Shown below are the investment weights for the securities held in four different portfolios: three mutual funds and the benchmark index that each of those funds uses.

Percentage Security Investment Weight:

Security Benchmark Index

$(\%)$ Fund X

$(\%)$ Fund Y

$(\%)$ Fund Z

$(\%)$

$11063611$

$210509$

$3107511$

$4108011$

$510509$

$61011011$

$71052611$

$81012259$

$9108011$

$1010112011$

Calculate the active share $($AS$)$ measure for Fund X$,$ Fund Y$,$ and Fund Z relative to the benchmark index. Do not round intermediate calculations. Round your answers to one decimal place.

Fund X:

$\%$

Fund Y:

$\%$

Fund Z:

$\%$

Using these AS calculations, indicate which fund is the most likely to be considered: $($i$)$ a passive index fund, $($ii$)$ a closet $($or enhanced$)$ index fund, and $($iii$)$ an actively managed concentrated stock$-$picking fund. Explain the reason for your classification.

Fund X is considered

$-$Select$-$

because, it

$-$Select$-$

in the investment weights of holdings relative to the benchmark index.

Fund Y is considered

$-$Select$-$

because, it is

$-$Select$-$

concentrated than the benchmark and has

$-$Select$-$

holdings and

$-$Select$-$

investment positions.

Fund Z is considered

$-$Select$-$

because its security holdings come closer to matching the benchmark,

$-$Select$-$

$.$