UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
College of Business – Department of Finance
FINANCE 432: Managing Financial Risk for Insurers
Professor Stephen D’Arcy
Homework #6 (10 points)
Lectures 16-19
Due April 9, 2008
(2 points)
1. Create a binomial tree from the following information:
The one-year spot rate is 4.5%
Two-year 5% annual coupon non-callable bonds are selling at par
Three-year 5.5% annual coupon non-callable bonds are selling at par
The one-year interest rate volatility is 25%
Show all interest rates to the nearest basis point.
(2 points)
2. Refer to the CMO spreadsheet included with this assignment. Assume that the current yield curve is flat at 8%. Also assume that the prepayment rate increases to 4% when interest rates decline to 7% and decreases to 1% when interest rates rise to 9%. Determine the effective duration and effective convexity of Tranche A and Tranche B.
(2 points)
3. Change the CMO spreadsheet by adding an “accrual” tranche (known as the ‘Z’ tranche). In a CMO, there is frequently an accrual tranche that receives no interest or principal until all previous tranches have been paid off. Then all interest and principal payments are made to the accrual tranche. (This tranche is called the ‘Z’ tranche since it is paid after A, B, and all other tranches.)
Based on the CMO example in the spreadsheet from question 2, adjust the spreadsheet to include a third tranche—an accrual tranche. Change the principal amount of the tranches as follows:
Tranche A: $400,000
Tranche B: $400,000
Tranche Z: $200,000
As in question 2, assume that the current yield curve is flat at 8%. Compute the effective duration and effective convexity of the accrual tranche using a 1% up and down shift in the initial yield curve. Assume the prepayments vary just as they did in problem 2.
(2 points)
4. Use the CDO spreadsheet that is attached to this assignment. Make the following changes to the starting values.
Floating note spread 3.00%
Management fees and expenses 0.75%
Default rates
years 1-5 4.00%
years 6-10 3.00%
Principal Amount Spread
Class A $225,000,000 1.00%
Class B 50,000,000 2.50%
Class C 15,000,000 4.50%
Equity 10,000,000
Run the waterfall and show the cash flows for each of the classes of investments for each year, 1-10.
(2 points)
5. Calculate the fixed rate for a 3 year quarterly payment swap to the nearest basis point based on LIBOR given the following Eurodollar prices. Assume that the current 3 month LIBOR, as of March, 2008, is 2.25%.
Maturity Index Price
June 2008 97.65
September 2008 97.36
December 2008 97.29
March 2009 97.10
June 2009 96.85
September 2009 96.57
December 2009 96.35
March 2010 96.18
June 2010 96.01
September 2010 95.86
December 2010 95.71
March 2011 95.45