Grace Hesketh is the owner of an extremely successful dress boutique in downtown
ID: 2764209 • 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
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
e)
Bond 2 is zero coupon bond and its duration will be YTM
YTM=(1000/405)^(1/10)-1=9.46%
Duration of Bond 1=8 years
Duration of Bond 2 (zero coupon bond)=10 years
Duration of Bond 3=6.8 years
Duration of Bond 4=8.36 Years
The required duration =7 years
Let investment I bond 1 =w1, bond 2 is w2 …and bond 4 is w4
Duration of portfolio=w1*Duration1+w2*Duration2+w3*Duration3+w4*Duration4
8w1+10w2+6.8w3+8.36w4=7
There can be several combination of w1,w2,w3,w4
For example let w2,w4=0
8w1+6.8w3=7
8w1+6.8(1-w1)=7
1.2w1=0.2
W1=0.1666
Thus portfolio of 16.67% in bond 1 and 83.33 in bond 2 will have duration=7 years
8*0.1667+6.8*0.8333=7
f)
No she she has a interest rate risk of sensitivity(duration) of 7 years. Now she can easily hedge the interest rate risk with constant duration of 7 years
Bond 1 Bond 3 Bond 4 year Cash flow P.V@9.46% Weight=P.V/Total weight*time Cash flow P.V@9.46% Weight=P.V/Total weight*time Cash flow P.V@9.46% Weight=P.V/Total weight*time 1 75 68.5 0.079 0.079 100 91.4 0.088 0.088 92.5 84.5 0.086 0.086 2 75 62.6 0.073 0.145 100 83.5 0.081 0.161 92.5 77.2 0.078 0.157 3 75 57.2 0.066 0.199 100 76.2 0.074 0.221 92.5 70.5 0.072 0.215 4 75 52.2 0.061 0.242 100 69.7 0.067 0.269 92.5 64.4 0.066 0.262 5 75 47.7 0.055 0.277 100 63.6 0.062 0.308 92.5 58.9 0.060 0.299 6 75 43.6 0.051 0.303 100 58.1 0.056 0.337 92.5 53.8 0.055 0.328 7 75 39.8 0.046 0.323 100 53.1 0.051 0.360 92.5 49.1 0.050 0.350 8 75 36.4 0.042 0.337 100 48.5 0.047 0.375 92.5 44.9 0.046 0.365 9 75 33.2 0.039 0.347 100 44.3 0.043 0.386 92.5 41.0 0.042 0.375 10 75 30.4 0.035 0.352 1100 445.5 0.431 4.309 92.5 37.5 0.038 0.381 11 75 27.7 0.032 0.354 92.5 34.2 0.035 0.383 12 1075 363.4 0.421 5.053 92.5 31.3 0.032 0.381 13 92.5 28.6 0.029 0.378 14 92.5 26.1 0.027 0.371 15 1092.5 281.6 0.286 4.294 Total 862.8 8.0 1034.0 6.8 983.5 8.6Related Questions
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