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ACTSC 445/845 - Assignment 1

Due on October 10th, 2013 by the end of class

Feel free to use Excel or any other software to complete the following questions.

1. A Canadian T-bill with face value $1000 on March 3, 2014 and expiring on September 12,

2014 (193 days until maturity) is quoted at 2.3%. On the other hand, a U.S. T-Bill with

the same expiration date and face value is currently quoted at 3%.

(a) Does an arbitrage opportunity exist? If so, explain in detail how you would construct

your portfolio so that you earn an arbitrage profit.

(b) If the U.S. T-bill was quoted at a rate of r, for what value(s) of r (if any) would an

arbitrage opportunity not exist?

2. (For this question, all computations must be correct to at least 8 decimal places.) Assume

a non-flat spot rate curve. You are given the following information on four zero coupon

bonds:

Bond Time to Maturity (in years) Price

1 1 $95.238

2 2 $89.845

3 3 $83.962

4 4 $77.732

Assume that each bond has face value F = 100.

(a) Compute the annual effective spot rates s1, s2, s3 and s4.

In what follows, assume that you have constructed a portfolio consisting

of one unit of each of the above bonds.

(b) If the price of bond 1 changed instantaneously to $95.138 but the other bond prices

remained the same, what is the exact percentage change in the price of your portfolio?

(c) If instead the each of the bond prices decreased instantaneously by $0.10, what is the

exact percentage change in the price of your portfolio?

(d) For each of the two previous parts, using a suitable duration measure, calculate the

approximate percentage change in the price of your portfolio.

(e) Disregard the previous 3 parts. Assume now that all spot rates instantaneously

increase by 10bp. Use the Fisher-Weil duration and convexity to approximate the

percentage change in value of the portfolio.

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ACTSC 445/845 - Assignment 1

Due on October 10th, 2013 by the end of class

Feel free to use Excel or any other software to complete the following questions.

1. A Canadian T-bill with face value $1000 on March 3, 2014 and expiring on September 12,

2014 (193 days until maturity) is quoted at 2.3%. On the other hand, a U.S. T-Bill with

the same expiration date and face value is currently quoted at 3%.

(a) Does an arbitrage opportunity exist? If so, explain in detail how you would construct

your portfolio so that you earn an arbitrage profit.

(b) If the U.S. T-bill was quoted at a rate of r, for what value(s) of r (if any) would an

arbitrage opportunity not exist?

2. (For this question, all computations must be correct to at least 8 decimal places.) Assume

a non-flat spot rate curve. You are given the following information on four zero coupon

bonds:

Bond Time to Maturity (in years) Price

1 1 $95.238

2 2 $89.845

3 3 $83.962

4 4 $77.732

Assume that each bond has face value F = 100.

(a) Compute the annual effective spot rates s1, s2, s3 and s4.

In what follows, assume that you have constructed a portfolio consisting

of one unit of each of the above bonds.

(b) If the price of bond 1 changed instantaneously to $95.138 but the other bond prices

remained the same, what is the exact percentage change in the price of your portfolio?

(c) If instead the each of the bond prices decreased instantaneously by $0.10, what is the

exact percentage change in the price of your portfolio?

(d) For each of the two previous parts, using a suitable duration measure, calculate the

approximate percentage change in the price of your portfolio.

(e) Disregard the previous 3 parts. Assume now that all spot rates instantaneously

increase by 10bp. Use the Fisher-Weil duration and convexity to approximate the

percentage change in value of the portfolio.

1