这道题会了问个题外话

问题如下：

McLaughlin and Michaela Donaldson, a junior analyst at Delphi, are now discussing how to reposition the portfolio in light of McLaughlin’s expectations about interest rates over the next 12 months. She expects interest rate volatility to be high and the yield curve to experience an increase in the 2s/10s/30s butterfly spread, with the 30-year yield remaining unchanged. Selected yields on the Treasury yield curve, and McLaughlin’s expected changes in yields over the next 12 months, are presented in Exhibit 1.

Donaldson suggests they also consider altering the portfolio’s convexity to enhance expected return given McLaughlin’s interest rate expectations. Donaldson tells McLaughlin the following.

Statement 1 Portfolios with larger convexities often have higher yields.

Statement 2 If yields rise, a portfolio of a given duration with higher convexity will experience less of a price decrease than a similar-duration, lower-convexity portfolio.

Which of Donaldson’s statements is correct?

选项：

Only Statement 1

Only Statement 2

Both Statements 1 and 2

解释：

B is correct.

Statement 2 is correct: If yields rise, a portfolio of a given duration with higher convexity will experience less of a price decrease than a similar-duration, lower-convexity portfolio.

Statement 1 is incorrect, as portfolios with larger convexities often have lower yields. Investors will be willing to pay for increased convexity when they expect yields to change by more than enough to cover the sacrifice in yield.