$13.$ A stock is expected to earn the following returns over the next year, depending on the state of nature. What is the expected return of the stock? The probabilities and rates are stated in decimal form.

Economic state of Nature

Probability

E$($r$)$

Depression

$0\mathrm{.}1$

$-0\mathrm{.}20$

Recession

$0\mathrm{.}3$

$-0\mathrm{.}05$

Normal

$0\mathrm{.}5$

$0\mathrm{.}05$

High growth boom

$0\mathrm{.}1$

$0\mathrm{.}20$

Enter rate in decimal form, rounded to the nearest basis point, as in $"0\mathrm{.}1234"$