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Problem $6-06$

Given:

E$($R$1)=0\mathrm{.}13$

E$($R$2)=0\mathrm{.}18$

E$(\backslash$sigma $1)=0\mathrm{.}04$

E$(\backslash$sigma $2)=0\mathrm{.}06$

Calculate the expected returns and expected standard deviations of a two$-$stock portfolio having a correlation coefficient of $0\mathrm{.}75$ under the conditions given below. Do not round intermediate calculations. Round your answers to four decimal places.

w$1=1\mathrm{.}00$

Expected return of a two$-$stock portfolio:

Expected standard deviation of a two$-$stock portfolio:

w$1=0\mathrm{.}75$

Expected return of a two$-$stock portfolio:

Expected standard deviation of a two$-$stock portfolio:

w$1=0\mathrm{.}40$

Expected return of a two$-$stock portfolio:

Expected standard deviation of a two$-$stock portfolio:

w$1=0\mathrm{.}30$

Expected return of a two$-$stock portfolio:

Expected standard deviation of a two$-$stock portfolio:

w$1=0\mathrm{.}10$

Expected return of a two$-$stock portfolio:

Expected standard deviation of a two$-$stock portfolio:

Choose the correct risk$$return graph for weights from parts $($a$)$ through $($e$)$ when ri$,$j $=-0\mathrm{.}75$; $0\mathrm{.}00$; $0\mathrm{.}75.$

The correct graph is

$-$Select$-$

$.$

A$.$

The risk$-$return graph shows expected return E$($R$)$ as a function of standard deviation of return, sigma, for three correlation coefficients. Expected return is measured from $0\mathrm{.}10$ to $0\mathrm{.}19$ on the vertical axis. Sigma is measured from zero to $0\mathrm{.}09$ on the horizontal axis. Each of the three graphs is a segmented line that starts at the common point A and passes through its own four points, B through E$.$ The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}051,0\mathrm{.}145),(0\mathrm{.}062,0\mathrm{.}160),(0\mathrm{.}060,0\mathrm{.}168),(0\mathrm{.}057,0\mathrm{.}175).$

The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}00$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}044,0\mathrm{.}141),(0\mathrm{.}047,0\mathrm{.}153),(0\mathrm{.}051,0\mathrm{.}164),(0\mathrm{.}054,0\mathrm{.}175).$

The graph corresponding to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}021,0\mathrm{.}143),(0\mathrm{.}026,0\mathrm{.}160),(0\mathrm{.}034,0\mathrm{.}165),(0\mathrm{.}051,0\mathrm{.}175).$

B$.$

The risk$-$return graph shows expected return E$($R$)$ as a function of standard deviation of return, sigma, for three correlation coefficients. Expected return is measured from $0\mathrm{.}10$ to $0\mathrm{.}19$ on the vertical axis. Sigma is measured from zero to $0\mathrm{.}09$ on the horizontal axis. Each of the three graphs is a segmented line that starts at the common point A and passes through its own four points, B through E$.$ The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}050,0\mathrm{.}120),(0\mathrm{.}052,0\mathrm{.}133),(0\mathrm{.}059,0\mathrm{.}150),(0\mathrm{.}062,0\mathrm{.}155),(0\mathrm{.}067,0\mathrm{.}165).$

The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}00$ passes through the following points:

$(0\mathrm{.}050,0\mathrm{.}120),(0\mathrm{.}044,0\mathrm{.}133),(0\mathrm{.}049,0\mathrm{.}150),(0\mathrm{.}054,0\mathrm{.}155),(0\mathrm{.}064,0\mathrm{.}165).$

The graph corresponding to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}050,0\mathrm{.}120),(0\mathrm{.}031,0\mathrm{.}133),(0\mathrm{.}036,0\mathrm{.}150),(0\mathrm{.}044,0\mathrm{.}155),(0\mathrm{.}061,0\mathrm{.}165).$

C$.$

The risk$-$return graph shows expected return E$($R$)$ as a function of standard deviation of return, sigma, for three correlation coefficients. Expected return is measured from $0\mathrm{.}10$ to $0\mathrm{.}19$ on the vertical axis. Sigma is measured from zero to $0\mathrm{.}09$ on the horizontal axis. Each of the three graphs is a segmented line that starts at the common point A and passes through its own four points, B through E$.$ The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}021,0\mathrm{.}143),(0\mathrm{.}026,0\mathrm{.}160),(0\mathrm{.}034,0\mathrm{.}165),(0\mathrm{.}051,0\mathrm{.}175).$

The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}00$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}034,0\mathrm{.}143),(0\mathrm{.}039,0\mathrm{.}160),(0\mathrm{.}044,0\mathrm{.}165),(0\mathrm{.}054,0\mathrm{.}175).$

The graph corresponding to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}042,0\mathrm{.}143),(0\mathrm{.}049,0\mathrm{.}160),(0\mathrm{.}052,0\mathrm{.}165),(0\mathrm{.}057,0\mathrm{.}175).$

D$.$

The risk$-$return graph shows expected return E$($R$)$ as a function of standard deviation of return, sigma, for three correlation coefficients. Expected return is measured from $0\mathrm{.}10$ to $0\mathrm{.}19$ on the vertical axis. Sigma is measured from zero to $0\mathrm{.}09$ on the horizontal axis. Each of the three graphs is a segmented line that starts at the common point A and passes through its own four points, B through E$.$ The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}042,0\mathrm{.}143),(0\mathrm{.}049,0\mathrm{.}160),(0\mathrm{.}052,0\mathrm{.}165),(0\mathrm{.}057,0\mathrm{.}175).$

The graph corresponding to r subscript $1,2$ end subscript equal to $0\mathrm{.}00$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}034,0\mathrm{.}143),(0\mathrm{.}039,0\mathrm{.}160),(0\mathrm{.}044,0\mathrm{.}165),(0\mathrm{.}054,0\mathrm{.}175).$

The graph corresponding to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75$ passes through the following points:

$(0\mathrm{.}040,0\mathrm{.}130),(0\mathrm{.}021,0\mathrm{.}143),(0\mathrm{.}026,0\mathrm{.}160),(0\mathrm{.}034,0\mathrm{.}165),(0\mathrm{.}051,0\mathrm{.}175).$