Evaluate a portfolio of U

$.$

S

$.$

$$equities drawn from the S&P

$5$

$0$

$0$

$.$

$$The five stocks in your portfolio have the FactSet identifiers as follows:

$$

$$STOCK

$1$

: ABT

$-$

US

$.$

$$Average annual return

$=$

$4$

$.$

$5$

$4$

$2$

$\%$

$$Annual Variance

$=$

$3$

$.$

$9$

$8$

$5$

$\%$

$$

$$STOCK

$2$

: AMZN

$-$

US

$.$

$$Average annual return

$=$

$8$

$.$

$5$

$8$

$5$

$\%$

$$Annual Variance

$=$

$3$

$.$

$7$

$0$

$0$

$\%$

$$

$$STOCK

$3$

: C

$-$

US

$.$

$$Average annual return

$=$

$1$

$8$

$.$

$5$

$6$

$0$

$\%$

$$Annual Variance

$=$

$3$

$.$

$2$

$1$

$6$

$\%$

$$

$$STOCK

$4$

: MSFT

$-$

US

$.$

$$Average annual return

$=$

$1$

$1$

$.$

$3$

$8$

$2$

$\%$

$$Annual Variance

$=$

$5$

$.$

$9$

$0$

$4$

$\%$

$$

$$STOCK

$5$

: XOM

$-$

US Average annual return

$=$

$5$

$.$

$1$

$0$

$3$

$\%$

$$Annual Variance

$=$

$3$

$.$

$8$

$9$

$2$

$\%$

$$

$$S&P

$5$

$0$

$0$

: SP

$5$

$0$

$.$

$$Average annual return

$=$

$8$

$.$

$7$

$7$

$3$

$\%$

$$Annual Variance

$=$

$1$

$.$

$1$

$9$

$8$

$\%$

$$

$$Assume the annualised risk

$-$

free rate is

$3$

$\%$

$.$

Suppose your utility function is

$$

$$

$=$

$$

$$

$($

$$

$$

$)$

$$

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$$

$$

$$

$$

$$

$.$

$$Form an optimal complete portfolio by combining P

$*$

$$with the risk

$-$

free asset. What is the portfolio weight on each of individual asset in this optimal complete portfolio? What is the max utility score that you can achieve?

Q

$1$

: complete portfolio weight in STOCK

$1$

Q

$2$

: complete portfolio weight in STOCK

$2$

Q

$3$

: complete portfolio weight in STOCK

$3$

Q

$4$

: complete portfolio weight in STOCK

$4$

Q

$5$

: complete portfolio weight in STOCK

$5$

Q

$6$

: complete portfolio weight in Risk

$-$

free asset

Q

$7$

: Utility score is

$?$