can someone explain the answer to me? Makes zero sense. the exhibit is attached and the question was,
“Determine whether Portfolio A and B in Exhibit 2 are most likely to outperform or underperform the index in the event of an instantaneous 50 bps parallel shift higher in rates. Justify your response for each using one key characteristic of the portfolio compared to the index (overall duration, convexity, curve positioning).”
In this question, we are asked about comparing the portfolio A & B with Index portfolio in event of 50bp instantaneous shift in rates. Since, the shift is instantaneous any change due to curve positioning is ruled out as where we are invested throughout the curve makes little difference is duration or convexity are same.
So, we need to look out for duration & convexity overall of Portfolio A & B with respect to the Index portfolio.
This you can do by weighted average method by looking the % allocation in a year to respective duration or convexity. We can do this as its instantaneous change in rates, so model risk etc doesn’t arise here.
For example, Effective convexity of portfolio A = 0.3*0.28 + 0.25*0.49 + 0.45*0.95 = 0.634
similarly, you can get other convexities and duration as given in the solution table.
Since, rates are about shift higher, we look out for portfolio with less duration & higher convexity compared to Index portfolio.
Since , duration is similar in all , convexity becomes the factor to decide here.