Part 1: Zero Curves and Mispricing

Suppose that you observe the following four bonds trading in the market.

Bond Coupon Time-to-maturity Price

A 0% 0.5 99.01

B 0% 1 97.07

C 0% 1.5 94.23

D 6% 1.5 102.30

Coupons are paid semi-annually. All four bonds have a $100 face value.

1. Calculate zero-coupon yields for maturities of 0.5, 1, and 1.5 years using bonds A, B,

and C.

2. Using the yields from (1), calculate the price of bond D if its price were consistent with

bonds A, B, and C. Is bond D underpriced or overpriced?

3. Replicate bond D's cash flows using a portfolio of bonds A, B, and C.

4. Using your results in (3), construct a long-short portfolio that takes advantage of this

mispricing.

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Part 2: Zero Curves and Mispricing Redux

Suppose that you observe the following four bonds trading in the market.

Bond Coupon Time-to-maturity Price

A 5% 0.5 101.99

B 3% 1 101.49

C 4% 1.5 102.96

D 6% 2 108.99

Coupons are paid semi-annually.

1. Calculate zero-coupon yields for maturities of 0.5, 1, 1.5, and 2-years.

2. Calculate the discount factors that the zero-coupon yields imply. Do you see any

potential problems? Why?

3. Suppose that you have a technology that allows you to store money for free (a "mat-

tress") between years 1.5 and 2. That is, if you put $x under your mattress at t = 1.5,

you will still have $x at t = 2. Construct a long-short trading strategy using the four

bonds that earns you free money today.

Hint: Identify which bond you view as overpriced and start by shorting that bond. Then,

use the other bonds to replicate its cash flows.

In particular, 1 unit of the "mattress" technology has the following cash flows:

Units t = 0 t = 0.5 t = 1 t = 1.5 t = 1

Mattress Technology 1 0 0 0 -1 + 1

Part 3: Duration & Convexity Calculations

Suppose that a bond has the following terms:

10-years-to-maturity

$1000 face value

Semi-annual coupons, with an annual coupon rate of 5%

Suppose that all discount rates are 7%.

1. Calculate the price of the bond.

2. Calculate the bond's modified duration.

3. Calculate the bond's convexity.

4. If discount rates increase to 10%, what is the new price of the bond. Do (i) the actual

calculation and (ii) approximate the new bond price using the duration and convexity.

How well does the duration and convexity approximation work?