Question

The US government typically uses the Dutch Auction method to raise long-term debt.

(a) How does the Dutch Auction method help the government to raise money at the best possible rates?

(b) This government debt is normally considered benchmark debt. What does this mean and why are the rates on government debt considered so appropriate as a benchmark?

(c) You have observed the following three bonds in the market:

· 2% coupon bond with exactly 2 years to maturity trading at a YTM (Yield to maturity) of 2.12%

· 2.50% coupon bond with exactly 3 years to maturity trading at a YTM (Yield to maturity) of 2.71%

· 3.75% coupon bond with exactly 5 years to maturity trading at a YTM (Yield to maturity) of 3.19% Calculate the clean prices of each of these bonds.

(d) What is the difference between the clean and the dirty prices of these bonds?

(e) If these are benchmark securities, we can use their yields to represent the yield curve. How would you describe the shape of the curve?

Answer 1

Part (a):

In Dutch auction, the bidders can bid for the amount they intend to invest at the minimum rate of yield they need. The lowest rate bid is accepted for the amount bid first, progressively increasing till the aggregate sum of bids reach the amount intended by Government. The rate applicable to all bidders selected will be the highest one of the selected bids. This method ensures adequate participation with flexibility of yield rates according to the requirement of bidders while the actual interest cost will be the lower than the rejected bids.

Part (b):

Benchmark rate indicates the rate based on which interest rates on other debt instruments are determined, with suitable markup (margin).

Rates on Government debt is considered benchmark because it is risk-free. Margins on other instruments represents risk premium which will be added to the benchmark rate in order to ascertain the nominal interest rate.

Part (c):

Clean prices of the given bonds are as follows:

2- year bond : 99.77%

3- year bond: 99.40%

5- year bond: 102.55%

Part (d):

Clean price is the sum of present value of future cash flows (periodical interest and redemption value) discounted at YTM, calculated as on the date of immediate previous coupon date.

Dirty price is the settlement price after deducting accrued interest from the clean price. Accrued interest is the interest for the period elapsed after last coupon payment.

Part (e):

Interest rates are lower for short term, progressively increase with increase in term. Hence the yield curve will be normal, slopping upward.