Suppose that you have a bond position worth $100 million. Your position has a modified duration...

Suppose that you have a bond position worth $100 million. Your position has a modified duration of 8 years and a convexity of 150. By how much does the value of the position change if interest rates increase by 25 basis points? Use the duration-convexity rule.

		a. ($1,953,125)
		b. ($1,906,250)
		c. ($2,046,875)
		d. ($2,187,500)

Solutions

Expert Solution

25 basis point = 0.25%

Percentage change in price = (-Modified duration * change in yield) + [0.5 * Convexity * (change in yield)^2]

Percentage change in price = (-8 * 0.0025) + [0.5 * 150 * (0.0025)^2]

Percentage change in price = -0.02 + [0.5 * 150 * 0.00001]

Percentage change in price = -0.02 + 0.00047

Percentage change in price = -0.02047 or -2.047%

Change in value of the position = 100,000,000 * -0.02047

Change in value of the position = (2,046,875)

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

You currently have a £100 million bond portfolio invested 30% in 5-year bonds with a modified...

You currently have a £100 million bond portfolio invested 30% in 5-year bonds with a modified duration of 4.05 years, 25% invested in 10-year bonds with a modified duration of 6.88 years and 45% in 20-year bonds with a modified duration of 10.09 years. The yield curve is currently flat at 8% across all maturities (5-year, 10-year and 20-year.) Calculate the modified duration for your entire bond portfolio. If the entire yield curve suddenly shifts down to yield 7.25%, what...

A manager is holding a $1.8 million bond portfolio with a modified duration of nine years....

A manager is holding a $1.8 million bond portfolio with a modified duration of nine years. She would like to hedge the risk of the portfolio by short-selling Treasury bonds. The modified duration of T-bonds is 10 years. How many dollars' worth of T-bonds should she sell to minimize the risk of her position? (Enter your answer in dollars not in millions.)

You have a portfolio with two bonds worth $100 each. Each bond has a 4% probability...

You have a portfolio with two bonds worth $100 each. Each bond has a 4% probability of defaulting. If the bond defaults it is worth $0. If it does not default it is worth $100. Defaults are independent of each other. What is the 95% VaR of each bond, and of the portfolio?

Compute the Macaulay duration and modified duration of a 6%, 25-year bond selling at a yield...

Compute the Macaulay duration and modified duration of a 6%, 25-year bond selling at a yield of 9%. Coupon frequency and compounding frequency are assumed to be semiannual.

An investor owns a bond with a modified duration of 0,5. At the moment YTM for...

An investor owns a bond with a modified duration of 0,5. At the moment YTM for that bond is equal to 3,28%. What will be the magnitude of bond price change if YTM for the bond changes to 3,58%. Explain how can you improve accuracy of estimation of a bond price change resulting from the change of market interest rates

You have two bonds (A and B) with a (modified) duration of 4.3. Bond A is a coupon bond with a semi-annual coupon of SEK 75 and Bond B is a zero coupon bond.

You have two bonds (A and B) with a (modified) duration of 4.3. Bond A is a coupon bond with a semi-annual coupon of SEK 75 and Bond B is a zero coupon bond.a) How much does the value of each bonds change if the interest rate changes by 0.1%-unit.b) What is the time to maturity for the zero coupon bond?c) Which bond has the longest time to maturity?d) Calculate the accrued interest of the coupon bond if you buy...

Suppose you are considering an investment in two bonds. Bond A has a duration of eight...

Suppose you are considering an investment in two bonds. Bond A has a duration of eight years and a market price of $950, and a bond B has a duration of four years and a market price of $1050. How should you invest $10 000 in these bonds if you have a desired holding period of seven years and wish to minimise interest rate risk?

4. You are managing a bond portfolio of $1 million. Your target duration is 10 years,...

4. You are managing a bond portfolio of $1 million. Your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a zero-coupon bond with maturity of 15 years, each currently yielding 5%. (1) What are your weights in these two zero-coupon bonds to have the target duration? (2) How will these factions change next year if the target duration is still ten years? .

Anderson bought a bond with a modified duration of 11.20. By approximately what percentage will the...

Anderson bought a bond with a modified duration of 11.20. By approximately what percentage will the bond price change assuming interest rates increase by 90 basis points? a. -11.20% b. -10.08% c. +10.08% d. +11.20%

Suppose that you are responsible for managing a $100 million bond portfolio at a large pension...

Suppose that you are responsible for managing a $100 million bond portfolio at a large pension fund. Because the pension fund has obligations to retirees in 2029, you want your portfolio to have a duration of 10 years. Suppose that you can only use 2-year and 12-year Zeros to immunize your portfolio. Assume that new 2-year Zeros and 12-year Zeros are issued only in 2019, 2021, etc. (i.e., odds years). Assume that interest rates are the same for all these...

Subjects