Saving it under a mattress is not investment, as "investment" is normally understood. It's just savings.
In any case, one of the major failings of modern macro is to assume you can think your way around the implications of economic actions. You have no way of knowing the consequences of stashing money under a mattress unless you actually do it, and even then there’s no guarantee the effect will be the same across different economies and in different eras. The world is just too complex for that.