Effect of risk free asset including, standard, only, because

mfleming1983

Standard deviation of risk free asset is 0 and covariance with an risky asset is also 0. As per the formula for standard deviation of a portfolio, if you replace these values, the only thing you will be left with weight of risky asset and standard deviation of the risky asset. Is it fair to assume that the result(portfolio standard deviation) only have risk of the risky asset because portfolio standard deviation is not dependent upon any other risks. However, theoretically, including risk free asset in a portfolio does decrease the risk of the portfolio. How do you derive this fact from the formula?

Ionutzakis

because the weight of the risk asset is <1

Finalnub

To flesh out what cfa_bombay said, If you add a rf asset, the resulting wieght of weigh of the risky asset decreases (relative to its weigh in the "risky asset only" portfolio).

So, since the sd of the portfolio equals weight of risky times sd of risky, the portfolio sd must decrease.

chetan86

yeah that makes sense...Thanks!