If you don’t want jquery then you can do it with javascript :-
@Html.DropDownList("Sortby", new SelectListItem[]
{
new SelectListItem() { Text = "Newest to Oldest", Value = "0" },
new SelectListItem() { Text = "Oldest to Newest", Value = "1" },
new { @onchange="callChangefunc(this.value)" }
});
<script>
function callChangefunc(val){
window.location.href = "/Controller/ActionMethod?value=" + val;
}
</script>