You have a portfolio with $80\%$ weight in corporate bonds with duration of $4,$ and $20\%$ weight in Treasuries with duration of $5.$ The benchmark you use to compare your performance has $60\%$ in corporates with duration of $5,$ and $40\%$ in Treasuries with

duration of $5.$

You over$-$invest into corporates. At the same time, your corporate bonds have a lower duration than the benchmark. You want to figure out how this all affects the overall interest rate and credit risk exposures of your portfolio relative to the benchmark.

$($a$)$ Compute the durations of your portfolio and the benchmark. If interest rates increase, will you outperform the benchmark?

$($b$)$ Compute the spread durations of your portfolio and the benchmark. If corporate spreads increase, will you outperform the benchmark?