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Economics 172 Intermediate Finance Spring 2013

Problem Set 2: Bond Markets

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Question 1

The 5.75% coupon, 10-yr US Treasury bond is priced at 100.83.

(i) What is its yield?

(ii) Its DV01 (dollar duration) is 8.00. If its yield moves instantaneously to 5.69%, what will its price be (asestimated using DV01)?

(iii) What is its real new price?

(iv) What does this tell us about the accuracy of this 10yr bonds duration as a measure of price sensitivity tovery small changes in yield?

Question 2

You have been asked to assist a pension plan which has the following liabilities (i.e., payouts) to fund, at theend of the following 3 years:

Year Liability1 $3,000,0003 $5,000,0005 $4,000,000

The pension plan wants to buy three semi-annual US Treasury bonds to fund these liabilities:

Bond A: 1-year maturity, 6% coupon, currently yielding 2.2%Bond B: 3-year maturity, 4.0% coupon, currently yielding 3%Bond C: 5-year maturity, 4.25% coupon, currently yielding 3.6%

Assume that you can hold the coupon payments in a bank account which pays no interest.

Find the lowest cost portfolio consisting of these 3 bonds that will deliver the required payments. Theps2_bonds.xls spreadsheet contains a template for you to complete that will help solve this optimizationproblem. All of the yellow highlighted cells need to be completed.

Hint: You can solve the problem using Solver in Excel. If you dont have the Solver add-in on your computer,the public cluster computers should have it.

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Economics 172 Intermediate Finance Spring 2013

Problem Set 2: Bond Markets

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Question 3

You have just purchased $5 million par amount of the 5yr and 30yr US Treasury bonds shown below, at theprices shown. (Assume all bonds are semi-annual compounding.)

Par Amt Bond Bond Bond $Duration$mil lions Coupon Matur ity Yield Pr ice (= DV01)

5.00 5yr 6.00% 100.00 4.00

10yr 6.00% 99.00 7.50

5.00 30yr 6.00% 100.50 13.00

(i) Calculate the market values of the 5yr and 30yr bonds you purchased.

(ii) Calculate the DV01 risk for both of the bonds that you purchased. DV01 risk, for a given bond, is thedollar amount that you would make/lose if the bonds yield moved by 1% instantaneously.

(iii) What par amount do you need to buy or sell of the 10yr US Treasury bond, so that the DV01 risk of theentire portfolio is negligable? (Negligable in this context means less than $100 of DV01 risk over the entireportfolio.) You must calculate the par amount of the 10yr bond to the 3rd decimal place (i.e., to the nearestthousand dollars).

(iv) What are the coupons on the three bonds?

(v) Here are the convexity values for the 3 bonds:

5yr convexity =0.06; 10yr convexity =0.50; 30yr convexity =2.30.

Using Duration and Convexity, estimate the change in market value of the portfolio to the nearest $1000 if allinterest rates increase by 50bp.

(vi) What does the answer in part (v) tell you about using duration alone as a portfolio risk measure? Whendoes convexity work in your favor, in terms of improving on a risk estimate from duration alone? When doesconvexity work against you?