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2. (25/33 points) An investor currently holds a portfolio comprised of one of each of the following three bonds each of which has a par value of $100: 1) a five-year, 1% coupon bond; 2) a five-year, zero-coupon bond; and 3) a three-year, 0.7% coupon-bond. Current zero-coupon rates are as follows (rates shown are annualized): 6 months 1 year 18 months 2 years 2.5 years 3 years 3.5 years 4 years 4.5 years 5 years 0.05% 0.1% 0.2% 0.3% 0.45% 0.60% 0.70% 0.80% 0.90% 1.0% a. What is the price, yield to maturity, and duration of each bond in the permitted portfolio? b. Assuming that the expectations approach to the term structure is correct, what is the expected value of this portfolio in four years' time? (Assume any interest or other cash flow received before four years have passed are reinvested at the expected rates). c. Find a new portfolio comprised of these same three bonds that costs the same as current portfolio but that has a portfolio duration of four. 3. (25/33 points) Assume that the 1-year zero-coupon rate is currently r = 0.35% and that it evolves over time according to the following process: r4+1 = r1 +0.15(2% r). Assume further that the current n-year zero coupon rate r satisfies the following relationship for n 22, nr = !=rt +0.07xDuration(n), where Duration (n) is the durations of an n-year zero coupon bond. That is, the current 2-year rate r satisfies the relation: 2r = r +r] +0.07Duration(2); the current 3-year rate r satisfies the relation: 3r3 = r) + r1 + r +0.07Duration(3); and so on. a. What is the price of a 4-year coupon bond with a coupon rate of 2% paid once at the end of the year and with a par value of $100? What is this bond's duration? b. What is the Treasury futures rate for a 2-year contract that starts in 2 years? c. An institutional investor currently holds five of the 4-year, 2% coupon bonds, each with a par vale of $100. . She wishes to sell off (borrow) a number of 2-year zero coupon bonds such that the Duration of her overall portfolio is zeroa process known as immunization. How many 2-year, zero coupon bonds must she sell to achieve her goal? 2. (25/33 points) An investor currently holds a portfolio comprised of one of each of the following three bonds each of which has a par value of $100: 1) a five-year, 1% coupon bond; 2) a five-year, zero-coupon bond; and 3) a three-year, 0.7% coupon-bond. Current zero-coupon rates are as follows (rates shown are annualized): 6 months 1 year 18 months 2 years 2.5 years 3 years 3.5 years 4 years 4.5 years 5 years 0.05% 0.1% 0.2% 0.3% 0.45% 0.60% 0.70% 0.80% 0.90% 1.0% a. What is the price, yield to maturity, and duration of each bond in the permitted portfolio? b. Assuming that the expectations approach to the term structure is correct, what is the expected value of this portfolio in four years' time? (Assume any interest or other cash flow received before four years have passed are reinvested at the expected rates). c. Find a new portfolio comprised of these same three bonds that costs the same as current portfolio but that has a portfolio duration of four. 3. (25/33 points) Assume that the 1-year zero-coupon rate is currently r = 0.35% and that it evolves over time according to the following process: r4+1 = r1 +0.15(2% r). Assume further that the current n-year zero coupon rate r satisfies the following relationship for n 22, nr = !=rt +0.07xDuration(n), where Duration (n) is the durations of an n-year zero coupon bond. That is, the current 2-year rate r satisfies the relation: 2r = r +r] +0.07Duration(2); the current 3-year rate r satisfies the relation: 3r3 = r) + r1 + r +0.07Duration(3); and so on. a. What is the price of a 4-year coupon bond with a coupon rate of 2% paid once at the end of the year and with a par value of $100? What is this bond's duration? b. What is the Treasury futures rate for a 2-year contract that starts in 2 years? c. An institutional investor currently holds five of the 4-year, 2% coupon bonds, each with a par vale of $100. . She wishes to sell off (borrow) a number of 2-year zero coupon bonds such that the Duration of her overall portfolio is zeroa process known as immunization. How many 2-year, zero coupon bonds must she sell to achieve her goal

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