[finance] calculate bond price

2012-12-16 8:31 pm

Q: You own a $1000-par zero-coupon bond that has five years of remaining maturity. You plan on selling the bond in one year, and believe that the required yield next year will have the following probability distribution:

Probability_____Required Yield (%)
0.1___________6.60%
0.2___________6.75%
0.4___________7.00%
0.2___________7.20%
0.1___________7.45%

a) what is your expected price when you sell the bond?
b) what is the standard deviation of the bond price?

Please list the steps and answers. Thanks.

回答 (1)

Tony Chan

2012-12-16 9:51 pm

✔ 最佳答案

<Answer A>

At year 1, present value of the bond shall be as follows given below required yields:

PV = FV / (1 + r)^4

PV (r=6.6%) = 1000/ 1.066^4 = $774
PV (r=6.75%) = 1000/ 1.0675^4 = $770
PV (r=7%) = 1000/ 1.07^4 = $763
PV (r=7.2%) = 1000/ 1.072^4 = $757
PV (r=7.45%) = 1000/ 1.0745^4 = $750

So, the expected price of the bond at year 1 shall be:
Bond price
= 0.1*774 + 0.2*770 + 0.4*763 + 0.2*757 + 0.1*750
= $763

2012-12-16 13:54:55 補充：

Average of bond price = 774+770+763+757+750/ 5 = 762.8

SD = [Probability * (actual X - average X)^2 ]^0.5
SD
= [ (0.1 * (774-762.8)^2) + (0.2 * (770-762.8)^2) + ....... ]^0.5

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