Question

1. What is the duration of a 10-year zero-coupon bond with a par value of $1,000?

2. An investor has a 15-year maturity, 8% coupon, 8% yield bond with a duration of 10 years and a convexity of 135.5. If the interest rate were to fall 75 basis points, what is your predicted new price for the bond (including convexity)?

Answer 1

1)

Duration of a 10 year bond = 10

As a zero coupon bond pays all it's cash flows at maturity, duration of a zero coupon bond will be equal to maturity.

2)

75 basis point = 0.75% = 0.0075

Modified duration = Macaulay duration / (1 + r)

'Modified duration = 10 / (1 + 0.08)

Modified duration = 9.259259

Percentage change in price = (-Modified duration * change in yield) + [0.5 * Convexity * (change in yield)^2]

Percentage change in price = (-9.259259 * -0.0075) + [0.5 * 135.5 * (-0.0075)^2]

Percentage change in price = 0.069444 * 0.003811

Percentage change in price = 0.000265 or 0.0265%

Assuming face value to be $1000

Since coupon rate of 8% is equal to yield of 8%, current price is equal to face value. Therefore, current price is equal to $1000

Predicted new price = 1000 (1 + 0.000265)

Predicted new price = $1,000.26