Portfolio $-$Basic Principles:

Suppose you are offered the two investments, $Z$ and $Y,$ whose characteristics are shown.

$\backslash$table$[[$Asset$,$Expected return $(\%),$Standard deviation $(\%)],[Z,15,20],[Y,35,40]]$

Correlation coefficient $ZY=-0\mathrm{.}25$; Covariance $ZY=-200$

Calculate the expected return and risk for:

$($a$.)$ All in $Y$

$($b$.)60\%$ in $Y$

$($c$.)40\%$ in $Y$

$2.$ CAPM$-$Portfolio Risk and Return

Worked Example $1$:

$3.$ An investor holds the following portfolio of four risky assets and a deposit in a riskfree asset. The table shows their respective portfolio weightings and the current returns on the assets, together with their Beta coefficients.

$\backslash$table$[[$Asset$,$Weighting $(\%),$Current return $(\%),$Beta$],[$A$,20,12\mathrm{.}0,1\mathrm{.}5],[$B$,10,18\mathrm{.}0,2\mathrm{.}0],[$C$,15,14\mathrm{.}0,1\mathrm{.}2],[$D$,25,8\mathrm{.}0,0\mathrm{.}9],[$Risk$-$free asset,$30,5\mathrm{.}0,0]]$

The overall return on the market portfolio of risky assets is $11$ per cent, and this is expected to continue for the foreseeable future.

Required:

$($a$)$ What is the current return on the whole portfolio, and its Beta value?

$($b$)$ Which of the four risky assets $($if any$)$ appear to be inefficient$/$efficient$/$super$-$efficient?

$($c$)$ In view of the answer to part $($b$),$ what predictions would you make regarding future asset values and, hence, their rates of return as the market moves to full equilibrium?