Question

If interest rates rise after a bond issue, what will happen to the bond’s price and YTM? Does the time to maturity affect the extent to which interest rate changes affect the bond’s price? The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices. Is that statement true or false? Explain. (Hint: Make up a “reasonable” example based on a 1-year and a 20-year bond to help answer the question.)

Answer 1

Answer:

The statement is:

False.

Explanation:

As the time to maturity of a bond increases sensitivity of bond price to change in interest rate increases. Hence short-term bond prices are less sensitive to interest rate changes than are long-term bond prices.

Let us take an example:

(a) Short term bond:

Bond face value = $1000

Annual coupon = 1000 * 10% = $100

Time to maturity = 1 year

Current interest rate = 10%

Hence bond price = $1,000

Let us assume interest rate increases to 11%

Bond price = PV (rate, nper, pmt, fv, type) = PV (11%, 1, -100, -1000, 0) = $990.99

So in case of this short term bond an increase of interest from 10% to 11%, has decreased the bond price from $1000 to $990.99

(b) Let us take an example of long term bond:

Bond face value = $1000

Annual coupon = 1000 * 10% = $100

Time to maturity = 20 years

Current interest rate = 10%

Hence bond price = $1,000

Let us assume interest rate increases to 11%

Bond price = PV (rate, nper, pmt, fv, type) = PV (11%, 20, -100, -1000, 0) = $920.37

So, in case of this long term bond an increase of interest from 10% to 11%, has decreased the bond price from $1000 to $920.37

So from above example we find that for same increase in interest rate, there is much higher change in price of long term bond as compared to change in price of short term bond.

Hence short-term bond prices are less sensitive to interest rate changes than are long-term bond prices.