FIXED INCOME
FINAL EXAM APRIL 2004
30 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) 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 ( 1 point)
Now that you’ve warmed up a little and well digested your lunch , let’s speed up a bit ….
3. (4 points)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 an 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?
An easy one now…
4. (1 points)Which convertible bond is cheaper and why?
Bond A
Bond B
CV = 20
CV= 50
Bond Price= 1100
Stock= $30
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 (and even the MsIF can answer !) , 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. A portfolio manager owns $5 million par value of Coke bond (symbol KO) shown in
handout 1. 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.
a. From the 2 other bond description (Citigroup and IBM), for which bond would you recommend the portfolio manager to swap his Coke bonds? Explain. (1 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.(4 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) ?
(1 point)
8. The theoretical value of a non callable bond is 100 and the theoretical value of a callable bond is 98. Determine the theoretical value of the call option? (1 point)
9. Consider the 5-year credit default swap (CDS) paid semi annually on a 300 million euro principal on Siemens using handout2. 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)
10.T/F (2 points)
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.
d. Total return swap are similar to repos.
11. What is the probability of default of Citigroup assuming a 40% recovery between year 3 and year 4 ? (Use the swap handout3 as benchmark and chose midswap price. (Don’t come ask me a question on “which” or “what” and think a bit !)(3 points) 12. Suppose that the Libor curve is flat at 4% and that 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)
13.Suppose you enter into a 1-year total return swap on a principal of $100 million using the KO bond. Assume 6-month Libor to be at 4%. Assume the bond’s redemption value after a year is 90% of face value.
What is the total return’s investor’s receipts (payments) ? (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 !
