# Risk-free assets

A risk-free asset or security has a zero variance or standard deviation. The risk-free security has no risk of default. The government treasury bill or bond is an approximate example of the risk-free security as they have no risk of default.

What happens to return and risk when we combine a risk-free and risky asset? Let us assume that an investor holds a risk-free security of which he has an expected return of 5 percent and risk security with an expected return of 5 percent and risky security j with an expected return of 15 percent and a standard deviation of 6 percent.
The portfolio return is =$E(R_{p})=E(R_{j})+(1.0))R_{f}$
=$0.5\times0.15+(1-0.5)0.005$
=$0.075+0.025=0.10=10%$