G-Spread calculation

Hello. This one question regarding the G-Spread calculation got me bugging (annual coupons).

Bond X:

Maturity = 2 years

coupon = 5%

Bond price = 101.7

Treasury bond:

Maturity = 2 years

coupon = 4%

Bond price = 100.5

The G-Spread is apparently 36bps, however I get a different result with my calculator (5.78% - 4.23% = 155bps). Anyone can help?

If you calculate the IRR of the two bonds:

IRR (X) = 4.1%

IRR (Treasury) = 3.74%

Hence, Spread = 0.36% or 36 basis points

Thanks for your answer. I do not really understand why we use IRR here though. We do not want the PV equal to 0 do we? I am clearly missing something here.

IRR is the same as YTM here.

The ‘NPV’ will be zero because you have an initial cash outlay (the PV of the bond).

So the calculation for a bond is

-PV +C/(IRR) +(C+FV)/(IRR)^2 = 0

Forget IRR ! if that is confusing you. Just calculate the YTMs on both bonds and substract the Government yield from the corporate yield(Bond X) you get your 36bps.

According to your calculations Bond X YTM cannot be higher than the coupon cause the bond is trading at a premium. Same goes for the Treasury bond.

I still do not understand… When I calculate the I/Y it gives me 5.78% for bond X and 4.23% for the G-bond.

For bond X: N = 2 PV = -101.7 PMT = 5 FV = 100

For T-bond: N = 2 PV = -100.5 PMT = 4 FV = 100

Is this what you are doing?

Yep! I understand that the YTM is a “uniform rate” that will equate the future cash flows (coupons and principle) discounted to the spot rates to the price of the instrument, and in that sense, the YTM can be referred to as an IRR. Is this where the right reasoning lies?

Did you get the right answer now?

And the YTM is the IRR for an when a bond is purchased at the market price and hold to maturity.

YTM is a uniform rate, correct, which is equivalent to all the spot rates that correspond to each period or ( “year”) so instead of discounting each period by it’s spot rate, the YTM is its equivalent for the full period.

Now as for your calculations, reset your calculator. Cause YTMs are 4.1% and 3.74%.

i think what you are doing is taking 101.7 as the future value for bond X and 100.5 for the G-Bond.

Oh My God. What I did was put the FV with a negative sign and the PV with a positive sign. Now i tried with PV negative sign and FV positive sign, and it gives me your numbers guys.

Seriously, what’s up with that? I thought we could put the negative sign either to the PV or the FV, as long as they had different signs?

You can…but the PMT must have the same sign as the FV.

Look at this equation:

-PV +PMT/(IRR) +(PMT+FV)/(IRR)^2 = 0

The PV always has the opposite sign of the PMT and the FV, and the FV and PMTs always have the same sign.

thank you very much!

you are probably better off using the 2nd Bond function on the TI BA Calculator

2nd Bond (Use down arrow for each next step and ENTER) [This is for the 2nd bond above]

  • SDT=12.31.1990
  • CPN=4
  • RDT=12.31.1992 (2 years)
  • RV=100 (Default do nothing)
  • ACT (Default - do nothing)
  • 2/Y (do nothing - pays 2 times a year)
  • YLD -> this you will calculate later - so skip by down arrow
  • PRI=100.5 (enter)
  • Use UP Arrow
  • Hit CPT
  • Ans: 3.7382

Not to put too fine a point on it, but YTM _ is an _ IRR.

While this is true for bonds, it’s not necessarily true for all (constant payment) TVM problems.

It’s better to remember that the TVM buttons are cash flow buttons: you have to use the correct sign for the direction of the cash flows.

For normal bonds, if you view it from the bondholder’s perspective, PV is negative (a cash outflow when he buys the bond), PMT and FV are positive (cash inflows that he receives from the issuer for the coupon and principal payments); if you view it from the issuer’s perspective, PV is positive (a cash inflow when he sells the bond), PMT and FV are negative (cash outflows when he makes the coupon and principal payments).

But you can also use the TVM buttons to analyze, say, a savings account in which the investor makes an initial deposit and periodic deposits. If you view this from the investor’s perspective, PV and PMT are negative (outflows when he makes deposits) and FV is positive (an inflow when he closes the account); if you view it from the account’s perspective, PV and PMT are positive (inflows into the account) and FV is negative (an outflow when the account is closed).

Fair !

LOL, that is a fine point that should be required! When in doubt when calculating anything in fixed income, find the YTMs and go from there. YTM is an IRR. Don’t forget that, friends.