To calculate the portfolio's beta, we need to take the weighted average of the individual stock betas using their respective portfolio weights.

Given:

Apple stock weight $=38\%,$ beta $=1\mathrm{.}50$

Green Mountain Coffee stock weight $=15\%,$ beta $=1\mathrm{.}44$

Disney stock weight $=27\%,$ beta $=1\mathrm{.}15$

Target stock weight $=20\%,$ beta $=1\mathrm{.}20$

Portfolio Beta $=\backslash$Sigma $($Stock Weight x Stock Beta$)$

$=(0\mathrm{.}38$ x $1\mathrm{.}50)+(0\mathrm{.}15$ x $1\mathrm{.}44)+(0\mathrm{.}27$ x $1\mathrm{.}15)+(0\mathrm{.}20$ x $1\mathrm{.}20)$

$=0\mathrm{.}57+0\mathrm{.}216+0\mathrm{.}3105+0\mathrm{.}24$

$=1\mathrm{.}3365$

Therefore, the portfolio's beta is $1\mathrm{.}3365.$

MyLab: Create and grade a Freehand Grader assignment $($Beta$)$

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$6-23.($Portfolio beta and security market line$)$ You own a portfolio consisting of the

stocks below:

STOCK OR SECURITY

PERCENTAGE OF

PORTFOLIO BETA EXPECTED RETURN

$120\%1\mathrm{.}0012\%$

$230\%0\mathrm{.}858\%$

$315\%1\mathrm{.}2012\%$

$425\%0\mathrm{.}607\%$

$510\%1\mathrm{.}6016\%$

The risk$-$free rate is $3$ percent. Also, the expected return on the market portfolio is

$11$ percent.

a$.$ Calculate the expected return of your portfolio. $($Hint: The expected return

of a portfolio equals the weighted average of the individual stocks$$ expected

returns, where the weights are the percentage invested in each stock.$)$

b$.$ Calculate the portfolio beta.

c$.$ Given the foregoing information, plot the security market line on paper. Plot

the stocks from your portfolio on your graph.

d$.$ From your plot in part $($c$),$ which stocks appear to be your winners and which

ones appear to be your losers?

e$.$ Why should you consider your conclusion in part $($d$)$ to be less than certain?