"Consider the following $4$ option portfolios: $(1)1-$year $25-$delta put $-1-$year $25-$delta call, $(2)1-$year $25-$delta call $+2-$year $25-$delta put, $(3)1-$year $75-$delta call $-2-$year $25-$

delta put, $(4)2-$year $40-$delta call $+2-$year $50-$delta put. $($a$)$ Which option portfolio leads to a delta$-$neutral position?

$($b$)$ Which portfolio leads to the

longest delta position:

$($c$)$ Which portfolio leads to the shortest delta position?

$($d$)$ Which combination leads to a vega$-$neutral

position?

$($Answer the questions using a clean integer number with no decimal, no dots, no parentheses$)"$