FIXED INCOME
FINAL EXAM APRIL 2005
40 POINTS TOTAL
Ok, let’s start with an easy problem to warm up !
1. Confirm, through calculations, that the price of a 2 year 6%corporate bond (semi annual payments) with a flat swap curve yielding 7% is priced at a discount. (2 point)
2. Consider the following portfolio of bonds :
BONDS MARKET VALUE DURATION CONVX
A $20 million 2 25
B $ 35 million 7 90
C $ 60 million 8 56
D $ 40 million 14 160
a. What is the portfolio’s duration and convexity? (1 points)
b. If interest rate for all maturities increase by 200 basis point, what is the new the value of the portfolio ( 2 point)
Now that you’ve warmed up a little and well digested your lunch , let’s speed up a bit ….
3. Suppose that a life insurance company issues a GIC that guarantees an interest rate of 7% annually (paid semi annually) for 3 years. A client needs a capital of $12 million in 3 years to celebrate his wedding and buy a home for his wife.
a. How much is needed from the client to reach his objective in 3 years (round the figure to the top fifth digit number. Ex: 15 465 876 becomes 15 466 000)
b. What type of investment must the bank do to guarantee that amount to its client in 3 years? Show calculation.
c. The bank’s immunized rate is 9%. Suppose the funds are invested in a par bond paying a 9% coupon maturing in 3 years with the characteristics found in b). What’s the life insurance company’s safety cushion if rates climb to 11% after 1 year? (5 points)
An easy one now…
Here’s the kind of question I’ve been dying to ask you…..Let’s really see who’s got it ?
5. From you fixed income background and previous derivative classes , explain (2 lines max.) how you could guarantee a client, at the same time, his initial invested capital
while making him benefit from any potential increase in a stock index. (2 points)
The toughest question on the final, I believe ……Good luck !
6. Use Handout1 for this question. A portfolio manager owns $4 million par value of Coke bond (symbol KO). The portfolio manager expects rates to climb 100BP in the near future and would like to swap the Coke bonds for other bonds shown in
handout1. (Round the numbers for this problem that is for example use 105.50 for the Coca Cola bond price 116.50 for the IBM and 101.70 for he Citigroup))
a. From the 2 other bond descriptions (Citigroup and IBM), for which bond would you recommend the portfolio manager to swap his Coke bonds? Explain clearly. (2 point)
b. How much in market value (or how many bonds) of the bonds you recommended should be purchased so that the initial portfolio duration is maintained? It is assumed the portfolio manager has enough funds for any purchase. You are suppose to calculate the modified duration of the Citigroup bond.(5 points)
That was a tough one I admit, so let’s take a break with this one !!
7. Suppose the present value of liabilities of some financial institution is $500 million and the economic surplus $700 million. The duration of the liabilities is 5 and that of the assets 20% higher.
a. What is the market value of the portfolio of bonds ? (1 point)
b. Suppose rates decrease by 50BP. What is the new economic surplus (deficit) ?
(2 point)
8. Consider the 5-year credit default swap (CDS) paid semi annually on a 300 million euro principal on Allianz using handout3. What would be the cash flow to the seller if a default occurs after 3 years and 3 months with a 40% recovery rate? (use the average between bid/ask prices) (2 points)
9. T/F (2 points)
a. Credit spread change more or less continuously whereas credit ratings changing discretely.
b. In an asset swap, the bond’s promised payments are swapped for Libor plus a spread
c. In a CDO structure, default losses on the bond portfolio would have to exceed 25% of the principal before investors in the low yield tranche are affected.
10.Use Handout 2 for this question. What is the probability of default of the IBM 5% 2014 yielding 5.676% assuming a 40% between years 5 and 6? Compare it to the other similar IBM bond on Handout2. What do you notice? Is your answer logic with your answer in question 4 above (Use the swap handout 1 as benchmark and chose
midswap price. (4 points)
11. Use handout 1 for this question. The six month Libor rate is at 3.38% and you own the Citigroup bond. How would an asset swap on this bond be structured? What is the asset swap that would be calculated in this situation ( 2 points)
12.Use handout 1 for this question. Suppose you enter into a 1-year total return swap on a principal of $10 million using the KO bond. Assume 6-month Libor to be at 4% and the spread on the swap 50BP. Assume the bond’s redemption value after six months is 98% of face value.
What are the total return’s investor’s receipts (payments) after 6 months (payments)?
(4 points)
13.What can an investor do if he wants to take advantage of GM bond yield without taking the credit risk for 5 years? At what point can your strategy be considered arbitraged? (2 points)
14.BONUS QUESTION : What is the 10 year yield as you’re writing it ? The closest answer will get a 1 point bonus.
I hope this final hasn’t been too hard for you! Let me tell you how much I enjoyed
working with you this semester! I hope you‘ve learned as much in fixed income as I have enjoyed discovering each one of your’ laughs, surprised faces and enthusiasm!
