A five year, 4.50% semiannual coupon government bond is priced at 98 per 100 of par value. Calculate the annual yield-to-maturity stated on a semiannual bond basis, rounded to the nearest basis point. Convert the annual yield to:
a) an annual rate that can be used for direct comparison with otherwise comparable bonds that make quarterly coupon payments.
The solution states the YTM on a semiannual bond basis is 4.96% (0.0248 x 2).
Thus, how would you convert 4.96% from a periodicity of two to a periodicity of four?
You calculate the yield first. N=10, PV=-98, PMT= 2.25, FV=100, CPT I/Y=2.47, since it’s semi-annual, multiply by 2 to get the annualized value,I.e., 4.96%. To convert this to a quarterly compounding period yield, the formular is [1+(annualized yield ÷ 2)]^2 = (1 + quarterly yield)^4. That is [1 + (4.96÷2)]^2 = (1+ quarterly yield)^4. Doing a little maths, you should get the quarterly yield as 0.0123. Multiply by 4 to annualize it. You get 0.0493. Hope I didn’t lose you.
Will anyone please give a guide solving the question below with a BA II Plus using ICONV? The quarterly compounding gives 5.05% rather than 4.93.
A five year, 4.50% semiannual coupon government bond is priced at 98 per 100 of par value. Calculate the annual yield-to-maturity stated on a semiannual bond basis, rounded to the nearest basis point. Convert the annual yield to:
a) an annual rate that can be used for direct comparison with otherwise comparable bonds that make_quarterly_ coupon payments
But could you please explain the reset to 4 after the initial setting of C/Y to 2 to get the 5.02& to rather than outright setting to 4 and getting the 4.93% straightaway?
I use ICONV to solve for the effective annual interest rate first. The effective rate then acts as a reference point from which I can calculate any nominal rate for any value of C/Y.
In the TVM worksheet, you could also set P/Y=2 and C/Y=4 to get the nominal rate compounded quarterly.
Make sure you know what the question wants. Here, you have created a _ nominal _, annual rate (compounded quarterly); if the question asked for an _ effective _ annual rate, this calculation would be incorrect.
Thanks for this tip. Could you correct my steps to correct calcualtion of EAR? Appreciate your help. I am also trying to understand formulas beside using my BA II Plus.
I have been using this formula for EAR so far (1+r/m)^n. m is frequency (2 for half of year, 4 for quarter etc…) and n is number of compounding periods. Fixed Income chapter is a bit confusing to me.
