问一道题：NO.PZ2019103001000044

问题如下：

In contrast, Northco’s chief economist forecasts that Canadian interest rates will increase or decrease by 100 basis points over the next 12 months. Based on the chief economist’s forecast, Hirji suggests increasing the convexity of the French institutional client’s portfolio by selling 10-year bonds and investing the proceeds in a duration-matched barbell position of Canadian government 3-year and long-term bonds. She notes that the duration of the 10-year bonds, along with the durations of the other portfolio bonds, aligns the portfolio’s effective duration with that of the benchmark. Selected data on Canadian government bonds are presented in Exhibit 1.

Based on Exhibit 1, the gain in convexity from Hirji’s suggestion is closest to:

选项：

0.423.

1.124.

1.205.

解释：

A is correct.

To maintain the effective duration match, the duration of the 10-year bond sale must equal the total weighted duration of the 3-year and long-term bond purchases.

9.51 = (Duration of 3-year bond × Weight of 3-year bond) + (Duration of long-term bond × Weight of long-term bond)

x = weight of 3-year bond

(1 – x) = weight of long-term bond

9.51 = 2.88x + 21.30(1 – x)

x = 0.64 or 64%

The proceeds from the sale of the 10-year Canadian government bond should be allocated 64% to the 3-year bond and 36% to the long-term bond:

9.51 = (64% × 2.88) + (36% × 21.30)

Gain in convexity = (Weight of the 3-year) × (Convexity of the 3-year) + (Weight of the long-term bond) × (Convexity of the long-term bond) – (Weight of the 10-year) × (Convexity of the 10-year)

Gain in convexity = (64% × 0.118) + (36% × 2.912) – (100% × 0.701) = 0.42284 or 0.423