For the period $2010-2022,$ calculate the arithmetic mean, standard deviation, skewness, kurtosis, and VaR $($at $5\%)$ for the industry portfolio equal$-$weighted monthly return $($ewret$)($Do not distinguish different industries, just report these summary statistics for ewret$).$

$($Arithmetic$)$ Mean industry monthly return $($Round it to $3$ decimal points, no percentage sign$).$

Standard Deviation of industry monthly returns $($Round it to $3$ decimal points, no percentage sign$).$

Skewness of industry monthly returns $($Round it to $3$ decimal points, no percentage sign$).$

Kurtosis of industry monthly returns $($Round it to $3$ decimal points, no percentage sign$).$

Value at Risk $($VaR$)$ at $5\%$ of industry monthly returns based on the empirical distribution $($percentile$)($Round it to $3$ decimal points, no percentage sign$).$

Question $2(10$ points$)$

Question $2$ options:

Perform a value strategy based on the book$-$to$-$market equity $($BM$)$ lagged by one month. Each month, identify your value portfolio to be the industry with the highest BM$,$ and your growth portfolio to be that with the lowest BM$.$ Create a long$-$short strategy that invests one dollar in the value portfolio and shorts one dollar in the growth portfolio each month. The value or growth portfolio is equal$-$weighted $($ewret$).$ Calculate the mean returns of the long leg $($L$),$ the short leg $($S$),$ and the long$-$short portfolio $($L $-$ S$),$ and the Sharpe ratios of the long$-$short portfolios over the sample period $2010-2022.$

Mean return of the long leg $($L$)($by investing $$1$ in the value portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Mean return of the short leg $($G$)($by investing $$1$ in the equal$-$weighted growth portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Mean return of the long$-$short portfolio $($L $-$ S$)($by investing $$1$ in the equal$-$weighted value portfolio and shorting $$1$ in the equal$-$weighted growth portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Standard Deviation of the long$-$short portfolio $($L $-$ S$)($by investing $$1$ in the equal$-$weighted value portfolio and shorting $$1$ in the equal$-$weighted growth portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Question $3(10$ points$)$

Question $3$ options:

Repeat the exercise in Q$2$ but select the top and bottom $2$ portfolios to be your value and growth portfolio $($based on BM$).$ The value $($growth$)$ portfolio is the equal$-$weighted portfolio invested in the selected two $($equal$-$weighted$)$ industry portfolios.

Mean return of the long leg $($L$)($by investing $$1$ in the value portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Mean return of the short leg $($G$)($by investing $$1$ in the equal$-$weighted growth portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Mean return of the long$-$short portfolio $($L $-$ S$)($by investing $$1$ in the equal$-$weighted value portfolio and shorting $$1$ in the equal$-$weighted growth portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$

Standard Deviation of the long$-$short portfolio $($L $-$ S$)($by investing $$1$ in the equal$-$weighted value portfolio and shorting $$1$ in the equal$-$weighted growth portfolio$)$: $($Round it to $3$ decimal points, no percentage sign$)$