Short Question $($SQ$3)$

$(15\%)$

Consider an economy with only two risky stocks Value and Growth and one risk$-$free asset, Tbill. CAPM holds in this economy, and the market portfolio in this economy consists of Value and Growth. You observe an investor's optimal portfolio, denoted as portfolio $Q,$ as below. Some statistics of the returns of the three assets and weights in portfolio $Q$ are also reported in the table below. All the returns are efficient under CAPM. Firm$-$specific surprises are uncorrelated.

$\backslash$table$[[$Assets$,\backslash$table$[[$Weights in$],[$Portfolio$]],\backslash$table$[[$Expected$],[$Return$]],\backslash$table$[[$Standard$],[$deviation$]],$Correlation$],[Q,,$Growth,Value,T$-$Bill$],[$Growth$,0\mathrm{.}35,,0\mathrm{.}20,1\mathrm{.}00,0\mathrm{.}30,-],[$Value$,0\mathrm{.}35,,0\mathrm{.}10,,1\mathrm{.}00,-],[$T$-$Bill,$0\mathrm{.}30,0\mathrm{.}03,0,,,-]]$

Based on the information in the table, please answer the following questions:

$($A$)$ What is the standard deviation of the market portfolio in this economy? $(3\%)$

$($B$)$ What is the standard deviation of the return on portfolio $Q(2\%)$

$($C$)$ If some investor wants only one half of the standard deviation of $Q,$ what are the weights he$/$she should allocate to the three assets? $(5\%)$

Growth:

Value:

T$-$bill:

$($D$)$ If the expected return on portfolio $Q$ is equal to $0\mathrm{.}058,$ what are the expected returns on Growth and Value stocks? $(5\%)$