Questions Set 74: Solution

Solution

Grace Hesketh is the owner of an extremely successful dress boutique in downtown Chicago. Although high fashion is Grace’s first love, she’s also interested in investments, particularly bonds and other fixed income securities. She actively manages her own investments and over time has built up a substantial portfolio of securities. She’s well versed on the latest investment techniques and is not afraid to apply those procedures to her own investments.
Grace has been playing with the idea of trying to immunize a big chunk of her bond portfolio. She’d like to cash out this part of her portfolio in seven years and use the proceeds to buy a vacation home in her home state of Oregon. To do this, she intends to use the $ 200,000 she now has invested in the following four corporate bonds (she currently has $ 50,000 invested in each one).
1. A 12 year, 7.5% bond that’s currently priced at $ 895.
2. A 10 year, zero coupon bond priced at $ 405.
3. A 10 year, 10% bond priced at $ 1,080.
4. A 15 year, 9.25% bond priced at $ 980. (Note: These are all noncallable, investment grade, nonconvertible / straight bonds.)
Questions
a. Given the information provided, find the current yield and the promised yield for each bond in the portfolio. (Use annual compounding.)
b. Calculate the Macaulay and modified durations of each bond in the portfolio and indicate how the price of each bond would change if interest rates were to rise by 75 basis points. How would the price change if interest rates were to fall by 75 basis points?
c. Find the duration of the current four bond portfolio. Given the seven year target that Grace has, would you consider this to be an immunized portfolio? Explain.
d. How could you lengthen or shorten the duration of this portfolio? What’s the shortest portfolio duration you can achieve? What’s the longest?
e. Using one or more of the four bonds described above, is it possible to come up with a $ 200,000 bond portfolio that will exhibit the duration characteristics Grace is looking for? Explain.
f. Using one or more of the four bonds, put together a $ 200,000 immunized portfolio for Grace. Because this portfolio will now be immunized, will Grace be able to treat it as a buy and-hold portfolio one she can put away and forget about? Explain.

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