Part B

Over one period, an investment in TiVo stock offers the following possible returns with corre$-$sponding probabilities: a low return of $8\mathrm{.}0\%$ with a $20\%$ chance, a medium return of $14\mathrm{.}0\%$ with a $50\%$ chance, and a high return of $17\mathrm{.}0\%$ with a $30\%$ chance. Over the same period, an invest$-$ment in Microsoft stock offers the following possible returns with corresponding probabilities: $6\mathrm{.}0\%$ with a $20\%$ Part B$2$chance, $11\mathrm{.}0\%$ with a $50\%$ chance, and $12\mathrm{.}0\%$ with a $30\%$ chance. The returns on the two investments are such that only three states are possible: low returns, medium returns, and high returns.

Now, suppose you invest $$1400$ in TiVo and put $$600$ into Microsoft. Call this portfolio Y$.$

$(1)$ Calculate the possible return on this portfolio under the low$-$return scenario.

$(2)$ Calculate the possible return on this portfolio under the medium$-$return scenario.

$(3)$ Calculate the possible return on this portfolio under the high$-$return scenario.

$(4)$ Now that you have three scenario$-$specific returns for this portfolio, along with the probabili$-$ties associated with each of the three scenarios, calculate the expected return on this portfolio.

$(5)$ Calculate the corresponding standard deviation that accompanies the investment in portfolio Y$.$