Hi all,
I'm slightly confused about the reinvestment assumption involved in calculating the YTM. I've always thought of the YTM as being the annualised yield earned by an investor who holds their bond to maturity, taking into account the initial price they paid for it, and assuming that all coupons are reinvested at the YTM rate. (It also represents the rate needed to discount all future cash flows of a bond into its present value (i.e. price)).
However, I am then confused at how a bond (say with a coupon rate of 4%), when bought at par, has a coupon rate that is equal to its YTM? I get that if a bond is bought at par, there will be no capital appreciation (since principal and price will be the same), but surely the reinvestment of the coupons would make the YTM greater than 4%, due to compounded interest? Explanations I see online only seem to be talking about the capital appreciation element, when comparing coupon rate with YTM, with no mention of the effect of reinvestments.
I guess this then brings into question whether the reinvestment assumption is even needed in calculating the YTM, as per this article?
https://www.economics-finance.org/jefe/issues/For…
Many thanks for your help.
Finding Price from Yield-to-Maturity (Originally Posted: 07/12/2010)
I'm reading Bruce Tuckman's Fixed Income book, and I'm trying to use one of the formulas to find a bond price from a yield. The problem is, the answer I'm getting seems like it has to be wrong (it's way too low to make any intuitive sense). So what exactly am I doing wrong?
Suppose a bond has a coupon of 5.75% (paid semi-annually), a yield of 4.525, and matures in 2-years.
Tuckman's book says: Price = (coupon/2) / (1 + yield/2)^1 + (coupon/2) / (1 + yield/2)^2 + (coupon/2) / (1 + yield/2)^3 + (face + coupon/2) / (1 + yield/2)^4
So, I let the face equal 100, the coupon equal 5.75, and the yield equal 4.525. This gives Price = (2.875) / (3.2625)^1 + (2.875) / (3.2625)^2 + (2.875) / (3.2625)^3 + (102.875) / (3.2625)^4 = 2.034003
This price seems ridiculously low. Why would someone only pay $2.03 for this cash stream? So, what did I do wrong? I don't think it's a typo, so I must be misunderstanding something.
You might want to consider that the yield listed above is a percentage and adjust accordingly. Bond price is $1,023.175.
Okay, so yields are always listed as percentages (in other words, always divide by 100)? Thanks a lot man.
Econ is right, I got a value of 102.31 per 100 of face value. When you're talking formulas interest rates are 99% of the time divided by 100. for example, 5%=.05 and so on. If you have a financial calculator (ba II plus pro):
PMT: 2.875 (coupon times face value/2) fv=100 N=4 i/y=2.2625
Remember you always need to adjust for semi-annual coupons and the easiest way (imo) is to just double the period and such as I did above. Hope this helps.
And just in case you want it in actual formula format:
=2.875(1/0.022625-((1/(0.022625(1+0.022625)^4))))+100/(1+0.022625)^4
Calculate yield to maturity on bond with prepayment of interest (Originally Posted: 06/25/2014)
I hope this is going in the right forum because the posting options don't exactly match the forum names.
How do I calculate yield to maturity on the following bond:
30-year bond Coupon of 5.62% Interest on the bond payable in advance
Many thanks in advance!
Annual interest payments?
Yessir, annual interest payments.
http://www.investinganswers.com/calculators/yield/yield-call-ytc-calcul…
How do you calculate YTM approximately? (Originally Posted: 07/13/2016)
How do you calculate YTM approximately? I know YTM is the IRR of a bond but how do you calculate it if there is more than 1 time period?
You use a financial calculator
BAII+
You can approximate quite closely in your head for bonds trading around par (give or take a few pts) by decomposing YTM into its current yield and capital appreciation components.
Eg a 5yr bond trading at 90 with a 10% coupon will have a yield of ~13pct. 10%/90 = 11.1% current yield + 10pts/5yrs = 2pts/year = 13.1%. Actual answer is 12.83% but that's about as good as you can do without a calculator.
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