$$ Consider a broad stock index and its projected holding period returns under a variety of different economic conditions over the next year:

$$ E$($r$)$ & Std$.$ Dev.?

State of Economy Probability

HPR

Boom

$0\mathrm{.}20$

$37\%$

Normal Growth

$0\mathrm{.}50$

$26\%$

Recession

$0\mathrm{.}30$

$-18\%$

$3$

Including the risk$-$free rate

$$ Assume that you can also invest in a safe investment $($for example, a T$-$Bill$)$ at the risk$-$free rate rf

$$ How much should you invest into the risky asset, and how much into the risk$-$free asset?

$$ Depends on two things: