# What would be a fair price for a bond, maturing on 25 March 2023, paying a 5% per annum coupon rate, with a semi-annual coupon?

1. It is 25 July 2022; you observe two treasury bills

(a) What are the appropriate discount factors for 2 months and 8 months?

(b) What are the spot rates, with semi-annual compounding, for 2 months and 8 months?

(c) What would be a fair price for a bond, maturing on 25 March 2023, paying a 5% per annum coupon rate, with a semi-annual coupon?

(d) Now suppose that you observed a bond, maturing on 25 September 2023, paying a 1% per annum coupon rate (with semi-annual coupons), trading at a yield to maturity of 2.75%. Use the DMO formula to calculate the bond’s price.

(e) What is an appropriate discount factor for 25 September 2023?

(f) Calculate forward rates (with semi-annual compounding) from 25 September 2022 to 25 March 2023, and from 25 March 2023 to 25 September 2023.

2. Over the last nine years, you have earned the following returns on the NZX

(a) For each tax year, calculate the inflation rate.

(b) Now calculate a real rate of return for the NZX50 (use the full formula, not the approximation) for each year.

(c) What is the mean nominal return for the NZX50? What is the mean real return?

(d) What is the nominal volatility for the NZX50? What is the real volatility of the NZX50?

(e) Suppose New Zealand had a 33% tax levied on capital gains and all dividends. Repeat your analysis, calculating after-tax mean real and nominal returns, along with real and nominal after-tax volatilities.

3. Third Avenue Railroad Company First Gold 5s were bonds (issued by the Third Avenue Railroad Company) that matured on 1 July 1937. They paid coupons on 1 July and 1 January. We observe the following prices

The bond had accrued interest calculated using US 30/360 (it was a corporate bond in the U.S.).

(a) Use the YIELD command in excel to calculate the bond’s yield to maturity on each of the dates.

(b) How is the bond’s yield to maturity related to its credit rating?

(c) What is happening on 30 June 1937?

(d) Calculate the dirty price (including accrued interest) on

i. 31 May 1927,
ii. 31 July 1931,
iii. 30 June 1937.
Hint: you may find the ACCRINT command in excel useful here.

(e) What was the holding period return for an investor who held the bond from

i. 31 May 1927 to 31 July 1931?
ii. 31 July 1931 to 30 June 1937?

(f) What was the effective annual return for

i. 31 May 1927 to 31 July 1931?
ii. 31 July 1931 to 30 June 1937?

4. (a) Treasury bond markets in New Zealand and the U.S. are dealer markets. What are the pros and cons of this market structure as compared to trading securities on an exchange?

(b) The Reserve Bank of New Zealand reports the following (annually compounded) treasury bond spot rates (as of 26 July 2022).

Can we conclude that the market is expecting short-term interest rates to rise over the next 10 years? Discuss.

(c) You are in the United States. The date is 26 July 2022. You decide that the market has underestimated the yield on long-term Treasury bonds. You observe the following bond:

Describe how you would use this bond to trade in order to profit from your beliefs.