Converting the annual yield on a bond | to comaparable bonds that make quartely coupon payments

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In page 417 Example 7:
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?
My calculation is wrong: (1+ 0.0496/4)^4 = 0.0505
The answer states: 0.0493
Any help on this would be really appreciated :)
 
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.
 
Thanks adekunle, do you mind showing the actual steps of how you solve to get APR4?
 
  • Find the nominal annual rate on a semi-annum bond basis:
N=10, PMT=2.25 (semi-annual coupon), PV=-98, FV=100
Compute I/Y we get 2.478261%, mutiply it by 2 to get 4.956522% which is the nominal annual rate on a semi-annum bond basis.
  • Change periodicity from 2 to 4:
(1+ 4.956522%/2)^0.5 - 1= 1.2315%, the effective quarterly yield
We mutiply it by 4 to get the nominal annual rate of 4.93% ,now on a quarterly bond basis.
hope it helps :)
 
adekunle and Ernest, this is fantastic! thank you! :)
 
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