturity for a set of future dates and cashflows.



Description of Inputs
Input Argument
Description

d_v
Value date

freq
The frequency (annual, semi-annual, …)

price
The present value of future cash flows (should include any accrued interest)

cfp_table
A 2-column table of dates and cashflows. In the function aaYTM(), it is a 2-column table of periods and cashflows.

acc
The accrual of the yield (e.g. act/365, …).





Description of Outputs
The functions aaYTM(), aaYTM2() and aaYTM3() all calculate the yield to maturity, Y, from the following formula:



Price = S cfi * (1 + Y/N) ^ -Pi N,



where, cfi is the ith cashflow, N is the frequency of the cashflows, and Pi is the length of the ith period (from the value date). The cashflows must all be positive.



The functions aaYTMirr(), aaYTM2irr() and aaYTM3irr() also calculate the yield to maturity, but negative cashflows are allowed. With this condition lifted, it is possible that the yield (or “internal rate of return”) is not unique. For example, suppose that there are cashflows of +$230 after 1 year, and -$132 after 2 years, and that the price is $100. The yield Y is obtained by solving:



100 = 230 / (1 + Y) - 132 / (1 + Y)^2.



This quadratic equation has two roots: Y = 10% or 20%. The aaYTM*irr functions return the smallest positive root (i.e., 10% in the example). If there are no positive roots, then the greatest negative root is returned. For example, if there were two roots and they were at Y = -8% and -3%, then the functions would return -3%. If there are no roots, then the functions return an error.



The function aaYTM_mmkt() calculates a money market yield. If the time to maturity of the instrument (i.e. the last cashflow) is less than or equal to one year, the yield to maturity, Y, is calculated from the formula:



Price = (S cfi * (1 + Y*Ti) ) / (1 + T*Y).



Where Ti is the time from the ith cashflow to maturity and T is the time from the value date to maturity. If the time to maturity, T, is greater than one year, the annually compounded yield to maturity is returned.



Note that in all functions, a combination of the Newton-Raphson method and the Bisection Method are used to solve for the yield.

for calculation please click on below link

http://www.karvy.com/perfin/yieldcalc.htm





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