Question

There are two bonds in a portfolio. One is a 5-year zero-coupon bond with a face...

There are two bonds in a portfolio. One is a 5-year zero-coupon bond with a face value of $5,000, the other is a 10-year zero-coupon bond with a face value of $10,000. The Macaulay Duration of the portfolio is 7.89, the Modified Duration of the portfolio is 7.3015. If the price of the 10-year bond is $3,999, what is the answer that is closest to the yield to maturity of the 5-year bond

Homework Answers

Answer #1

The Duration of a zero-coupon bond is equal to its maturity.

Duration of 10 year zero-coupon bond = 10 years

Duration of 5year zero-coupon bond = 5years

w(10), w(5) are the weights of 10 year and 5 year bonds in the portfolio

w(10) + w(5) =1

Portfolio duration is the weighted average of the individual duration of bonds

10*w(10) + 5*w(5) = 7.89

10*w(10) + 5*(1-w(10)) = 7.89

w(10) = 2.89/5 = 0.578

w(5) = 1- 0.578 = 0.422

Weights are based on the market price of the bonds

w(10) = 3999/(3999+x)

0.578 = 3999/(3999+x)

where x is the price of the 5-year zero coupon bond

We get, x = 2919.68

Hence, for a 5-year zero coupon bond

Current price = 2919.68

Yield =

Yield of 5-year bond = (5000/2919.68)^(1/5) -1

Yield to maturity of 5-year bond = 0.11359 = 11.359%

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The yield-to-maturity (YTM) on one-year bond with zero coupon and face value $ 1000 is 5...
The yield-to-maturity (YTM) on one-year bond with zero coupon and face value $ 1000 is 5 %. The YTM on two-year bond with 5 % coupon paid annually and face value $ 1000 is 6 %. (i) What are the current prices of these bonds? (ii) Find Macaulay durations of these bonds. Consider a third bond which is a zero coupon two-year bond with face value $ 1000. (iii) What must be the price of the third bond so that...
10. Assume you have a portfolio comprising 5 zero-coupon bonds that have 2 years to maturity...
10. Assume you have a portfolio comprising 5 zero-coupon bonds that have 2 years to maturity and 6 zero-coupon bond with a maturity of 20 years. Assuming semi-annual compounding and that all bonds have a face value of 100 and that the yield curve is flat at 5% pa, what is the modified duration of this portfolio? Group of answer choices None of the answers provided are correct 7.752 13.711 10.732 7.609
The price of one-year bond (A) with zero coupon and face value $ 1000 is $...
The price of one-year bond (A) with zero coupon and face value $ 1000 is $ 961.5. The price of two-year bond (B) with zero coupon and face value $ 1000 is $ 907. Consider a third bond (C), a two-year bond with $ 100 coupon paid annually and face value of $ 1000. (i) What must be the price of bond C so that the Law of One Price holds. Explain where you use LOOP. (ii) Suppose that the...
A bond portfolio is made up of $14 million in zero-coupon bonds maturing in 2 years,...
A bond portfolio is made up of $14 million in zero-coupon bonds maturing in 2 years, and $9 million in zero-coupon bonds maturing in 24 years. The yield curve is flat at 8%. What is the Macaulay duration of this bond portfolio? Please enter your answer in years rounded to two decimal places.
Betty and Bob a 2-year coupon bond with a face and maturity value of $1,000 and...
Betty and Bob a 2-year coupon bond with a face and maturity value of $1,000 and a coupon rate of 8% per annum payable semiannually and a yield to maturity of 10% per annum compounded semiannually. A. Algebraically find the price of the bond. Your final answer should be correct to 2 places after the decimal point. The price of the portfolio is __________________. B. Algebraically find the exact Macaulay Duration of the portfolio. Your final answer should be correct...
Suppose you own following bond portfolio Face Value Bond Type Maturity yield to maturity Portfolio I...
Suppose you own following bond portfolio Face Value Bond Type Maturity yield to maturity Portfolio I $88 million Zero Coupon 5 years 4% You expect interest rate to rise in near future(hence decrease the value of bond portfolio). You decided to sell some of 5-year bond and use that proceed to buy 1.5-year zero coupon bonds with yield to maturity 3%. If you want new duration of the portfolio to be 3 years (that mean after selling 5-year bond and...
Sun Bank has six-year zero coupon bonds with a total face value of $20 million. The...
Sun Bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds us 10%. A) what is the modified duration of these bonds? B) what is the price volatility if the max potential adverse move in yields is estimated at 20 basis points? C) what is the daily earnings at risk of this bond portfolio? d) what is the 10-day VAR assuming the daily returns are independently distributed?
What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face...
What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9,350 when released?
What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face...
What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9400 when released?
A two-year corporate bond has a coupon rate of 4 percent. The one-year spot rate is...
A two-year corporate bond has a coupon rate of 4 percent. The one-year spot rate is 3 percent and the forward rate is 5 percent. The bond’s credit spread is 1 percent for both the one-year and the two-year maturities a. What is the price of the bond expressed as a percentage of its face value? b. What is the bond’s yield to maturity? c. What is the bond price calculated with the bond’s yield to maturity? d. Calculate the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​...
    asked 2 minutes ago
  • A cameraman on a pickup truck is traveling westward at 19 km/h while he videotapes a...
    asked 4 minutes ago
  • Records over the past year show that 1 out of 380 loans made by Mammon Bank...
    asked 7 minutes ago
  • Homework 7 The following are well-known car brands: Hyundai, Ferrari. Maserati, Mitsubishi, Subaru, Chrysler, Nissan, Jaguar,...
    asked 14 minutes ago
  • The appraised values of three recently sold houses in the Columbus area are (in thousands of...
    asked 16 minutes ago
  • A professor would like to conduct a regression analysis to determine whether a student’s final exam...
    asked 17 minutes ago
  • What are the semantic differences between a for loop and a while loop? Can you convert...
    asked 19 minutes ago
  • Confidence Interval for μ: You poll 25 students and record each student’s height. You find that...
    asked 22 minutes ago
  • A very long, straight solenoid with a cross-sectional area of 1.91 cm2cm2 is wound with 93.2...
    asked 22 minutes ago
  • Towards the end of the chapter (The Culture Code by Daniel Coyle), Coyle addresses “Collective Intelligence”...
    asked 30 minutes ago
  • Illustrate the use of (a) capacitive and (b) inductive sensors in a circuit where they are...
    asked 37 minutes ago
  • Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation...
    asked 38 minutes ago