Beta vs std deviation

CFA Level III
#1

Hey guys,

We all know that std dev = systematic risk (beta) + unsystematic risk (company risk). Lets say we have a well diversified portfolio and that we have removed unsystematic risk, is it safe to say that std dev = beta when portfolios are well diversified?

#2

Standard deviation of returns does not equal beta, even in the absence of unsystematic risk.

Some obvious clues are that:

  • Standard deviation of returns is nonnegative, whereas beta can be negative
  • Standard deviation of returns is usually expressed as a percentage of portfolio value, whereas beta is simply a number (i.e., it is unitless)