Which of the following statements are correct about returns?

$1.$ In expectation, geometric average return or the so$-$called time$-$weighted average return is not necessarily larger or smaller than arithmetic average return $($assuming stock return volatility is not zero$).$

$2.$ Time$-$weighted average return differs from arithmetic average return because a volatility adjustment.

$3.$ Time$-$weighted average return is smaller than arithmetic average return. Such a difference is even more dramatic when volatility of return is higher.

$4.$ Arithmetic average return can be less informative about the total holding period return than the geometric average return because it does not consider the compounding effect of each one$-$period return. For example, an arithmetic average return of $\backslash (\backslash$mathrm$\{$R$\}1=10\backslash \%,\backslash$mathrm$\{$R$\}2=10\backslash \%\backslash ),$ and $\backslash (\backslash$mathrm$\{$R$\}3=-20\backslash \%\backslash )$ is $\backslash (0\backslash \%\backslash ).$ But the compounded total holding period return is $\backslash ((1+$R $1)\backslash$times$(1+$R $2)\backslash$times$(1+$R $3)-1=-3\mathrm{.}2\backslash \%\backslash ),$ implying a negative geometric average return.

$2,4$

$2,3,4$

$2,3$