How does diversification impact systematic risk in a portfolio?

a$.$

It has no impact on systematic risk.

b$.$

It transforms systematic risk into unsystematic risk.

c$.$

It increases systematic risk.

d$.$

It decreases systematic risk $($WRONG ans.$)$

Your portfolio contains $25\%$ of stock A$,35\%$ of stock B$,$ and $40\%$ of stock C$.$ Assume that stock A earned a $4\%$ return, stock B earned $5\%$ return, stock C earned $3\%$ return this year. Which of the following codes is CORRECT to calculate total portfolio return this year?

a$.$

$0\mathrm{.}25*4\%+0\mathrm{.}35*5\%+0\mathrm{.}4*3\%($WRONG$)$

b$.$

$25\%*3\%+35\%*5\%+40\%*3\%$

c$.$

$0\mathrm{.}25*0\mathrm{.}04+0\mathrm{.}35*0\mathrm{.}05+0\mathrm{.}4*0\mathrm{.}03$

d$.$

$25\%*0\mathrm{.}03+35\%*0\mathrm{.}05+40\%*0\mathrm{.}03$

What would be the output of the following R code? f $<-$ function$($x$)\{$ x $+2\}$ f$(5)$

a$.$

$[1]10($WRONG$)$

b$.$

$[1]8$

c$.$

$[1]7$

d$.$

$[1]5$

What will the following function return when called as avg$($c$(1,2,3,4,5))?$ avg $<-$ function$($numbers$)\{$sum$($numbers$)/$ length$($numbers$)\}$

a$.$

$2\mathrm{.}5($WRONG$)$

b$.$

$15$

c$.$

$5$

d$.$

$3$

What happens to the variance of a two$-$asset portfolio when assets are less than perfectly correlated?

a$.$

Variance is reduced compared to the individual asset variances.

b$.$

The variance is always equal to the sum of the individual asset variances.

c$.$

The variance is a weighted average of the individual asset variances.

d$.$

Variance increases as the correlation between the assets decreases. $($WRONG$)$

What is the significance of a Sharpe ratio of zero in a portfolio?

a$.$

It implies that the portfolio has the highest possible risk.

b$.$

It signifies that the portfolio's return is equal to the risk$-$free rate. $($WRONG$)$

c$.$

It means the portfolio offers no excess return over the risk$-$free rate.

d$.$

It indicates that the portfolio has no risk.