3. The following table summarizes prices of various default - free zero - coupon
ID: 2796072 • Letter: 3
Question
3. The following table summarizes prices of various default - free zero - coupon bonds (expressed as a percentage of face value):
Maturity (years)
1
2
3
4
5
Price (per $100 face value)
96.15
89.85
85.16
82.27
8 0.25
3.1 Compute the yield to maturity (YTM) for each of the five zero - coupon bonds and plot the zero - coupon yield curve (for the first five years). For a typical coupon bond, what are the two conditions that have to be met for the computed or promised YTM to be realized? If these two conditions or assumptions are not m et, wh at kind of risk would you have?
(15 %)
3.2 Based on your answer in 3.1, compute, under the pure expectations theory, the two - year forward rate three years from now. What can you conclude about forward rates when the yield curve is flat?
3.3 Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. Under the pure expectations theory, what rate would you obtain if there are no arbitrage opportunities? Show your calculations.
3.4 There are three main theories for the term structure of interest rates: (1) Pure expectations (unbiased); (2) Liquidity preference (term premium); and (3) Market segmentation. According to the pure expectations theory, the term structure is determined solely by the market’s expectations regarding future interest rates. Discuss how the other two theories differ from the pure expectations theory and provide empirical evidence for each of these three theories.
(10 %)
Maturity (years)
1
2
3
4
5
Price (per $100 face value)
96.15
89.85
85.16
82.27
8 0.25
Explanation / Answer
Solution 3.1
a) Zero Coupon Bond Yield to Maturity Calculation
Zero coupon bonds do not have re-occurring interest payments, which makes their yield to maturity calculations different from bonds with a coupon rate. Most time value of money formulas require some interest rate figures for each point in time. This makes the yield to maturity easier to calculate for zero coupon bonds, because there are no coupon payments to reinvest, making it equivalent to the normal rate of return on the bond.
The formula for calculating the yield to maturity on a zero coupon bond is:
Yield to Maturity = (Face Value / Current Price of Bond) ^ (1 / Years to Maturity) – 1
Particulars
Bond A
Bond B
Bond C
Bond D
Bond E
Bond Price
96.15
89.85
85.16
82.27
80.25
Term to Maturity in Years
1
2
3
4
5
Par Value of Bond
100
100
100
100
100
Yield to Maturity (YTM)
4.00%
5.50%
5.50%
5.00%
4.50%
b) Yield Curve
c) Assumptions and Associated Risk
For a typical coupon bond, the two conditions that have to be met for the computed or promised YTM to be realized are changes in interest rates in the market and changes in the issuer’s creditworthiness. If these two conditions are not met, the bond holder is exposed to Interest Rate Risk and Credit Risk.
Interest rate risk is the risk that interest rates will change.Bond prices and interest rates are inversely related; that is, bond prices increase as interest rates decrease and bond prices decrease as interest rates increase. Prices of zero-coupon and fixed-rate bonds can decline significantly in an environment of rising interest rates.
Credit risk, sometimes referred to as default risk, is the risk of loss if the borrower, or bond issuer, fails to make full and timely payments of interest and/or principal. If market participants suspect that a particular bond issuer will not be able to make its promised bond payments because of adverse business or general economic conditions, the probability of future default will increase and the bond price will likely fall in the market. Consequently, investors holding that particular bond will be exposed to a price decline and a potential loss of money if they want to sell the bond.
Particulars
Bond A
Bond B
Bond C
Bond D
Bond E
Bond Price
96.15
89.85
85.16
82.27
80.25
Term to Maturity in Years
1
2
3
4
5
Par Value of Bond
100
100
100
100
100
Yield to Maturity (YTM)
4.00%
5.50%
5.50%
5.00%
4.50%
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