﻿ Grace Hesketh is the owner of an extremely successful dressboutique in downtown Chicago. Although hi
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### Question

Grace Hesketh is the owner of an extremely successful dressboutique in downtown Chicago. Although high fashion is Grace’sfirst love, she’s also interested in investments, particularlybonds and other fixed income securities. She actively manages herown investments and over time has built up a substantial portfolioof securities. She’s well versed on the latest investmenttechniques and is not afraid to apply those procedures to her owninvestments. Grace has been playing with the idea of trying toimmunize a big chunk of her bond portfolio. She’d like to cash outthis part of her portfolio in seven years and use the proceeds tobuy a vacation home in her home state of Oregon. To do this, sheintends to use the \$ 200,000 she now has invested in the followingfour corporate bonds (she currently has \$ 50,000 invested in eachone). 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% bondpriced at \$ 1,080. 4. A 15 year, 9.25% bond priced at \$ 980. (Note:These are all noncallable, investment grade, nonconvertible /straight bonds.)

Questions

e. Using one or more of the four bonds described above, is itpossible to come up with a \$ 200,000 bond portfolio that willexhibit the duration characteristics Grace is looking for?Explain.

f. Using one or more of the four bonds, put together a \$ 200,000immunized portfolio for Grace. Because this portfolio will now beimmunized, will Grace be able to treat it as a buy and-holdportfolio one she can put away and forget about? Explain.

### Solution

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Duration xx xxxx x=x years

Duration xx Bond x (zxxx xxxxxx bond)=10 yxxxxxxxxxxxx of xxxx x=x.x yxxxxxxxxxxxx of xxxx 4=8.36 Yxxxxxxx xxxxxxxx xxxxxxxx =7 yxxxxxxx investment x xxxx x =w1, xxxx 2 xx xx &#xxxx;xxx bond x is xxxxxxxxxx xxxxxxxxxxx=xx*xxxxxxxxx+xx*xxxxxxxxx+xx*xxxxxxxxx+xx*xxxxxxxxxxxx+xxxx+x.xxx+x.xxxx=xxxxxx xxx be xxxxxxx combination xx xx,xx,xx,xxxxx xxxxxxx let xx,xx=xxxx+x.xxx=xxxx+x.x(x-xx)=xx.xxx=x.xxx=x.xxxxxxxx portfolio xx xx.xx% xx bond x and xx.xx xx xxxx 2 xxxx haveduration=7 yxxxxx*x.xxxx+x.x*x.xxxx=xx)xx xxx xxx has x interest xxxx xxxx xx sensitivity(duration) xxx years. xxx xxx xxx easily xxxxx the xxxxxxxx xxxx xxxx withconstant xxxxxxxx of x yxxxx