Markowitz portfollo optimization: Harry Markowitz recelved the $1990$ Nobel Prize for his path$-$breaking work in portfolio optimization. One version of the Markowitz model is based on minimizing the variance of the portfolio subject to a constraint on return. The below table shows the annual return $(\%)$ for five $1-$year perlods for the six mutual funds with the last row that gives the S&P S$00$ return for each planning scenario. Scenario $1$ represents a year in which the annual returns are good for all the mutual funds. Scenario $2$ is also a good year for most of the mutual funds. But scenario $3$ is a bad year for the small$-$cap value fund; scenario $4$ ls a bad year for the intermedlate$-$term bond fund; and scenario $5$ is a bad year for four of the sixMUTUAL FUND PERFORMANCE IN FIVE SELECTED YEARLY SCENARIOSPlanning ScenariosMutual FundScenario $1$Scenario $2$Scenario $3$Scenario $4$Scenario $5$Foreign Stock$10\mathrm{.}0613\mathrm{.}1213\mathrm{.}4745\mathrm{.}42-21\mathrm{.}93$Intermediate$-$Term Bond$17\mathrm{.}643\mathrm{.}257\mathrm{.}51-1\mathrm{.}337\mathrm{.}36$Large$-$Cap Growth$32\mathrm{.}4118\mathrm{.}7133\mathrm{.}2841\mathrm{.}46-23\mathrm{.}26$Large$-$Cap Value$32\mathrm{.}3620\mathrm{.}6112\mathrm{.}937\mathrm{.}06-5\mathrm{.}37$Small$-$Cap Growth$33\mathrm{.}4419\mathrm{.}403\mathrm{.}8558\mathrm{.}68-9\mathrm{.}02$Small$-$Cap Value$24\mathrm{.}5625\mathrm{.}32-6\mathrm{.}705\mathrm{.}4317\mathrm{.}31$S&P $500$ Return$25\mathrm{.}0020\mathrm{.}008\mathrm{.}0030\mathrm{.}00-10\mathrm{.}00$If each of the scenarios is qually likely and occurs with probability $1/5,$ then the mean return or expected return of the portfolio isThe variance of the portfolio return isvar$--$Using the scenario return data given In Table above, the Markowitz mean$-$variance model can be formulated. The objective function is the variance of the portfollo and should be minimized. Assume that the required return on the portfollo Is $10\%.$There Is also a unity constraint that all of the money must be Invested in mutual funds.Most investors are happy when their returns are "above average," but not so happy when they are "below average." In the Markowitz portiollo optimization model given above, the objective function Is to minimize variance, wilch is given byMin $5$E$,($R$,-$ R$)3$where Rs is the portfolio return under scenario s and R is the expected or average return of the portiollo.With this objective function, we are choosing a portfolio that minimizes deviations both above and below the average, R$.$ Howevor, most investors are happy when R$.>$ R$,$ but unhappy when Rs $<$ R$.$ With this preference in mind, an alternative to the