UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

College of Business – Department of Finance

FINANCE 432: Managing Financial Risk for Insurers

Professor Steve D’Arcy

Homework #1 (10 points)

Lectures 1–4

Due February 4, 2008

(2 points)

1.Go to the St. Louis Federal Reserve website ( and obtain the Consumer Price Index for All Urban Consumers for All Items (CPIAUCNS) and the 3 Month Treasury Bill Secondary Market Rate (TB3MS). Plot the actual interest rate and the change in CPI on a chart where the x axis is the month from January 1934 through December 2007. Then determine the correlation between these two variables for the entire time period (1934-2007), and then for 1934-1970 and for 1971-2007.

(2 points)

2.Draw the risk profiles depicted by the following situations:

  1. A life insurer owns $200 million in 20 year annual payment fixed rate bonds with an 8% coupon. Assume that the current interest rate for this bond is 5%. Draw the risk profile with respect to changes in interest rates.
  2. Aproperty-liability insurer invests in $200 million in floating rate Euro-denominated bonds. Show the risk profile with respect to changes in the Euro/U.S. dollar exchange rate. Assume the current exchange rate is 1 EUR = $1.46.

(1 point)

3.You own a 3-year, 5.75% coupon U. S. Treasury bond that pays interest semiannually. If the current price of the bond is $105.50, find the yield to maturity of the bond.

(1 points)

4.You have the following information about Treasury bonds and their prices:

Maturity / Coupon / Price
6 months / None (Zero-coupon) / $99.00
1 year / None (Zero-coupon) / $97.50
18 months / 3.625% coupon / $101.00
24 months / 4.25% coupon / $101.75

Find the implied 2-year spot rate using the bootstrap method.

(2 points)

5.You also own a bond issued by a U. S.company that makes automobiles. The bond is a 2-year, 6.5% semiannual coupon bond, and it is currently priced at $98.25. Find the static spread of this issuer using the spot rate curve you found in Question #4. Also, find the yield to maturity of this bond and calculate the credit risk using the traditional approach of comparing yields of this bond with the U. S. Treasury bond of the same maturity.

(2 points)

6.Given the following yields on US Treasuries, determine the spot rates and one-year and two year forward rates at each date. Assume that the 1-year Treasury is a discount security and that all longer instruments are coupon-bearing bonds. For simplicity, assume that all bonds pay ANNUAL coupons and that all rates are effective (annual) interest rates. That is, do NOT assume semiannual compounding.

Note that you will not be able to fill in EVERY box. Part of the exercise is for you to understand what boxes you cannot fill in. The appropriate symbols are given for the first few rates in order to help you get started.

One YearTwo Year

TimeYieldCouponSpot RateForward Rate Forward Rate

1 year2.55% 0.00% 0r1 1f1 2f1

2 years2.95% 2.25% 0r2 1f2 2f2

3 years3.45% 5.50% etc. etc. etc.

4 years3.80% 3.00%

5 years3.95% 6.50%

6 years4.00% 5.00%

7 years4.05% 4.625%