I want to make a part move locally so lag isn't caused by players?

This is my script and it works in a regular script but not in a local script? can anybody help me

fish = script.Parent

while true do
for i=1,20 do
fish.CFrame = fish.CFrame + Vector3.new(0.1,0,0)
wait(0.1)
end
for i=1,31 do
fish.CFrame = fish.CFrame * CFrame.fromEulerAnglesXYZ(0,0.1,0)
wait(0.01)
end
for i=1,20 do
fish.CFrame = fish.CFrame - Vector3.new(0.1,0,0)
wait(0.1)
end
for i=1,31 do
fish.CFrame = fish.CFrame * CFrame.fromEulerAnglesXYZ(0,-0.1,0)
wait(0.01)
end
end

To make a part only visible to one player you would use Local Parts. These parts are only seen by the specific player.

Here's the Wiki Link: http://wiki.roblox.com/index.php?title=Local_parts