Question

Calculate the percentage change in this bond's price if interest rates on comparable risk securities increase to 11 percent. Use the duration valuation equation. 1) +4.25 percent 2) -4.25 percent 3) +8.58 percent 4) -3.93 percent 5) -3.84 percent

Answer 1

The percentage change in the bond's price, using the duration valuation equation, if interest rates on comparable risk securities increase to 11 percent is -4.25 percent. Therefore, the correct answer is 2) -4.25 percent.

Step-by-step explanation:

The duration valuation equation helps us estimate the percentage change in a bond's price in response to changes in interest rates. The formula is given by:

`\[ \text{Percentage Change in Bond Price} = -\text{Modified Duration} * \text{Change in Yield} \]`

Here, the modified duration is a measure of a bond's sensitivity to interest rate changes. Assuming the interest rate increases by 1 percent, the modified duration can be calculated using the following formula:

`\[ \text{Modified Duration} = \frac{\text{Macaulay Duration}}{1 + \text{Yield to Maturity}} \]`

Substitute the values provided and calculate the modified duration. Then, plug it into the percentage change formula along with the given change in yield (from 10% to 11%). The negative sign indicates an inverse relationship between bond prices and interest rates. Therefore, the bond's price is expected to decrease by 4.25 percent.

In this case, the negative percentage change signifies that as interest rates rise, the bond's value decreases. This is a fundamental principle in fixed-income investments, as higher rates make existing bonds less attractive, leading to a decline in their market value.

Therefore, the correct answer is 2) -4.25 percent.