Professor Dastidar

Assignment #1

Question 1

Consider the following data. The column marked n gives the price today of one dollar delivered in half-year n, i.e., of a zero coupon bond which pays $1 in half-year n. In the next two columns there are the cash flows of two bonds, A and B. Essentially, bond A pays a 20% semi-annual coupon and bond B pays a 10% semi-annual coupon. Both bonds mature in 2.5 years, when each also pays its principal of 100. Assume semi-annual compounding.

Half

Year

1

2

3

4

5

n

Bond A Bond B

.95

.91

.87

.80

.70

10

10

10

10

110

5

5

5

5

105

A. Calculate the price of each bond assuming there are no arbitrage opportunities in the market. (That is, calculate the

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Portfolio Y consists of a 5.63 year zerocoupon with a face value of $5000. The current yield on all the bonds considered is 10% per annum, and compounding happens semi-annually. i What is the modified duration of the two portfolios?

ii Use modified duration to estimate the impact of a decrease in the yield from 10% to

9.5% on the percentage price change of the two portfolios.

Question 6: Bond price volatility

Access the data in the file E4721-Assign1-data.xls. The first and second worksheets in this file provide zero coupon bond yields for ten-year and six-month maturities observed at weekly frequency.

1. Compute percentage changes in yields and compute the annualized standard deviation of the yield changes (to do this, compute the standard deviation and multiply by sqrt(52)). 2. Compute zero coupon bond prices for both maturities. Be careful to get the compounding correct.

3. Compute percentage changes in bond prices and compute the annualized standard deviation of bond price changes (again, multiply by sqrt(52)).

4. Are 6-month or 10-year bond yields more volatile? Are 6-month or 10-year bond prices more volatile? How can you explain this?

Question 7: Bond Prices, Yield Risk and Duration

The goal is to show how the yield risk in bonds is a function of coupons and time to maturity.

Consider the following 4 US Treasury bonds (the par value is $100):

ii Use modified duration to estimate the impact of a decrease in the yield from 10% to

9.5% on the percentage price change of the two portfolios.

Question 6: Bond price volatility

Access the data in the file E4721-Assign1-data.xls. The first and second worksheets in this file provide zero coupon bond yields for ten-year and six-month maturities observed at weekly frequency.

1. Compute percentage changes in yields and compute the annualized standard deviation of the yield changes (to do this, compute the standard deviation and multiply by sqrt(52)). 2. Compute zero coupon bond prices for both maturities. Be careful to get the compounding correct.

3. Compute percentage changes in bond prices and compute the annualized standard deviation of bond price changes (again, multiply by sqrt(52)).

4. Are 6-month or 10-year bond yields more volatile? Are 6-month or 10-year bond prices more volatile? How can you explain this?

Question 7: Bond Prices, Yield Risk and Duration

The goal is to show how the yield risk in bonds is a function of coupons and time to maturity.

Consider the following 4 US Treasury bonds (the par value is $100):