Calculation of IRR

General
1

Hi!
I try to calculate IRR for a bond with
start date: 2022-01-03
maturity date: 2025-01-03
settlement date: 2022-11-04
coupon: 2% (annual)
frequency: semiannual (Frequency.P6M)
day count: act/365 (DayCounts.ACT_365L)
clean price: 97

Using yieldFromDirtyPrice, I’ve a irr of 0.0345149172.
Using MS XIRR I’ve a irr of 0.0347078830.

Discounting cashflow with MS XIRR I got, exactly, the dirty price (97.6794520548),
Using strata irr I got 97.7180266080.

this is my code

public static void test() {
LocalDate settlementDate = LocalDate.of(2022,11, 4);
LocalDate startDate = LocalDate.of(2022,1, 3);
LocalDate maturityDate = LocalDate.of(2025,1, 3);
double couponRate = 0.02;

    BusinessDayAdjustment businessDayAdj = BusinessDayAdjustment.of(
            BusinessDayConventions.NO_ADJUST, HolidayCalendarIds.NO_HOLIDAYS);

    PeriodicSchedule accrualSchedule = PeriodicSchedule
            .builder()
            .startDate(startDate)
            .endDate(maturityDate)
            .lastRegularEndDate(maturityDate)
            .businessDayAdjustment(businessDayAdj)
            .frequency(Frequency.P6M)
            .stubConvention(StubConvention.NONE)
            .rollConvention(RollConventions.EOM)
            .build();

    FixedCouponBond fcb = FixedCouponBond
            .builder()
            .accrualSchedule(accrualSchedule)
            .currency(Currency.EUR)
            .securityId(SecurityId.of("CUSIP", "135087WL4"))
            .notional(100.)
            .fixedRate(couponRate)
            .dayCount(DayCounts.ACT_365L)
            .yieldConvention(FixedCouponBondYieldConvention.DE_BONDS)
            .legalEntityId(LegalEntityId.of("LegalEntity", "DUMMY"))
            .settlementDateOffset(DaysAdjustment.ofBusinessDays(3, HolidayCalendarIds.CATO))
            .build();

    ResolvedFixedCouponBond resolvedBond = fcb.resolve(ReferenceData.standard());
    double cleanPrice = 97 / 100.;
    double dirtyPrice = DiscountingFixedCouponBondProductPricer.DEFAULT.dirtyPriceFromCleanPrice(resolvedBond, settlementDate,cleanPrice);
    double accrual = DiscountingFixedCouponBondProductPricer.DEFAULT.accruedInterest(resolvedBond, settlementDate);
    double yield = DiscountingFixedCouponBondProductPricer.DEFAULT.yieldFromDirtyPrice(resolvedBond, settlementDate, dirtyPrice);
    double calculatedDirty = DiscountingFixedCouponBondProductPricer.DEFAULT.dirtyPriceFromYield(resolvedBond, settlementDate, yield);
    double macaulayDuration = DiscountingFixedCouponBondProductPricer.DEFAULT.macaulayDurationFromYield(resolvedBond, settlementDate, yield);
    double modifiedDuration = DiscountingFixedCouponBondProductPricer.DEFAULT.modifiedDurationFromYield(resolvedBond, settlementDate, yield);

    System.out.println("yield: " + yield);
    System.out.println("dirty: " + dirtyPrice);
    System.out.println("calculatedDirty: " + calculatedDirty);
    System.out.println("macaulayDuration: " + macaulayDuration);
    System.out.println("modifiedDuration: " + modifiedDuration);
    System.out.println("accrual: " + accrual);
    System.out.println("accrual days: " + DiscountingFixedCouponBondProductPricer.DEFAULT.accruedYearFraction(resolvedBond, settlementDate) * 365.);

}

What it’s wrong?

irr
irr775×583 172 KB

2

IRR stands for Internal Rate of Return and it is a metric used to evaluate the profitability of an investment. IRR is the discount rate at which the net present value (NPV) of all cash flows of an investment is equal to zero. In other words, it is the rate at which the present value of future cash flows equals the initial investment.

To calculate IRR, you can use the following steps:

  1. List all cash inflows and outflows of the investment, including the initial investment (which is negative).
  2. Calculate the present value of each cash flow using a discount rate. The discount rate is the rate at which future cash flows are discounted to their present value.
  3. Add up the present values of all cash inflows and outflows. This will give you the net present value (NPV) of the investment.
  4. Use a trial and error method or a software program to find the discount rate at which the NPV equals zero. This rate is the IRR.

Alternatively, you can use an Excel spreadsheet to calculate IRR using the IRR formula. Here are the steps:

  1. List all cash inflows and outflows of the investment, including the initial investment (which is negative) in a column.
  2. Use the Excel formula “=IRR(values)” to calculate the IRR, where “values” is the range of cells that contains the cash inflows and outflows.

The resulting value is the IRR of the investment. If the IRR is greater than the required rate of return, the investment is considered profitable. If the IRR is less than the required rate of return, the investment is considered unprofitable. If the IRR is equal to the required rate of return, the investment is considered break-even.

3

Thanks for reply Milycyrus1. Ok, but i’ve
BusinessDayConventions.NO_ADJUST
HolidayCalendarIds.NO_HOLIDAYS
StubConvention.NONE
RollConventions.EOM
with no holidays on maturity date
So i don’t understand why, if i discount cashflow with strata yield, I don’t got (exactly) the dirty price.
For tenor I use ACT_365L so I calculate time as (maturity - starting)/365.
If I use xirr I got it