Question

Fixed Income HW due 6/29/19

Assume today is June 19, 2019 and that all bonds pay interest annually with a face value of $1,000. YTM = Current yield + Capital Gains yield; CY = Annual Interest/Current Price

GE is A rated; AA Treasuries yield 3-year is 1.90%, 10-year 2.10%

5 Years ago GE issued 6% coupon paying bonds with a face value set to mature on June 19, 2029. Growth concerns have forced monetary authorities throughout the world to lower interest rates during the past several years and as such, the price of these GE bonds has risen to 1175.00

1. What is yield to maturity for an investor who buys the bonds today at the current price?
2. Is the bond trading at a premium, discount or at par? Explain what your answer means
3. What is the capital gains yield of this bond and interpret what the sign of the CGY means?
4. What would happen to the price of the bond you calculated in 1 if GE became the subject of a liability issue where it hypothetically gets sued for $50 billion?
5. Ignoring the scenario in question 4 and focusing on the information given, do you think GE would call the bonds if they could? WHY? Suppose that the bonds were callable in 3 years at 1050. Calculate the yield to call. Which rate here is more relevant, the YTM or the YTC?
6. List two factors that would increase the riskiness of a bond as it relates to a change in interest rates.
7. Calculate your annualized return if you assume that you buy the bonds today and they are not called, and you reinvest the interest in years 1-5 at 3% and in year 6-10 at 5%.

Explain why your answer differs from the YTM that you calculated in question 1.

8. Calculate the Macaulay Duration and Modified Duration for these bonds based on today’s price. Given your calculations estimate what would happen to the price of the bonds if interest rates were to rise 1% from current (today’s levels). Assume the change is immediate and dissect the change in price due to duration and compare it to the actual calculated change in price.

Answer 1

SOLUTION:-

Bond is trading at

a premium if the current market price of the bond is higher than its face value

a discount if the current market price of the bond is lower than its face value

par if the current market price of the bond is equal to its face value

In our case, the bond price is 1175 which higher than the face value of 1000. So, the bond is trading at a premium.

In the case of price appreciation, the CGY is positive. But, in this case as the bond is trading above its face value, there would be a capital loss at maturity equivalent to 1175-1000. So, the CGY is negative at this point.