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Math Help - Bond Math questions

  1. #1
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    Bond Math questions

    1. Shown below are selected annualized spot interest rates, rt, for U.S. Treasury Strips for Monday, January
    28, 2008.

    Maturity t
    (in years) rt
    1 2.08%
    2 2.17%
    3 2.48%
    4 2.72%
    5 2.86%

    (a) Calculate the price of a Strip for each maturity, per $100 of par value.

    My Solution
    Year 1
    100/(1.0208)
    Year 2
    100/(1.0217)^2

    (b) Calculate the forward rates, ft, for t=2, 3, 4, and 5.

    My Solution
    Year 2
    (1.0217^2/1.0208) -1

    (c) Using the spot rates, calculate the price (per $100 par) of a Treasury note that matures in 5 years and has a coupon rate of 5.5% (assuming annual coupon payments).

    My solution
    ?? help

    (d) Calculate the yield to maturity on the bond in (c) above.

    My solution
    I plan to use the yield function in excel

    (e) Calculate the modified duration (MD) of the bond in (c) above.

    My solution
    I plan to use excel's mduration function
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  2. #2
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    I am really interested in question 3, but any help is appreciated.
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  3. #3
    Member Last_Singularity's Avatar
    Joined
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    Quote Originally Posted by bondhelp View Post
    1. Shown below are selected annualized spot interest rates, rt, for U.S. Treasury Strips for Monday, January
    28, 2008.

    Maturity t
    (in years) rt
    1 2.08%
    2 2.17%
    3 2.48%
    4 2.72%
    5 2.86%

    (a) Calculate the price of a Strip for each maturity, per $100 of par value.

    My Solution
    Year 1
    100/(1.0208)
    Year 2
    100/(1.0217)^2

    (b) Calculate the forward rates, ft, for t=2, 3, 4, and 5.

    My Solution
    Year 2
    (1.0217^2/1.0208) -1

    (c) Using the spot rates, calculate the price (per $100 par) of a Treasury note that matures in 5 years and has a coupon rate of 5.5% (assuming annual coupon payments).

    My solution
    ?? help

    (d) Calculate the yield to maturity on the bond in (c) above.

    My solution
    I plan to use the yield function in excel

    (e) Calculate the modified duration (MD) of the bond in (c) above.

    My solution
    I plan to use excel's mduration function
    For part c, use the discounted cash flow model:

    PV = \frac{FV}{(1+r_t)^T} + \sum_{t=1}^T \frac{C}{(1+r_t)^t}
    PV = \frac{5.5}{1.0208} + \frac{5.5}{1.0217^2} + \frac{5.5}{1.0248^3} + \frac{5.5}{1.0272^4} + \frac{5.5+100}{1.0286^5} = $112.33

    Essentially, the price of your bond is equivalent to the sum of several zero-coupon bonds being paid off annually. In this case, your $100 face value bond that is worth $112.33 today is equivalent to getting $5.5 in periods t=1,2,3,4,5 plus $100 in period t=5. In other words, you would get the same value if you had instead buy: (1) one $100 bond expiring five years from now plus (2) five $5.5 bonds, each expiring one year after another.

    Note that in general, if the coupon rate is higher than the discount rate, the present value of the bond will be greater than its value (as in, it's sold at a premium).

    To find the yield in part d, recall that the yield of a bond is sort of a weighted average of the spot rates. So to solve for yield, denoted by the variable "Y", solve:
    $112.55 = PV = \frac{FV}{(1+Y)^T} + \sum_{t=1}^T \frac{C}{(1+Y)^t}
    $112.55 = \frac{5.5}{1+Y} + \frac{5.5}{(1+Y)^2} + \frac{5.5}{(1+Y)^3} + \frac{5.5}{(1+Y)^4} + \frac{5.5+100}{(1+Y)^5}

    I have not done the calculation, but I suspect that the yield should be close to the period 5 spot rate, as that is when the largest cash flow is placed (the payment of $100 face value). So the yield should be slightly below 2.86%.
    Last edited by Last_Singularity; December 30th 2008 at 11:58 AM.
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  4. #4
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    Is part a and b correct?

    for part e I am using this formula

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