Question 1

Consider a bond with 2 years to maturity, Face (Par) Value = $1,000, 10% annual coupon rate,  semi-annual coupon payments and YTM = 3% per 6 months. The bond price now is $1,074.32.

a)         Suppose that 6 months later, right after the coupon payment, the YTM of the bond still is 3% per 6 months. What is the market price of the bond? What is the HPR of buying the bond today   and selling it then?

b)  Suppose that 6 months later, right after the coupon payment, the YTM has gone down to  2.7% per 6 months. What is the market price of the bond? What is the HPR of buying the bond today and selling it then? Express this HPR as an APR rate with semi-annual compounding and as an EAR.

Question 2

According to Standard & Poor’s, the probability that a bond issued with an “A” rating will default DYRING ANY GIVEN PAYMENT PERIOD is 2.3% i.e. the probability that a bond issued with an “A” rating will never default is (1 - 2.3%). Suppose that the average maturity of the bonds (when issued) is 7 years, and that default can only happen once per semester, at the time of coupon payments. Furthermore, assume that the default probability is constant throughout the bond’s life.  What is the default probability PER SEMESTER consistent with these numbers and assumptions?

Question 3

Consider a corporate bond rated “A”, with 7 years to maturity, face value $1,000, annual coupon rate of 5.5%, and semi-annual coupon payments. The default probability is constant over the bond’s life, and equal to 0.166% per semester. When the corporation defaults, bondholders receive $400 at  the time of default. The fair interest rate to discount the bond’s cash flows is 3% per semester.

a)  What is the fair price of the corporate bond?

b)  What is the fair yield-to-maturity of the corporate bond?

c)   What is the expected fair price one semester in the future? And what is the expected coupon payment one semester in the future?

d)  What is the expected holding period for buying the bond for its fair price today and selling it for its expected fair price one semester ahead?

Question 7

You observe the following information about bonds A and B, both of which make semiannual   coupon payments (with payments occurring at the end of each semiannual period). The YTM is stated as an APR. When solving for the YTM, please state your final answer as an APR. When  computing coupon payments and par value, you can round your answer to the nearest cent.

Please fill in the missing information in the table below.

Question 8

Assume that there are only 5 Treasury Bonds traded in the bond market. These bonds are zero- coupon bonds and have face value of $100. The bond prices and maturities for these bonds on  November 7, 2023 at 10:30am were:

On 11:00pm of the same day, the bond prices were:

Find the yields-to-maturity for all the above bonds. In two separate graphs, draw the two yield curves for November 7, 2023. What was the state of the economy in the morning and what was the state of the economy the same night? What were the changes in the demand of these bonds thatpossibly lead to these price changes?

Note: Another name for the yield-curve is the term structure of interest rates.