Consider the following six treasury bonds (two of which are T-Bills), all with notional amounts of $100.00, that are trading in a liquid market on April

28th 2022,

i.

T-bill I: 1-year maturity, no annual coupon, market price = $97.6345

ii.

T-bill II: 3-year maturity, no annual coupon, market price = $92.6365

iii.

T-bond I: 2-year maturity, 2.25% annual coupon, market price = $99.5029

iv.

T-bond II: 4-year maturity, 2.75% annual coupon, market price = $100.5500

v.

T-bond III: 5-year maturity, 1.00% annual coupon, market price = $92.5024

vi.

T-bond IV: 6-year maturity, 3.00% annual coupon, market price = $101.9794

Assume that all coupon and maturity dates align with all cashflows (coupons and notional amounts), paying on April 28^th of each year.

1)

How would you characterize the market that these bonds are trading in? What does this

imply with respect to pricing a new bond that is just introduced into the market, with

cashflow dates that align with the existing bonds?

2)

Given this market, what are the discount factors and implied zero-coupon rates associated

with annual terms 1 6 years? (Show all your work)

3)

What would be the price of a new bond introduced into the market with a $100 notional,

6-year maturity and an annual coupon rate of 2.50%?

4)

Suppose another T-bill exists in the market with a $100 notional (no coupon), a maturity

date of 8 years and a market price of $80.6470.

a.

What would be the discount factor and zero rate associated with year 8?

b.

What would be the discount factor and zero rate associated with year 7?

5)

Given the addition of the T-bill in Question A.4, what would be the price of another new

bond introduced into the market with a $100 notional, 10-year maturity and an annual

coupon rate of 3.50%?