Summary of Facts
Gilda Sears who is enrolled in an Investments class has picked a project on bond price theorems. The two main theorems that she decided to illustrate dealt with coupon rate and term-to-maturity and how these factors influence the price. Thus she included 2 bonds with the same rating and term with a different coupon rate, as well as two bonds with the same rating and coupon rate with different terms. She thought that if the bond markets were efficient, bonds with similar characteristics would be priced so that there would be little difference in the YTM. Besides S&P, she also looked at Moody’s for additional information.
There was an increase in the interest rates over 1984-1986 and hence observed the actual YTM at different point in time. Three periods were selected: November 1, 1984, 1985, and 1986. The theorem states that YTM and price, as well as coupon rate and price, should have an inverse relationship, while bond duration and price should have a direct relationship. ** Please refer to Annexure 1 for a summary on the Factual Numbers in the case.
The following are the problems of the case:
Q1: Using the prices given, calculate the percentage price changes for the three periods for the Boston Edison and American Brand bonds and explain the difference between the changes. Q2: Using the prices given, calculate the percentage price changes for the three periods for the AT&T and Batimore Gas bonds and explain the difference between the changes. Q3: Also, assuming there is a significant decline in interest rates, which of the four bonds would provide the largest potential capital gain?
Analysis and Solution
** Please Refer to Annexure 2 for Solution to I and II
I. Boston Edison and American Brand
* The two bonds have the same rating and maturity dates, but different coupon rates. * American Brand has a higher coupon rate (5.87%) than Boston Edison (4.25%) * The percentage change in the bond prices is inversely related to the YTM and the Coupon Rate. * The difference in the price increase was more significant in the second and the third period. * While the two bonds had comparable percentage price increase in the first period (1985 to 1986), the difference became much more significant in the subsequent periods, where the bond with a lower coupon rate was much higher. * Hence, this is in sync with the Bond Price Theorem.
II. AT&T and Baltimore Gas and Electric
* The two bonds have the same rating and coupon rates, but different maturity dates. * AT&T has a longer term (2/15/01) than Baltimore Gas and Electric (12/15/98) * The percent increase in price was much more significant in the first period, where the bond with the longer YTM had almost doubled the bond with the shorter YTM. * The percent decline in interest rate was also slightly greater for the bond with a longer maturity date, as longer maturity makes bond price more sensitive to interest rates.
III. Largest potential capital gain
** Please Refer to Annexure 3 for Solution to III
* I calculated the duration of the bond to make a selection of the bond with the potential capital gain in the advent of a decline in the interest rates. * Though shorter duration minimizes the risk of actively trading in bonds, bonds with longer durations are less susceptible to fluctuation. * Hence, among the 4 bonds, AT&T is the one with the maximum duration and hence will entail a larger potential gain.