Cougars Case
Riskless zero-coupon bond is the bond bought at a price lower than its face value, with the face value repaid at the time of maturity. The zero-coupon bond is riskless because the investors know exact money they will receive when the bond is maturity. The investors purchase the bond in a lower price and get more money. No coupon is paid before maturity. The investors do not need to pay interest. Besides, because zero-coupon bond is riskless, the bondholders are willing to hold it for long-term investment in order to diversity the portfolio. So it is important in the fixed income security market.
If a bond trades at a discount, its yield to maturity will exceed its coupon rate. Zero coupon bonds always sells at a discount. The sensitivity of a bond’s price to changes in interest rates is measured by the bond’s duration. A bond with high durations，its price is highly sensitive to interest rate changes. In other words, the prices of bonds with low durations are less sensitive to interest rate changes. That means interest rates of longer-term bonds are higher than shorter-term bonds’. The term structure of interest rates should be graphed as a curve line of zero-coupon bonds, in fact, it describe the relationship between matures and coupon date.
Using the date provided in the case, we can construct the following three yield curves:
COUGARs Strip Yield Curve
This is the adjusted COUGARs strip yield curve that takes the discounted rate (8.11%) into account. The adjustment is necessary because the prices provided in Exhibit 1 are prices for settlement on December 6, 1983, while Treasury quotes are 20 days before, which is the date of November 16, 1983. The discount factor is 1.0045, which is calculated as 1+8.11%*20/360. The yield curve has an obvious upward trend before Nov. 1987 and then the curve keeps flat. To highlight the upward trend, our team set 8% as the minimum number of the vertical axis.
b. Treasury Coupon Yield Curve
To build the treasury coupon yield curve, we select some bonds in the