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Fix Income Answer

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Submitted By sean701
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1. Using Excel, I calculated the duration of each instrument in each portfolio. Then the averaging the durations of all the instruments in each portfolio with the assigned weights of 0.4, 0.25, 0.2, 0.1 and 0.05 gives us the durations of these two portfolios. The duration of portfolio A is 3.659 and the duration of portfolio B is 3.541. Since that the investor is kind of concerned about the volatility in the market, portfolio B is more adequate because it has a short duration, which means it’s less sensitive to the changes in interest rate. 2. A.
The durations of Portfolio A and B are 3.659 and 3.541. Multiplying their duration with their prices, which are both 100 millions, gives us the dollar duration of these two portfolios. The dollar durations are 365929587.04 and $354071810.21.
B.
The loss of the value of portfolio A cause by 1 basis point up in the interest rate is -$365929587.04 *0.0001=-$36592.96. The loss of the value of portfolio B cause by 1 basis point change in the interest rate is -$$354071810.21*0.0001=-$35407.18
C.
The conclusion reached in this part is consistent with that in exercise 1. With 1 basis point change in interest rate, the value of portfolio B decrease less that portfolio A, which means portfolio B is better immune to the risk of interest rate. 3. A.
The price of the 7-year bonds paying 2.5% semiannually is $81.12.
The price of the 7-year bonds paying 10% semiannually is $122.78.
The number of the 7-year bonds paying 2.5% semiannually the investor has to short is ($50 million-$100 million*0.25)/ $81.12=308185.
The number of the 7-year bonds paying 10% semiannually the investor has to short is ($50 million-$100 million*0.4)/$112.78=88668
B.
The new weights for the instruments in portfolio A are 0.8, -0.5, 0.4, 0.2 and 0.1.
The new weights for the instruments in portfolio B are -0.2, 0.5, 0.4, 0.2 and 0.1.
The

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