Investment Management Case
COUGARS TEAM8: Kun Mao Xiaobin Yang Ruoxi Cao Yang Qiao Jing Liu 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 ate (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.
Treasury Coupon Yield Curve
To build the treasury coupon yield curve, we select some bonds in the Exhibit2. We have eliminated those bonds with extremely low coupons and with multiple maturity designations. The treasury coupon yield curve also shows an upward trend before Nov. 1987. And then the curve stays flat as a whole and just fluctuates slightly. Also we set 8 as the minimum number of the vertical axis to highlight the trend of the yield curve.
Implied Spot Yield Curve Because of the lack of data from May 1996 to Nov. 000, we can only build the implied spot yield curve from May 1984 to Nov. 1993. But the incomplete yield curve has successfully reflected the trend, moving upward and then keeping flat. According to the curves, we can observe that Strips yields show the yield of a separate zero-coupon security which is actually converted by coupon and principal payments of the Treasury bonds. Treasury coupon yield, which is the yield curve based on the treasury quotes, is the stated interest rates of a bond. The rates in three curves should nearly be the same.
It is obvious to see that these three curves have the same trend as a whole. All of them go upward before Nov. 1987 and then stay flat. Treasure bond price : (300000000*11. 875%/11. 89%)*[1-1/(1+11. 89%)^20]=267944276 The value of United States Treasure Bond A. G Becker bought is 267944276. Then A. G Becker separated coupons from the principal of coupon bonds then sold the coupons to investors, each of these investments then paid a single lump sum. We can calculate the value of coupon: 300000000*11,875%/2=17812500.
The value of coupon in each payment period equals to the face value of each zero coupon bonds. Investors bought the zero coupon bond at a price lower than par value. The fund A. G Becker collected in 1984 equals to sum of zero coupon bonds’ price. The difference between value of treasure bond and capital raised by zero coupon bonds is the value created through COUGARS. Capital raised by zero coupon bonds: 11. 875%/2*300000000*15. 30606=272639193. So we can easily see that the value created by COUGARS is 272639193. 8-267944276=4694917. 8.
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