The stock of Business Adventures sells for $$50$ a share. Its likely dividend payout and end$-$of$-$year price depend on the state of the economy by the end of the year as follows:

Dividend Stock Price

Boom $ $3\mathrm{.}00$ $ $58$

Normal economy $1\mathrm{.}4052$

Recession $0\mathrm{.}7043$

Required:

a$.$ Calculate the expected holding$-$period return and standard deviation of the holding$-$period return. All three scenarios are equally likely. $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

b$.$ Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is $3\%.($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$