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Duration is the Central Measure of IRR to be Introduced Next Week(1)

By Lorraine Harris,2014-08-09 02:33
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Duration is the Central Measure of IRR to be Introduced Next Week(1)

    06-4

    BOSTON COLLEGE

    Edward J. Kane

    Financial Institution Management

    WEEK 4 EXERCISES

    Duration is the Central Measure of IRR to be Introduced in Week 4

    The Following Exercises will Be Discussed in Class

    1. Please calculate the Macaulay Duration of a 10-year, 6-percent annual-coupon bond

    when the market rate is 10 percent. Show all work.

    2. The “weighted average life” of a security is found by weighting the “futurity” in years of each promised cash flow by the percentage of the security’s total cash flows that it

    represents. Find the weighted average life of the bond described in question #1. Why is the bond’s weighted average life larger than its duration?

    3. Using r to represent the relevant market rate of interest, the following formula gives the duration D of a perpetual annuity (or “consol”) that pays C dollars once a year

    1;rforever: Dr

    a. What is the present discounted value (PDV) of this perpetuity?

    b. What is the present discounted value of the part of this perpetuity that accrues

    after n years?

    c. Why would zero be the present value of a costless forward contract to deliver

    1the perpetuity in n years to another party in exchange for receiving the price r

    at that time?

    d. What is the combined present value to day of the perpetuity and a forward

    1contract to sell the bond for in n years? r

    e. Using the idea of a “forward sale,” try to explain either formally or intuitively

    why the duration of an n-year annuity might turn out to be:

06-4

    1;rn.D nn1r(1;r)

    4. Why would the duration of a 10-year annuity be less than the duration of a perpetuity?

    Why would the duration of a 10-year coupon bond be larger than that of a 10-year

    annuity?

    Follow-on Question to Be Addressed in Week 6:

    5. Extension of Misplaced Trust Company Problem

    Remember that, on the day the Misplaced Trust Co. opened as a new bank,

    borrowers convinced the bank to make $100 million in three-year loans, while all

    depositors put their money in one-year certificate accounts. The principal and interest

    on all loans are compounded at 8 percent and payment is due at maturity. Simple

    interest is paid on the deposits once a year. Finally, the bank holds no other assets

    and issues $80 million in deposits at 5 percent per annum, raising the rest of its

    loanable funds entirely from stockholders.

     Assuming the loans are certain to be repaid on schedule and that all market yields

    move up and down with r, please calculate what you regard to be an adequate A

    measure of the interest-rate risk exposure the bank’s portfolio passes through to its

    stockholders.

     The bank’s managers ask you to help them to design a $10.73 million issue of

    subordinated debt that would eliminate interest-rate risk as you chose to measure it in

    part d. Suppose that the yield curve facing the bank on such bonds was flat at 5

    percent. What choice of bonds would accomplish this goal? Show that the bond

    issue has the desired effect.

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