Consider two bonds, as before, but this time assume the yield to maturity decreases to 5 per cent, as follows:

• 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 decreases to 5 per cent. Then:

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

Insert numeric values without thousand separators.

Working out

As before, the price of the zero-coupon bond ($1,000 face value) selling at a yield to maturity of 6 per cent is $519.17 and the price of the coupon bond is $1275.30.

Assuming yield to maturity falls to 5 per cent, then the price of the zero-coupon bond increases to $[?], and the price of the coupon bond increases to $[?].

Please report results up to two decimals for this exercise.

Zero-coupon bond

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

= [?] to four decimal places

= [?]% gain

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

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

= [?] to four decimal places

= [?]% gain

Coupon bond

Actual % gain = ( $[?] $[?] ) / $[?]

= [?]

= [?]% gain

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

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

= [?]

= [?]% gain