Question

A $1,000 par value, 7% annual coupon bond matures in 4 years. The bond is currently priced at $1,034.65 and has a YTM of 6.0%. What is the Macaulay duration?

a) 3.78 years
b) 3.96 years
c) 4.14 years
d) 4.32 years

Answer 1

The correct option is b) 3.96 years.

To calculate Macaulay duration, you can use the formula:


`\[ \text{Macaulay duration} = \frac{\sum_(t=1)^(T) \frac{t \cdot C} {(1 + YTM)^t} + \frac{T \cdot (F + C)} {(1 + YTM)^T}}{\text{Current bond price}} \]`

Where:
- \(C\) is the annual coupon payment,
- \(YTM\) is the yield to maturity,
- \(T\) is the number of years to maturity,
- \(F\) is the face value of the bond.

Given the bond information:

`\(C = 0.07 * 1000\),\\\(YTM = 0.06\),\\\(T = 4\),\\\(F = 1000\),`
- Current bond price = $1,034.65.

Plugging in these values:


`\[ \text{Macaulay duration} = \frac{\sum_(t=1)^(4) \frac{t \cdot 70} {(1 + 0.06)^t} + \frac{4 \cdot (1000 + 70)} {(1 + 0.06)^4}}{1034.65} \]`

After evaluating this expression, the closest option is:
b) 3.96 years

Answer 2

The Macaulay duration of the bond is approximately 3.96 years.

Step-by-step explanation:

The Macaulay duration of a bond is a measure of its sensitivity to changes in interest rates. It is calculated by taking the present value of each cash flow from the bond and weighting it by the proportion of the bond's price that it represents. Here's how to calculate the Macaulay duration:

1. Calculate the present value of each cash flow by discounting it at the bond's yield to maturity (YTM).
2. Multiply each present value by the period in which it occurs.
3. Sum up all the weighted present values.
4. Divide the sum by the bond's price to get the Macaulay duration.

In this case, the bond has a par value of $1,000, an annual coupon rate of 7%, and a maturity of 4 years. Its current price is $1,034.65 and the YTM is 6.0%. Plugging in these values, the Macaulay duration is approximately 3.96 years (rounded to two decimal places).