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Problem $6-04$

You are considering two assets with the following characteristics.

E$($R$1)=0\mathrm{.}13\backslash$sigma $1=0\mathrm{.}08$ w$1=0\mathrm{.}3$

E$($R$2)=0\mathrm{.}21\backslash$sigma $2=0\mathrm{.}14$ w$2=0\mathrm{.}7$

Compute the mean and standard deviation of two portfolios if r$1,2=0\mathrm{.}50$ and $-0\mathrm{.}75,$ respectively. Do not round intermediate calculations. Round your answers for the mean of two portfolios to three decimal places and answers for standard deviations of two portfolios to five decimal places.

Mean of two portfolios:

Standard deviation of two portfolios if r$1,2=0\mathrm{.}50$:

Standard deviation of two portfolios if r$1,2=-0\mathrm{.}75$:

Choose the correct risk$$return graph.

The correct graph is

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$.$

A$.$

Expected return is plotted as a function of risk. Expected return is measured from zero to $30$ percent on the vertical axis. Risk in form of standard deviation is measured from zero to $20$ percent on the horizontal axis. Point A is marked at $(8\mathrm{.}2,18\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $0\mathrm{.}50.$ Point B is marked at $(11\mathrm{.}2,18\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75.$ A straight horizontal line goes from the horizontal axis to point B through point $\text{'}$A$\text{'}.$

B$.$

Expected return is plotted as a function of risk. Expected return is measured from zero to $30$ percent on the vertical axis. Risk in form of standard deviation is measured from zero to $20$ percent on the horizontal axis. Point A is marked at $(11\mathrm{.}2,18\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $0\mathrm{.}50.$ Point B is marked at $(8\mathrm{.}2,18\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75.$ A straight horizontal line goes from the horizontal axis to point A through point B$.$

C$.$

Expected return is plotted as a function of risk. Expected return is measured from zero to $30$ percent on the vertical axis. Risk in form of standard deviation is measured from zero to $20$ percent on the horizontal axis. Point A is marked at $(11\mathrm{.}2,16\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $0\mathrm{.}50.$ Point B is marked at $(4\mathrm{.}2,16\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75.$ A straight horizontal line goes from the horizontal axis to point B through point $\text{'}$A$\text{'}.$

D$.$

Expected return is plotted as a function of risk. Expected return is measured from zero to $30$ percent on the vertical axis. Risk in form of standard deviation is measured from zero to $20$ percent on the horizontal axis. Point A is marked at $(11\mathrm{.}2,13\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $0\mathrm{.}50.$ Point B is marked at $(8\mathrm{.}2,13\mathrm{.}6)$ and corresponds to r subscript $1,2$ end subscript equal to $-0\mathrm{.}75.$ A straight horizontal line goes from the horizontal axis to point B through point $\text{'}$A$\text{'}.$

Explain the results.

The negative correlation coefficient

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risk without sacrificing return