Question

1. a) Plot the treasury zero-rate yield curve. Is it increasing or decreasing? Is this normal?

b) What is the market price of a treasury maturing in 5 months?

c) Of the bonds listed, which has a price closest to 98.00?

Extra Credit: Suppose a friend offers to give you a $1,000 bond that matures in 11 months in exchange for $990 two months from now. Always the wary consumer, you ask if they would be willing to pay you $990 in two months in exchange for the same bond today. After some consideration they agree to take either side of that trade.

Explain how you could use these offers to make arbitrage profits assuming that you can borrow or lend at the same rate as treasuries with no transaction costs.  

D WN Expiration (month: Zero-Coupon Yield (%) 0.662 0.874 3 0.934 1.044 1.077 1.112 1.161 1.203 1.252 1.277 1.289 1.294 1.334 24 1.39 36 1.52 60 1.817 120 2.152 240 2.492 600 10 o lcim stilu 18 nmn numit in

Answer 1

Yield % 50 100 150 200 250 300

a)Based on the details given, we can plot the treasury yield curve as above.

From the graph itself its showing an increasing trend in the yield from the treasury bond.

The longer the time frame on a Treasury, the higher the yield. Investors require a higher return for keeping their money tied up for a longer period of time. So the increasing trend is normal only.

b) Market price of a treasury maturing in 5 months with the yield of 1.077% will be less than Rs.99.55using YTM(This price reflects a yield to maturity ie 100)

Detailed calculation of price =100-(1.077 x 5/12)= Rs.99.55.

c)Of the bonds listed, Bond invested for 18 months with yield of 1.334%has a price closest to 98.00

Detailed calculation of price=100-(1.334 x 18/12) = Rs.98 (Approx)

Arbitrage with Changing Interest Rates

Although interest rates do not have a major effect on bond prices in the environment of near-zero rates, an increase in interest rates would cause call(buy) option prices to rise, and put(Sell) prices to decline. If these option premiums do not reflect the new interest rate, the fundamental put-call parity equation – which defines the relationship that must exist between call prices and put prices to avoid potential arbitrage – would be out of balance, presenting an arbitrage possibility.

Moreover, The price reflects a yield to maturity , yield as % annualized rather than given month wise and hence presents an arbitration possibility.