when calculating PV of a bond by individual spot rates to compare for arbitrage: Example: Given, a 1.5 year 4% coupon treasury trading at $965. SEMI ANUAL-PAY yields to maturity are: 6 month: 4%, 1 Year: 5%, 1.5 Year: 6% Answer: you’re supposed to calculate PV of cash flows by dividing $20(4% coupon/2)by 1.02, (1.025)^2 and (1.03)^3. This is the part i dont get. If the spot rates are given as a semi annual YTM why would you have to divide them again by 2 to use 2%, 2.5%, and 3% on the denominator?
keyword: semiannual
the actual rate is calculated so by the nominal rate
zenji Wrote: ------------------------------------------------------- > keyword: semiannual yep. but now why are you multiplying 20$ by? (1.02)??
CFABLACKBELT Wrote: ------------------------------------------------------- > zenji Wrote: > -------------------------------------------------- > ----- > > keyword: semiannual > > > yep. > > but now why are you multiplying 20$ by? (1.02)?? dividing by 1.02 because 1/1.02 is a discount factor because spot rates are also semiannual. 1/1.02 = 1/(1+4%/2) - 6-months discount factor 1/(1.025)^2 = 1/(1+5%/2)^2 - 12 months discount factor, etc
immatic, i think i know where you’re getting confused… although the ytm’s are semi-annual, they are quoted as an annual yield. so the 6 month rate at 4% is an annual nominal rate. but since the question says semi-annual pay, you receive a 2% coupon every 6 months. so to discount the first coupon received in 6 months, you divide by 1.02, the semi-annual rate for the calc. let’s just put this example aside for a second. if i say a bond is paying 10% semi-annually (par value = 1000), then you receive $50 per 6 months. the total amount you get at the end of the year is $100, or 10%. hope this helps.