Grace Hesketh is the owner of an extremely successful dress boutique in downtown
ID: 2762286 • Letter: G
Question
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.
Explanation / Answer
Answer a
Current Yeild => Annual Interest Income/ Current market price o fbond
12 year Bond => 75 / 895 => 8.38%
Yield to Maturity: 895 => 75 × PVIFAr%,12 period + 1,000 × PVIFr%,12 period => 8.96%
10 year Zero Bond => 0 / 405 => 0%
Yield to Maturity: 405 = 1000 + PVIF 405 => 9.45%
10 year Bond=> 10/1080 => 9.26%
Yield to Maturity: 1,080 = 100 × PVIFAr%,10 period + 1,000 × PVIFr%,10 period => 8.77%
15 year Bond=> 92.5 /980 => 9.44%
Yield to Maturity: 980 = 92.50 × PVIFAr%,15 period + 1,000 × PVIFr%,15 period=> 9.5%
Answer b
12 year Bond
Using Lotus 1-2-3, duration of this bond is => 8.07 years
Modified duration => 8.07 / ( 1+ 8.96%) => 7.40
Percent change in bond price => -1 × Modified duration × Change in interest rate
=> -1 * 7.40 * 0.75 => -5.55%
The price of the bond will rise by 5.55% if interest rate falls 0.75% and vice versa.
10 year zero bond
The duration of a zero coupon bond is the same as its maturity ie 10 years
Modified duration => 10 / ( 1+ 9.45%) => 9.14
Percent change in bond price => –1 × 9.14 × 0.75 = –6.85%
The price of the bond will fall by 6.85% if interest rate rise 0.75% and vice versa.
10 year bond
Using Lotus 1-2-3, duration of this bond is => 6.89 years
Modified duration => 6.89 / ( 1+ 8.77%) => 6.33
Percent change in bond price => -1 × 6.33 × 0.75 = –4.75
The price of the bond will rise by 4.76% if interest rate falls 0.75% and vice versa.
15 year Bond
Using Lotus 1-2-3, duration of this bond is => 8.62 years
Modified duration => 8.62 / ( 1+ 9.5%) => 7.87
Percent change in bond price => -1 × 7.87 × 0.75 = –5.90
The price of the bond will fall by 5.90% if interest rate rise 0.75% and vice versa.
Answer c
The duration of the current four bond portfolio
The weighted average duration of the portfolio is 8.34 years and Grace’s investment horizon is 7 years, therefore, the bond portfolio is not immunized because the weighted average of the portfolio is greater than the investment horizon.
Answer d
The bond with the highest duration is the zero-coupon bond ie 10 years & the bond with the lowest duration is the 10%, 10-year bond ie 6.89 years. To lengthen the portfolio’s duration, She can invest in higher duration bonds and shorten the duration by investing in lower duration bonds. By investing the entire sum of $200000 in the 10-year bond, Grace can achieve the shortest duration portfolio and similarly by investing the entire portfolio in the zero coupon bond will give her longest duration portfolio.
Answer e
Grace is planning to cash out of the bond portfolio in about 7 years and wants to immunize the portfolio. To do so, we must find a portfolio with a weighted average duration of 7 years. The easiest way to immunize her portfolio from interest rate risk is to invest all of the $200,000 in the 10-year, 10% bond, with its 6.89 year duration.
To achieve a fully immunized portfolio with a duration of exactly 7 years, we can consider the 12year, 7.50% bond with its 8.07 year duration and the 10-year, 10% bond with its 6.89 year duration. The following portfolio has a 7.01 year duration and is therefore immunized from interest rate risk:
Answer f
Immunization is not meant to be a passive strategy that she can “put away and forget about.” Immunization is a continued portfolio a rebalancing process that reflects changes in market interest rates.
Bond Particulars Amount Invested Weight Bond Duration Weighted Duration 1 12 years, 7.50% 50000 0.25 8.07 2.0175 2 10 years, zero 50000 0.25 10 2.50 3 10 years, 10% 50000 0.25 6.89 1.7225 4 15 years, 9.75% 50000 0.25 8.62 2.155 TOTAL 8.395 or 8.4 YearsRelated Questions
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