Question

The following table summarizes prices of various default-free zerocoupon 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	80.25

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 met, what 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? (5 %)

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 %)

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.

Answer 1

Yield to Maturity = (Face Value / Current Price of Bond) ^ (1 / Years to Maturity) - 1
FV	100	100	100	100	100
Maturity(years)	1	2	3	4	5
Price(per $100 face value)	96.15	89.85	85.16	82.27	80.25
YTM	4.004%	5.497%	5.501%	5.000%	4.499%

3.1) Two conditions to be met for computed YTM to be realized are a) Bonds to be held till maturity b) the interest rate remains flat over the tenure of bond If these two conditions are not met, then bond holders faces a) interest rate risk which is if the interest rate in the market has risen and hence this results in the decrease in price of the bond that you are holding. In other words, your return on the existing bond that your are holding is lesser than the prevailing rate of return in the market. b) reinvestment risk which is if the bond is sold before maturity or it is called by issuer before maturity. In both the case, the risk is of reinvesting at a lower rate of return

3.2)

Forward rate - F1,5 (starting 1-yr from now and maturing 5-yr from now) (1+0.04499)^5 =   (1+0.04004)^1 * (1+F1,5)^4

F1,5 = 4.62%

3.3) Liquidity premium is an extension of pure expectation theory as it states that long term forward rates are deteremined by short term rates and in addition to this investor must be paid premium as a compensation for taking position in long term bonds and locking their returns Segmentation theory states that each investor have preference to stay invested in their current positions with the given yield and maturity. Such preferences can't be chaged and hence yield for a given maturity is primarily driven by demand and supply for the gien segment