I am trying to understand how they calculated "asked yield". If anyone can explain it, I really appreciate it. I would like to see the mathematical formula and the calculation.
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1The answer from @rhaskett is generally correct, but WSJ messes up the quote which is in 1/32nd, not decimals. You can look here for a complete replication of YTM.– AKdemyFeb 10 at 14:04
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1@AKdemy Your comment is very helpful.– VajiraFeb 11 at 17:09
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1 Answer
0 The ask yield is
annualized percentage return that the purchaser will receive if the note is purchased on the day of the quotation at the ask price and held until maturity.
This is called the (annualized) yield-to-maturity, which is just the effective interest rate (i) that you get if you bought the bond today and took all the coupons never selling it. There is formula for the price of bond where C is the coupon, M is the payment at maturity and P is the present value...
This appears a little complicated but it looks like you just have to solve for i in this equation (annualize it) and you would be done. The problem is this equation has no simple solution. You have to use a specialized financial calculator to solve it, but your problem is actually even harder than that. Let's see why...
Let's take your first line, C would equal C=0.875/2 (half the coupon because it is paid twice a year) P=100.0156 (ask price), M=100 (value of a treasury at maturity) and the number of periods N is... crap this is more complicated.
We have a bond that matures in 9 days so we have a partial period and calculate the accrued interest so C is really C=0.875*(9 days/365 days) and now N=0 since we have no full coupons left. Now, you can solve for i is you are mathematically inclined, but for bonds with longer time left N>0 and we need that financial calculator again.
After all this you still have to annualize i on a 365 day basis, not hard compared to the above, but still a lot for a stack exchange answer.
You can see why professionals use specialized software or just rely on Bloomberg or the WSJ. But while this is all a complicated calculation the idea is simple. The ask yield is just the yield you get buying the treasury now and holding and we annualize this yield so investors can easily compare one treasury to another.
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Ok. I tried that method and it didn't give me the stated "asked yield". I solved following equation . 100.0156(1+j)^k=100+(0.875*9/365), where k=9/365. The "j" I get is not what stated here. The method we used here is "semi-practical" method to get accrued coupon. Maybe WSJ using another method.– VajiraNov 7, 2017 at 12:23
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Hmmm... I am unable to reproduce the results exactly myself. I am doing at least two things wrong above. The price you actually pay P is the "dirty price" including accrued interest up to that point for the 182-9 days since the last payment (183? how does the government divide 365 by 2 exactly?). Rather than the "clean price" which is quoted.– rhaskettNov 7, 2017 at 16:19
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The second thing is I'm not correctly taking into account the the accrual method (and calendar!). Note on the 4th line the ask price is exactly 100, but the ask yield is not equal to the coupon. So there are some details on that side I'm missing. Maybe a holiday calendar?– rhaskettNov 7, 2017 at 16:25
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I'm happy to remove my answer so you can hopefully get a more complete one. I was unable to find documentation into the details here. You might have more luck on quant.SE.– rhaskettNov 7, 2017 at 16:30
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Yes, I forgot to add accrued interest. Assuming coupon paid every six months, (for first entry)last time coupon paid is May 15,2017. Form there to Nov 15, 2017 we have 184 days(actual). If the bond sold at asked price, then buyer has to pay Asked price+Accrued interest Nov 06 and he will get $100 and coupon amount at Nov 15. From last coupon date(May 15) to Nov 06, there are 175 days(actual). So the accrued interest is (0.875/2)(175/184)=0.4161. So he has to pay 100.0156+0.4161=100.4317. He will get 100+(0.875/2) Nov 15. Still I do not get the stated yield– VajiraNov 7, 2017 at 18:03