Please help me to solve this

QUESTION 1

12. Find the Macaulay duration and the modied duration of a 15-year, 7.5% corporate bond priced to yield 5.5%. According to the modied duration of this bond, how much of a price change would this bond incur if market yields rose to 5.5%? Using annual compounding, calculate the price of this bond in one year if rates do rise to 6.5%. How does this price change compare to that predicted by the modied duration? Explain the difference. The Macaulay duration is years. (Round to two decimal places.) The modied duration is years. (Round to two decimal places.) If market yields rose to 6.5%, the change would be %. (Round to two decimal places.) Using annual compounding, the price of this bond in 1 year if rates do rise to 5.5% is $ . (Round to the nearest cent.) The actual percentage change in bond price is ". (Round to two decimal places.) Which of the following is true? (Select the best choice below.) 0 A. Duration is not a good predictor of price volatility if interest rates undergo a big swing because of the convex relationship of a bond's price-yield relationship. 0 B. Duration is a good predictor of price volatility if rates change less than 2%. O C. Duration is a good predictor of price volality because of the convex relationship of a bond's price-yield relationship. 0 D. Duration is not a good predictor of price volatility it rates change more than a basis point. 14. Elliot Karlin is a 35-year-old bank executive who has just inherited a large sum of money. Having spent several years in the bank's investments department, he's well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, Elliot intends to use $1 million of his inheritance to purchase 4 U.S. Treasury bonds: 1.An 8.50%, 13year bond that's priced at $1,045.00 to yield 7.47%. 2. A 7.875%, 15-year bond that's priced at $1020.00 to yield 7.60%. 3. A 20-year stripped Treasury (zero ooupon) that's priced at $202.00 to yield 8.22%. 4. A 24-year, 7.50% bond that's priced at $955.00 to yield 7.90%. Note that these bonds are semiannual compounding bonds. 3. Find the duration and the modied duration of each bond. b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds. :2. Find the duration of the portfolio if Elliot puts $360,000 each into bonds 1 and 3 and $140,000 each into bonds 2 and 4. d. Which portfoliob or cshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as possible? Explain. From which portfolio does he stand to make more in annual interest income? Which porttolio would you recommend, and why? a. The duration and modied duration can be calculated using a spreadsheet, such as Excel. It gives the precise duration measure because it avoids the rounding-off errors, which are inevitable with manual calculations. Bond 1: 13 years, 8.50%, priced to yield 7.47%. The duration of this bond is years. (Round to two decimal places.) The modied duration of this bond is years. (Round to two decimal places.) Bond 2: 15 years, 7.875% priced to yield 7.60%. The duration of this bond is years. (Round to two decimal places.) The modied duration of this bond is years. (Round to two decimal places.) Bond 3:20 years, zero coupon, priced to yield 8.22%. The duration of this bond is years. (Round to two decimal places.) The modied duration of this bond is years. (Round to two decimal places.) Bond 4 :24 years, 7.50%, priced to yield 7.90%. The duration of this bond is years. (Round to two decimal places.) The modied duration of this bond is years. (Round to two decimal places.) b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds. The duration of this portfolio is years. (Round to two decimal places.) c. Find the duration of the portfolio if Elliot puts $360,000 each into bonds 1 and 3 and $140,000 each into bonds 2 and 4. The duration of this portfolio is years. (Round to two decimal places.) (I. Which portfoliothe portfolio in part b or the porfolio in part cshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as possible? (Choose the best answer below.) 0 A. o B. o c. o D. He should invest in either portfolio. The port'olio in part c has a higher duration than the portfolio part b. If rates are about to rise, then it is equally safe to invest in either portfolio, because both portfolios would be equally price volatile. He should invest in the por olio in part c. The portfolio in part b has a higher duration than the portfolio in part c. If rates are about to rise, then it is safer to invest in the portfolio in part 1:, because it would be less price volatile than the other portfolio. He should invest in the por olio in part b. The portfolio in part c has a higher duration than the portfolio in part b. If rates are about to rise, then it is safer to invest in the portfolio in part b, because it would be less price volatile than the other portfolio. He should invest in the portfolio in part c. The portfolio in part c has a higher duration than the portfolio in part b. If rates are about to rise, then it is riskier to invest in the portfolio in part b, because it would be more price volatile than the other portfolio