A bond currently sells for $1,120, which gives it a yield to maturity of 5%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to $1,070. What is the duration of this bond?
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To calculate the duration of a bond, we need the interest rate sensitivity and the present value of the bond cash flows.
1. Calculate the current yield and yield change:
- The current yield is the annual interest paid divided by the bond price:
Current yield = Annual interest payment / Current bond price
- The yield change is the difference between the new yield and the current yield:
Yield change = New yield - Current yield
2. Calculate the price change:
- The price change is the difference between the new bond price and the current bond price:
Price change = New bond price - Current bond price
3. Calculate the duration using the following formula:
- Duration = -1 * (Price change / (Current bond price * Yield change))
Let's calculate step by step.
First, calculate the current yield:
Current yield = Annual interest payment / Current bond price
We are given the yield to maturity of 5%, so we have:
0.05 = Annual interest payment / 1120
From this, we can calculate the annual interest payment:
Annual interest payment = 0.05 * 1120
Next, calculate the yield change:
Yield change = New yield - Current yield
Since the yield increases by 25 basis points (0.25%), we have:
Yield change = 0.05 + 0.0025 - 0.05
Now, calculate the price change:
Price change = New bond price - Current bond price
We are given that the new bond price is $1070 and the current bond price is $1120, so:
Price change = 1070 - 1120
Finally, calculate the duration:
Duration = -1 * (Price change / (Current bond price * Yield change))
Substitute the values:
Duration = -1 * (Price change / (1120 * Yield change))
By plugging in the values, you will get your answer for the duration of the bond.