If all interest rates in the economy fall by 1%, which of the following bonds would have the greatest percentage increase in value?
a. 20-year, 10% coupon bond.
b. 20-year, 5% coupon bond.
c. 10-year, zero coupon bond.
d. 1-year, 10% coupon bond.
e. 20-year, zero coupon bond.

E

Explanation:

The longer the maturity of a bond, the more of an effect a change in interest rates will have on it. The reason for this is that the price change is compounded into the bond price for more longer time frame. Since NPV of all the future cash flows, both the coupon payments and the par value paid at maturity. Therefore, a zero coupon bond is most affected by interest rate changes. Therefore, the longest zero coupon bond is the correct answer, which is option E.

B. 20-year, 5% coupon bond

Explanation:

The characteristics of are Bond are Interest rate, period and coupon. All these characteristics have a relationship with the value of the bond

Interest rate of a bond is a percentage of the Bond price that will be earned per period. Interest rate has an inverse relation with the price of the bond. An interest rate increase will lead to a decrease in the value of a bond this is known as the inverse effect.

Coupon is the payment per period that the bond holder will receive from the bond’s issue date until the bond matures. Coupons are commonly expressed has a percentage of the fair value. Bonds with low coupon rate are more sensitive to interest rate changes than bonds with high coupon rate.  

When it comes to period of a Bond, Bonds with long term period are more sensitive to interest rate changes than bonds with short term period, this is known as the Maturity effect.

Therefore a bond that will have the greatest percentage increase in value when interest falls is the bond that has the lowest coupon rate and the longest period of time.  Out of the four bond option in the question the first Bond (BOND A) and the second Bond have longest time period of 20 years but  the second bond (BOND B) meets the criteria of lowest coupon rate and longer time period. Based on the criteria of lowest coupon and longer time period we can conclude that the second Bond (Bond B) will have the greatest percentage increase in value.  

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