5. To create a portfolio with a duration of 4 years, using a 5-year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest % of the portfolio value in the zero-coupon bond. (Hint: First find duration of the coupon bond and use the fact that the duration of a bond portfolio is equal to the sum of duration of each bond x each bond's portfolio weight) A) 50 B) 55 C) 60 D) 65

5. To create a portfolio with a duration of 4 years, using a 5-year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest % of the portfolio value in the zero-coupon bond. (Hint: First find duration of the coupon bond and use the fact that the duration of a bond portfolio is equal to the sum of duration of each bond x each bond's portfolio weight) A) 50 B) 55 C) 60 D) 65

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Consider an investment portfolio consisting of two zero-coupon bonds: . a 4-year zero-coupon bond with maturity value 4,000 and a yield of 4% • a 7-year zero-coupon bond with maturity value 7,000 and a yield of 7% What is the modified duration of this 2-bond portfolio? (All of the interest rates in this problem are annual effective rates.) A) 5.31 B) 5.36 C) 5.46 D) 5.56 E) 5.91
To create a portfolio with a duration of 4 years using a 5 year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest % of the portfolio value in the zero-coupon bond. (Remember, we calculated the duration of the 3 year bond in class) 19.
Consider a coupon bond with an 8% annual coupon rate, a 10% interest rate, and a$1000 face value. The bond will mature in 4 years. What is the duration of this bond? Duration isdefined as a weighted average of the maturities of the cash payments. Suppose the weightassigned to the maturity of 1 year is W. Show your work A: Duration=2.28 and W=7.77%B: Duration=3.56 and W=20.5%C. Duration=3.56 and W=23.1%D. Duration=3.56 and W=7.77%
Portfolio A consists of a 6-year zero-coupon bond with a face value of $6,000 and a 11-year zero-coupon bond with a face value of $4,000. The current yield on all bonds is 4.75% per annum. (Answer with two decimal digits accuracy) The duration of portfolio A is Your Answer: Answer
Consider that you have in your portfolio a 3-year 3% coupon bond with face value of $100. The coupons of this bond are paid semi-annually. We assume that the current yield to maturity on the bond is 4% per annum with continuous compounding. a. Could you please first describe the two concepts of bond duration and convexity? Then, please compute the duration and the convexity of the bond described above? b. You expect a steepening of the interest rates yield curve very soon, either through a bull steepening or a bear steepening. Could you please first define these two market phenomena and then propose strategies taking advantage of such market environments given your existing portfolio?
Suppose you purchase a $1000 Face-Value Zero-Coupon Bond with maturity 30 years and yield to maturity 4% quoted with annual compounding. Show the bond cash flows on a time line and compute the current price of the bond Draw a graph to illustrate how the price of this bond will change as it gets closer to maturity – Price (on y axis) vs Time (on x axis). Why is a zero-coupon bond more sensitive to interest rate changes than similar coupon bearing bonds (2 or 3 sentences)?
2. Consider a bond with a 7.5% annual coupon rate and a face value of $1,000. Calculate the bond price and duration & show your work. Years to Maturity Interest rate Bond Price Duration 4 6. 6. 9. What relationship do you observe between yield to maturity and the current market value? What is the relationship between YTM and duration?
The duration of a portfolio is equal to the value-weighted average of the durations of the bonds in the portfolio. If you have the following portfolio of bonds and its mod duration is 5.6 years. Mod Duration 3.3 X=? Bond A B Value in $$ 220,000 440,000 then the mod duration of Bond B is Hint. Compute the weight of each bond in the total first. years.
2.Consider a portfolio of 3 bond A and 2 Annuity B, the yield rate is i=5% for A and B. Bond A: F= C = $1000, 4-year with annual coupon at 4%, Annuity B: A one-year deferred annuity-immediate with 3 level payments 50. (1) What is the PV of this portfolio? (2) Find the Macaulay Duration D, and Dg (3) Find the Modified Duration MD and MDg (4) Find the Modified Duration for the portfolio. (5) Use modified approximation to estimate the change in PV when both bond yield rate rise by 0.2%
Suppose you are reviewing a sheet for a bond portfolio and see the following information. These bonds have a par value of 100 and make semiannual coupon payments. Bond Annual coupon rate Number of years Annual yield to maturity A B с 6% 8% 10% 2 3 5 5% 10% 8% What is the bond portfolio's yield to maturity based on the IRR calculation?
9. An investor purchases 5 zero-coupon bonds, with terms of 1, 2, 3, 4, and 5 years. Each bond has a maturity value of 1,000, and is priced based on the following yield curve: Term (yrs.) Spot rate 2.4% 1 3.0% 3.4% 4 3.7% 5 3.9% What is the modified duration of the investor's portfolio? 2 3
An investor with an investment horizon of 6 years buys a bond with a modified duration of 6.0. if the yield-to-maturity (YTM) is 0.0214, this investment will have a negative duration gap. Select one: True False

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