²The assumption that returns are normally distributed is highly implausible. This means that with some positive probability, $RT < 0$ . So, owning a $1 of the risky asset in period $T − 1$ could result in negative wealth in period $T$ . You can lose more than everything, which is a violation of the legal principle of limited liability. (For a detailed history of limited liability, see Micklethwait and Wooldridge (2002).) Lognormally distributed returns are therefore much more plausible.