The Distributions of Rates of Return for Companies AA and BB

True/False

The distributions of rates of return for Companies AA and BB are given below:
? $$\begin{array} { l l r r } \text { State of the } & \text { Probability of } & & \\\text { Economy } & \text { This State Occurring } & \underline { \text { AA } } & \underline { \text { B B } } \\\text { Boom } & 0.2 & 30 \% & - 10 \% \\\text { Normal } & 0.6 & 10 \% & 5 \% \\\text { Recession } & 0.2 & - 5 \% & 50 \%\end{array}$$
?
We can conclude from the above information that any rational,risk-averse investor would be better off adding Security AA to a well-diversified portfolio over Security BB.