Consider two bonds:

• An 11.25-year maturity zero-coupon bond selling at a yield to maturity of 6 per cent has convexity of 152.7 and duration of 10.31 years.
• A 30-year maturity 8 per cent coupon bond making annual coupon payments also selling at a yield to maturity of 6 per cent has nearly identical duration10.29 yearsbut considerably higher convexity of 238.

Suppose the yield to maturity on both bonds increases to 7 per cent. Then:

• What will be the actual percentage capital loss on each bond?
• What percentage capital loss would be predicted by the duration-with-convexity rule/approximation?

Insert numeric values without thousand separators. Please report results up to two decimals for this exercise.

Working out

The price of the zero-coupon bond ($1,000 face value) selling at a yield to maturity of 6 per cent is $[?] and the price of the coupon bond is $[?].

At a YTM of 7 per cent, the actual price of the zero-coupon bond is $[?] and the actual price of the coupon bond is $[?].

Zero-coupon bond

Actual % loss = ( $[?] - $[?] ) / $[?]

= -[?] to four decimal places

= [?]% loss

The percentage loss predicted by the duration-with-convexity rule is:

Predicted % loss = (-[?] 0.01 ) + ( 0.5 [?] 0.01²)

= -[?] to four decimal places

= [?]% loss

Coupon bond

Actual % loss = ([?] [?] / [?]

= -[?]

= [?]% loss

The percentage loss predicted by the duration-with-convexity rule is:

Predicted % loss = (-[?] 0.01 ) + ( 0.5 [?] 0.01²)

= -[?] to four decimal places

= [?]% loss

Answer

• For the zero-coupon bond, the predicted % loss, to two decimal places is [?]
• For the coupon bond, the predicted % loss, to two decimal places is [?]